A Heuristic Fuzzy Logic Approach to EMG Pattern ...

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IEEE TRANSACTIONS ON NEURAL SYSTEMS AND REHABILITATION ENGINEERING, VOL. 13, NO. 3, SEPTEMBER 2005

A Heuristic Fuzzy Logic Approach to EMG Pattern Recognition for Multifunctional Prosthesis Control Abidemi Bolu Ajiboye and Richard F. ff. Weir

Abstract—This paper presents a heuristic fuzzy logic approach to multiple electromyogram (EMG) pattern recognition for multifunctional prosthesis control. Basic signal statistics (mean and standard deviation) are used for membership function construction, and fuzzy c-means (FCMs) data clustering is used to automate the construction of a simple amplitude-driven inference rule base. The result is a system that is transparent to, and easily “tweaked” by, the prosthetist/clinician. Other algorithms in current literature assume a longer period of unperceivable delay, while the system we present has an update rate of 45.7 ms with little postprocessing time, making it suitable for real-time application. Five subjects were investigated (three with intact limbs, one with a unilateral transradial amputation, and one with a unilateral transradial limb-deficiency from birth). Four subjects were used for system offline analysis, and the remaining intact-limbed subject was used for system real-time analysis. We discriminated between four EMG patterns for subjects with intact limbs, and between three patterns for limb-deficient subjects. Overall classification rates ranged from 94% to 99%. The fuzzy algorithm also demonstrated success in real-time classification, both during steady state motions and motion state transitioning. This functionality allows for seamless control of multiple degrees-of-freedom in a multifunctional prosthesis. Index Terms—Clustering, electromyogram (EMG), fuzzy logic, heuristics, multifunctional control, myoelectric prostheses, pattern recognition.

I. INTRODUCTION

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HE SURFACE electromyogram (sEMG) is the current state-of-the-art technique for the control of externally-powered transradial (below-elbow) prostheses. Although many users choose some form of mechanical control (shoulder switches, cables, etc.) in lieu of, or in addition to, myoelectric control, mechanical control is excluded from the scope of this

Manuscript received October 8, 2004; revised January 24, 2005; accepted January 30, 2005. This work was supported by the Department of Veterans Affairs, Rehabilitation Research and Development Service and is administered through the Jesse Brown Veterans Affairs Medical Center, Chicago, IL. The work of A. B. Ajiboye was supported by the National Institute on Disability and Rehabilitation Research (NIDRR) of the Department of Education under Grant H133E980023. Opinions contained in this publication are those of the grantee and do not necessarily reflect those neither of the Department of Veterans Affairs nor of the Department of Education. A. B. Ajiboye is with the Department of Biomedical Engineering, Rehabilitation Engineering Research Center and Prosthetic Research Laboratory, Northwestern University, Chicago, IL 60611 USA (e-mail: [email protected]). R. F. ff. Weir is with the Jesse Brown Veterans Affairs Medical Center, Department of Veterans Affairs, Chicago, IL 60611 USA, with the Department of Physical Medicine and Rehabilitation, Feinberg School of Medicine, Northwestern University, Chicago, IL 60611 USA, and also with the Department of Biomedical Engineering, Rehabilitation Engineering Research Program, Northwestern University, Chicago, IL 60611 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TNSRE.2005.847357

paper. Most commercially available myoelectric transradial prostheses are two-site single degree-of-freedom (DOF) devices, but some are capable of controlling two DOFs. However, to switch from one DOF to another, the majority of these devices rely on the ability of the control algorithm to recognize a preset co-contraction pattern in the myoelectric activity. In these cases, myoelectric control of one component is suspended to control a second component. Standard recognition algorithms for two-site devices involve comparing a signal to a preset threshold, with some including the recognition of a rapid co-contraction to switch control from one DOF to another [1]. In some devices, such as the myo-pulse modulation systems from Hosmer Dorrance Corporation (Campbell, CA) [2] and Otto Bock Corporation’s standard two-site systems [3], the recognition algorithm implemented is a method we refer to as the “first on, or lockout strategy.” This algorithm involves controlling the DOF with the first signal to cross a preset ON threshold (hence, “first on”), and only relinquishing control after the signal has crossed a second preset OFF threshold (i.e., all other signals are “locked out” and prevented from taking control). The second threshold does not necessarily have to be the same as the first, thereby, allowing hysteresis for greater system stability. An alternative strategy implemented in two-site myoelectric prostheses, specifically Motion Control Inc.’s (Salt Lake City, UT) Utah Arm [4], is what we refer to as the “most on, or difference strategy.” This recognition algorithm performs classification based on which signal is the largest, or “most on,” relative to its preset threshold. This strategy operates on a sample-by-sample basis. No signals are locked out even after one has crossed the threshold. While these algorithms work well for one DOF control, it has not been shown that they work well in situations of true multifunctional myoelectric control. True multifunctional myoelectric control exists when control over one function does not inhibit independent simultaneous myoelectric control over other functions. The success of a multifunctional myoelectric transradial prosthesis is partly dependent upon, and arguably determined by, its ability to function in as natural and intuitive a manner as the physiological wrist and hand. Furthermore, the key step in myoelectric prosthesis control is accurate recognition of the user’s intent based upon the EMG signal. This issue is not new. Researchers in the early 1970s [5]–[7] investigated the use of multielectrode arrays for the control of humeral, elbow, and forearm movements of an upper-limb prosthesis. Also investigated was the separability and reproducibility of EMG signals during the motions of finger flexion-extension, wrist flexion-extension, and hand supination-pronation. Reported recognition rates ranged from 59% to 100% for amputee subjects. These systems were not

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AJIBOYE AND WEIR: A HEURISTIC FUZZY LOGIC APPROACH TO EMG PATTERN RECOGNITION

clinically practical because of the high number of myoelectric sites required by the control algorithm, which was up to ten in some instances. Modern researchers have attempted to remedy the requirement of a high number of control sites by investigating feature extraction methods [8]–[11]. These approaches in effect serve to maximize the ratio of the number of controllable functions to the number of myoelectric control sites. In their 1993 seminal paper, Hudgins et al. [10] proposed the use of two myoelectric control sites and extraction of five signal parameters of each EMG signal collected during the first 300 ms of contraction. These parameters served as inputs to an artificial neural network (ANN) recognition system, which was used to discriminate between elbow flexion-extension and humeral medial-lateral rotation EMG patterns. The authors reported subject-dependent recognition rates ranging from 70% to 98%. Extending this work, Englehart and Hudgins have reported work on a “continuous classifier” approach, using both wavelet analysis [12] and the same features of Hudgins et al. [11]. Using the parameters of the steady-state EMG signal and a “majority vote” algorithm, the authors reported classification error rates of 5% in the continuous control of four DOF using four myoelectric sites. This result was based upon an analysis window of 32 ms and a system delay of 128 ms. These same features have also been used in combination with genetic algorithms [13], and a fuzzy logic algorithm [14] with reported recognition rates in the range of 80%–97.5% on the same data reported in [10]. We present a simple heuristic fuzzy system, with a 45.7 ms update rate, for use in the classification phase of multifunctional myoelectric control of transradial (below-elbow) hand–wrist prostheses. Heuristics is a genre of problem solving based upon simplifications and general “rule-of-thumb” approaches to focus the search of solutions to normally complex problems or situations lacking complete information. Most notable in this area is the formalized concept of fuzzy logic, which uses a set of simple vernacular language rules (inference rule base) to analyze highly complex problems [15], [16]. This heuristic approach is of great benefit given the microcontroller and DSP technology of today, which have the ability to parse through simple inference rule bases very quickly. While the use of fuzzy logic for prosthesis control is a relatively new concept, the literature reports many variations of its use in aspects of control and recognition [14], [17]–[20]. These approaches generally combine fuzzy logic with more complex algorithms such as artificial neural networks, autoregressive coefficients, or advanced statistical techniques that are complex, have slow update rates, and/or have not been assessed on individuals who have experienced limb-loss. The authors demonstrate a system for the classification of multiple EMG signals for use in multifunctional control, using a simple vernacular language approach that is easily understood, quickly and automatically generated for different users, executable in real-time, and has a 45.7 ms update rate. It is our contention that one of the chief advantages of this fuzzy system over previous approaches is its simplicity. Furthermore, we take advantage of current clinical myoelectric prosthesis fitting practices in locating myoelectric EMG signal sites that attempt to maximize physiological separability between signals.

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II. METHODS A. Subject Information Five subjects took part in these experiments: three individuals with intact limbs (subjects , , and ), one individual with a trauma-induced unilateral transradial amputation (subject A), and one individual with a unilateral transradial limb-deficiency from birth (subject C). Subjects were included because their intact musculature presented a physiologically best case scenario for the initial development of the fuzzy algorithm. Also, subject was included to demonstrate the real-time behavior of the fuzzy system. Subjects A and C were included to investigate the algorithm behavior on standard end-users, namely those who have experienced amputation or a congenital limb-deficiency. All subjects gave informed consent to the procedures as approved by the Northwestern University Office for the Protection of Research Subjects (NUOPRS) Institutional Review Board. Intact-limbed subjects are men 30, 41, and 23 years of age, respectively. Subject A is an 86 year-old male with a right transverse deficiency of the forearm by traumatic injury. The amputation surgery occurred 65 years before the date of data collection. An examination by a trained prosthetist revealed a residual limb length of 14.5 cm from the lateral epicondyle to the distal end of the bone (the contra-lateral limb length was 38.5 cm from lateral epicondyle to radial styloid, putting the subject’s amputation in the middle third). The subject was able to achieve, from anatomical position, pronation and supination to 90 and 15 , respectively. The subject had recent experience with a myoelectric prosthesis, but the proficiency and preference of the individual was with his body-powered prosthesis. An examination of subject C (27 year-old female) by a trained prosthetist revealed an affected limb length of 7 cm from the lateral epicondyle to the distal end of bone (the contra-lateral limb length was 24.5 cm from lateral epicondyle to radial styloid, putting the subject’s deficiency in the proximal third). The subject had previous experience controlling a two-site myoelectric prosthesis (an Otto Bock six and three-quarters size hand) for about three years, 15 years before this examination. This experience gave her competency in eliciting and controlling sites for myoelectric control, but the subject eventually opted for a body powered transradial prosthesis with split hook due to the excessive size and weight of the electrically powered prosthesis. The subject reported that she experienced no phantom sensation on the side of the affected limb. B. Myoelectric Site Selection Practical prosthetic fitting considerations in the selection of control sites for a transradial myoelectric prosthesis include choosing sites that are distal to the trim line of the socket. In addition, one must strike a balance between choosing sites that the user can easily elicit and choosing sites that are most naturally mapped to the appropriate DOF of the prosthesis. We selected myoelectric control sites that would be located within the geometry of a standard prosthetic socket, that could be controlled most proficiently by the subject, and that produced the most natural mapping to the controlled DOF of the user’s prosthesis.

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silver/silver chloride (Ag/AgCl) snap-electrodes (Noraxon Dual Electrodes, spacing 2.0 cm center-to-center) for use in surface EMG applications was placed over each of the located EMG sites. These electrodes are the same as those used in electrocardiogram (ECG) monitoring. A Velcro strap was used to keep the electrodes in place and ensure uninterrupted skin contact during the remainder of the protocol. C. Fuzzy System Data Collection, Generation, and Testing

Fig. 1. Myoelectric sites for normal-limbed subjects. (1) Extensor digitorum. (2) Extensor carpi ulnaris. (3) Flexor digitorum superficialis. (4) Flexor carpi ulnaris.

For the subjects with intact limbs, the motions chosen to elicit EMG signals were wrist extension (state 1), ulnar deviation (state 2), finger flexion (state 3), and wrist flexion (state 4). The four myoelectric control sites were located over the extensor digitorum, extensor carpi ulnaris, flexor digitorum superficialis, and flexor carpi ulnaris muscles, as shown in Fig. 1. These sites were located according to standard anatomical text, using the medial and lateral humeral epicondyles as landmarks. The electrode sites for subjects A and C were determined by palpation while the subjects performed the appropriate contractions. For the subject with the congenital limb deficiency (subject C), the elicited contractions were extension (state 1), supination (state 2), and flexion (state 3), as determined by the ability of the subject. The myoelectric control sites were selected accordingly, as shown in Fig. 2(a). For the subject with the trauma-induced limb deficiency (subject A), the three elicited contractions were extension (state 1), pronation (state 2), and flexion (state 3), as determined by the ability of the subject. The myoelectric control sites were selected accordingly, as shown in Fig. 2(b). Subject A was not able to consistently and adequately perform supination, while subject C was not able to consistently and adequately perform pronation. It is telling that for those subjects with limb deficiencies, only three independent surface sites could be obtained. Location of the myoelectric control sites was performed by a trained prosthetist in a manner consistent with current clinical practice. Electrode sites were prepared by shaving any excessive body hair in the site regions, and applying an alcohol prep pad. A pair of commercially available disposable self-adhesive

1) Data Collection and Pre-Processing: With suitable control sites identified and the electrodes attached, subjects were seated with their forearm/residual limb resting on the arm of the chair, roughly forming a right angle at the elbow. Quiescent data sets were collected from the identified EMG sites using the Noraxon (Phoenix, AZ) Telemyo 8 System. Subjects with intact limbs performed eight trials each of wrist extension, ulnar deviation, finger flexion, and wrist flexion. All contractions were performed at a speed and strength determined by the subject. Each trial covered the subject’s full range-of-motion (ROM). Upon hearing a command signal, these subjects began the instructed contraction, covered the full ROM, and held the final position until hearing a signal instructing them to relax the contraction and return to the starting position. The subjects with a congenital limb deficiency or amputation performed eight trials each of extension, flexion, and supination (subject C) or pronation (subject A). These subjects were instructed to simultaneously perform the same motion with their contra-lateral limbs, so as to aid them in visualizing the task. When applicable, this mirroring technique also would take advantage of the phantom-limb phenomenon that many individuals with amputations experience [21], [22]. Subjects covered the full ROM with the contra-lateral limb, and held it at the final position (and held the contraction of the residual limb) until a rest command was given. Subjects waited until the subsequent contraction command was given to perform the next trial. Subjects were instructed to use moderate contractions, and trials were spaced such that subject fatigue was not an issue. Data collection began about 2 s prior to contraction initiation in order to collect premovement quiescent data, and ended immediately prior to the rest command being given. Contractions lasted between 3 and 5 s, and the rest periods were 5 s between successive contractions. Raw EMG data sets were bandpassed with an analog filter with cutoffs at 10 and 500 Hz and a total gain of 2000, then sampled at 1400 Hz per channel. The root-mean-square (rms) of each EMG was calculated and stored using a 64-sample binning window to determine the signal envelope, resulting in a system update rate of 45.7 ms (i.e., 64 samples/1400 Hz). The rms of the myoelectric signal is an accepted maximum likelihood estimator of EMG amplitude, and has been suggested as the choice method of data reduction for EMG signal processing because it provides physiologically significant information of the average power of the muscle [23]. Odd numbered trials for each contraction were saved and used for fuzzy system generation and training, while even numbered trials were saved and used for system verification. In this way, the biasing effects of fatigue and learning could be eliminated since both the training and verification data span the entire length of the experiment. Each file consisted of the contraction name, trial number, and the sampled rms electromyographic

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Fig. 2. (a) Myoelectric sites for subject with congenital left transverse forearm deficiency: (1) extensors; (2) supinators; (3) flexors. (b) Myoelectric sites for subject with transradial amputation after traumatic injury: (1) extensors; (2) pronators; (3) flexors.

Fig. 3. Histograms of the rms EMG before a contraction (OFF distribution) and during a contraction (ON distribution). Means of the OFF and ON signal distributions are used to construct the input MBF. Mean value of the OFF signal (x ) is given unity membership in the OFF membership function, and the mean value of the ON signal (x ) is given unity membership in the MED membership function. LOW and HIGH membership functions are constructed such that 50% overlap exists between adjacent MBFs.

data. Onset for each contraction was automatically determined as the point when the active rms signal was greater than the rms quiescent signal mean plus three standard deviations [24]. The detected onsets were verified through visual inspection, and the EMG files were stored with this information. Data samples prior to the time of contraction onset were assigned to be OFF (state 0), while data samples at and after the time of onset were assigned the appropriate contraction (states 1–4). 2) Fuzzy System Generation–Membership Functions and Inference Rule Base: The multiinput-single-output fuzzy

system consists of three parts: 1) input membership functions that fuzzify numerical inputs, converting them to linguistic variables; 2) an inference rule base that performs pattern classification by processing the linguistic inputs, returning linguistic outputs and associated degrees of truth; and 3) an output membership function that defuzzifies the inference rule base linguistic outputs, converting them to one numerical value. The input membership functions (iMBFs) for each control site are constructed with four levels of signal gradation (OFF, LOW, MED, HIGH), as shown in Fig. 3. A set of membership functions

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TABLE I POINTS OF INTERSECTION AND ASSOCIATED DOM FOR VERTEXES OF THE FOUR MBFS CONSTRUCTED FOR THE th INPUT EMG SIGNAL ( = 1 . . . 4 FOR - , = 1 . . . 3 FOR SUBJECTS A AND C). ALL CONNECTIONS BETWEEN VERTEXES OF A SINGLE MBF ARE LINEAR, RESULTING IN TRIANGULAR SUBJECTS ) IS CALCULATED FROM THE COLLECTED QUIESCENT REST DATA, WHILE THE MEAN ACTIVE rms ( ) OR TRAPEZOIDAL MBFS. MEAN REST rms ( IS CALCULATED WHEN THE RESPECTIVE MUSCLE IS MODERATELY AND DELIBERATELY CONTRACTED. max rms FOR THE th INPUT SIGNAL IS DEFINED AS THE MAXIMUM CONTRACTION LEVEL OBSERVED FROM THE RESPECTIVE CONTROL SITE DURING ALL TRIALS OF THE PROTOCOL

N N i

i

x

for each input channel is constructed based upon the mean quiescent rms value of the EMG ( ) and the mean rms value of the EMG during contraction ( )[ for subjects , for subjects A and C]. is the mean rms of the th input EMG site during collection of the quiescent data and is the mean rms of the th input EMG site, through the full duration of the contraction (transient and steady-state), when the respective muscle is moderately and deliberately contracted (as opposed to inadvertently co-contracted during contraction of a different muscle). The values of and are given unity membership in the OFF and MED membership functions, respectively, of the th input membership set. The LOW and HIGH membership functions (MBFs) are constructed such that 50% overlap exists between adjacent MBFs. This practice is to ensure that any value of the EMG has a total membership of unity among all membership functions in the universe-of-discourse. While not always required, this practice seems to be standard protocol in MBF construction [25], [26]. Table I lists the resulting intersection points and degrees-of-membership (DOM) for each constructed MBF. Thus, if the amplitude of the signal recorded from the control site is slightly higher than , it is accurately characterized as “mostly medium but somewhat high.” As the signal amplitude decreases, its characterization moves to “somewhat medium but mostly low” to “completely low” to “mostly low and minimally off” to “somewhat low but mostly off” to “completely off.” In between the characterizations listed are other levels of signal characterization. Consequently, a “fuzzy threshold” is set by the intersection of the OFF and LOW MBFs, such that if a signal is higher than this threshold, it is considered “more on than off,” and “more off than on” if it is less than this threshold. Because the vertex points are derived directly from the calculable signal statistics (mean rms of the quiescent and on signals), the construction of the input MBFs can be automated and requires no manual intervention. The inference rule base (IRB) is the brain of the fuzzy system and performs classification of the myoelectric signal patterns based upon the relative amplitudes of the elicited EMG signals, as determined by the input MBFs. Specifically, the IRB consists

i

i

x

of a set of vernacular language rules of the form “IF (input signal 1 has a certain characterization) and (input signal 2 has a certain characterization) and … THEN (the user’s intended motion is ___________).” Rules may be weighted differently depending on the likelihood of the scenario captured by each rule, and all rules are processed simultaneously. All input possibilities map to some output. The number of rules in the IRB is dependent on the different patterns presented within the input training data. Many ways to capture trends in data exist. In this particular application, we used fuzzy -means (FCM) clustering [26], [27] because it allowed us to automate the generation of the inference rule base. Fuzzy clustering seeks to group sampled data together so as to minimize the variance between data in the same cluster and maximize the variance between data in different clusters. This reduction method allows each cluster of data to be represented by a “cluster center” that can be translated into a rule in the IRB. All data sets can belong to all cluster centers, with a DOM in each cluster in the interval [0,1]. The DOM is directly related to the Euclidean distance between each data sample and the cluster center. Data samples and cluster centers are ( ) length vectors, where is the total number of EMG inputs and is the total number of outputs (number of DOFs to be controlled). is four for subjects and three for subjects A and C. is one for all subjects. Equations (1)–(3) represent the restrictions on the clusters: 1) Every data sample must belong to a cluster; 2) the membership of each data sample in the universe of clusters must sum to one; and 3) no single cluster is equivalent with the null set or the universal set (i.e., , the number of clusters, is greater than one and less than , the number of data samples) (1) (2) (3)

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A matrix is defined to express the membership of each sample (denoted by columns) in each cluster (denoted by rows), where membership of the th sample in the th cluster is denoted on the inclusive interval [0,1]. Given a vector of cluster centers , an objective function is defined (4)

(4)

is the Euclidean distance between the th data sample where and the cluster center. Minimization of (4) is performed through an iterative process implemented in standard mathematical software such as Mathworks’ MATLAB (Natick, MA). The results are a final membership matrix that denotes the membership of each data sample in each cluster, and a final cluster matrix of dimension , where is the number of cluster centers and ( ) is the number of inputs and outputs. is comprised of the DOMs of each data sample in each cluster group that minimizes the Euclidean distance between samples belonging to the same cluster and maximizes Euclidean distances between the cluster centers themselves [26]. is comprised of the locations of the cluster centers in parameter space. Each cluster center in the matrix is then converted to one linguistic rule in the inference rule base. Each cluster center is ( ) dimensional in parameter space, and each value of the center in each dimension is fuzzified using the membership function of the corresponding parameter. For example, if Fig. 3 gives the MBF set for an EMG input and the value of a given cluster center is 0.225 V in the first dimension, then the corresponding linguistic value of this parameter in the associated rule would be MED (medium) because 0.225 V has the highest DOM in the MED MBF. Hence, the rule would read, “If EMG Input 1 is MED and … then the output is …” The same is done for all other dimensions of the cluster center to produce one rule. The output is also determined by fuzzification of the output dimension of the cluster center. This rule conversion is done for all cluster centers to build the linguistic rules governing the behavior of the EMG inputs during a specific movement. The process is repeated for all movements. Finally, a degree-of-strength (DOS) is associated with each rule in the IRB. The membership of each data point in a particular cluster is given in the optimized membership matrix , and the DOS of each rule is simply the average of the memberships of all data points in the cluster used to create the rule. Illustrative examples specific to the collected data sets can be found in [28]. It should be noted that fuzzy -means (FCM) clustering is simply a method of data reduction and is not a method to optimize the fuzzy logic systems. Methods of fuzzy system optimization, such as neuro-fuzzy techniques, optimize the vertexes of all membership functions and the weights of the rules in the inference base of a pre-designed fuzzy system. Specifically, neuro-fuzzy algorithms apply artificial neural networks to train fuzzy systems to best fit training data, resulting in an optimized system. No such method was applied in the development of the presented systems. The optimization that FCM performs is to assess the best way to cluster the data, not to change the

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parameters of the fuzzy system. Hence, the presented systems are not optimized, although they are tailored to each individual. FCM was applied to the training data set for each subject as described above, with a slight modification. Instead of applying FCM to all the training data as one group, the data were first subdivided into groups representing known motions. Hence, sample rms data related to wrist extension was clustered separately from wrist flexion, finger flexion, and ulnar deviation, hence simplifying the minimization of the objective function. In any given optimization problem, it is possible to reach solutions at local minima or maxima that are not close to the global minima or maxima. This is more likely when a large number of data points need to be clustered. Clustering smaller groups of homogenous points is more likely to converge to a global minima or maxima. Using this approach, a matrix is returned for each motion classified. The rule base was then automatically built from this set of cluster center matrices using an in-house MATLAB script. As with standard fuzzy logic systems, the rules in the inference base are processed in parallel, and the results are defuzzified using a standard mean-of-maximum (MoM) algorithm. MoM is the most widely used and preferred defuzzification method in applications of recognition and classification [25]. A set of output MBFs is used to generate the output of the fuzzy system. Each membership function in this set represents one output possibility for the user’s intent, as shown in Fig. 4(d). As with the input MBFs, the output MBFs overlap by 50% to preserve the unity membership requirement within the system. In some cases, the optimal number of centers for clustering is known, and minimization of the objective function in (4) proceeds directly through the iterative technique. In most cases, where real world sample inputs are involved, the optimal number of clusters is not predetermined [29]. Thus, part of the investigation of automating the fuzzy system design was to experimentally determine the optimal number of clusters. The optimal number of clusters was defined as that which returned the highest recognition accuracy with repeatability. Clustering was performed with 10, 15, 20, 25, 30, 50, and 100 centers for each movement. As the number of cluster centers increases, it is possible that linguistic rules may be duplicated because two centers, while having different numeric values, may translate to the same membership function. In such a case, the instance of the rule with the higher DOS was retained. Because the cluster centers span the full set of samples, the generated rules cover all scenarios present in the data. Hence, all inputs map to one and only one output. The overall size of the inference rule base was also observed and reported. 3) Fuzzy System Testing: An in-house MATLAB script was written to perform the automated generation of fuzzy systems as described above. These systems were tested using Inform Technologies’ (Chicago, IL) fuzzyTECH ver. 5.52 MCU-320 edition development environment on the verification data previously collected from each subject. The fuzzy systems process the data offline on a sample-by-sample basis. One decision is made per sample, resulting in a stream of pattern classification output states ranging from 0 to 4, corresponding to the desired motion states. System accuracies are reported as the percentage of data samples in the verification data set for which the fuzzy system correctly identified the output

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Fig. 4. Input and output membership functions and inference rule base for subject with congenital limb deficiency (subject C). Input membership functions [(a)-(c), corresponding to input EMGs 1–3, respectively] were automatically generated based upon signal statistics. Inference rule base and associated DOS was automatically generated using fuzzy c-means clustering of training data.

state. These results are compared to systems based on the “first on, lockout strategy” and “most on, difference strategy,” as described in the introduction. These comparative systems were designed from the “training” data set and tested on the “checking” data set. The three “first on, lockout strategy” based systems implemented hysteresis, with [onset, offset] thresholds of [ ], [ ], and [ ] above the quiescent mean , where is the standard deviation of each quiescent signal. Two “most on, difference strategy” based systems were designed, one with a threshold of , and the other of above each signal’s quiescent mean , where again is the standard deviation of each quiescent signal. D. Fuzzy System Real-Time Behavior To demonstrate the ability of the fuzzy system to perform real-time recognition of myoelectric patterns, a single subject experiment was performed with subject . This subject represented a best-case scenario for surface EMG recognition for several reasons. The subject possessed intact forearm musculature. He possessed full independent control over the motions of interest, and was able to obtain adequate physiological separation of EMG signals, as determined through preliminary tests. In addition, the subject’s forearm musculature was well defined, making the search and selection of potential control sites relatively straightforward.

The same protocol was followed for acquisition of electromyographic data as that used for the other normal-limbed subjects. The fuzzy system was designed as previously described, using a heuristic approach to automate membership function generation and automatic fuzzy data clustering techniques for generation of the inference rule base (IRB). The system was then tested in real-time using in-house software created for data acquisition and processing. Specifically observed were the system’s ability to perform real-time recognition of independent motions, and the system’s recognition ability during instances of the subject’s seamless transition from one motion to the next. The test of independent motions consisted of instructing the subject to perform each independent motion and return to a fully relaxed state in between each motion. The test of seamless transition was a repeat of the test of independent motions, except the subject was instructed to intentionally not return to a state of rest, but rather to seamlessly proceed from one active state to the next. The results of these tests were both qualitatively and quantitatively assessed. III. RESULTS A. Fuzzy System Generation and Testing Fig. 4 shows the components of a typical fuzzy system that results from the automated generation of membership functions

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TABLE II SUCCESS RATE OF FUZZY SYSTEMS IN THE CORRECT CLASSIFICATION OF THE SUBJECTS’ INTENDED MOTIONS. BLANKS INDICATE THAT THE MOTION WAS NOT ELICITED FOR THE SUBJECT

Fig. 5. (a) Effect of the number of cluster centers per motion on the overall size of the inference rule base. As expected, the IRB size generally increases with increasing cluster size. This implies that there is more information in the data to be captured, and that more clusters do not produce redundancy in rule production. This, however, does not necessarily imply a greater level of recognition accuracy with an increase in the number or rules in the IRB. (b) Effect of number of cluster centers per motion on size of inference rule base using fuzzy c-means clustering. With the exception of 10 cluster centers for subject A (amputee), the number of cluster centers used to create the inference rule base did not seem to greatly effect the accuracy of the heuristic systems generated. Accuracy rates are reported as the percentage of individual samples correctly classified versus the total number of samples processed by the algorithm.

is not trivial in myoelectric pattern recognition prosthesis control. In general, the number of clusters used for IRB production, and hence the number of rules in the IRB, did not have a consistent effect on the accuracy of the fuzzy systems i.e., more clusters did not necessarily produce greater accuracy. A quick calculation suggests that a 4 input system with 4 possible levels has a maximum of possibilities, implying that between 50 and 100 clusters should provide the best accuracy. In the end, 50 cluster centers were used as they offered the best compromise between inference rule base size and classification accuracy rate. Table II reports the success of the 50 cluster fuzzy system for each subject to accurately recognize each intended activity. Activity specific recognition rates were in the range of 74% to 100%, with all average recognition rates ranging from 94% to 99%. Fig. 6 compares the recognition rates of the 50 center fuzzy logic systems to the “first on, lockout strategy” and “most on, difference strategy” recognition systems. Looking at Fig. 6 it can be seen that the fuzzy logic system consistently outperformed the other investigated classification algorithms across all subjects, except in the case of subject C. However, the difference in this case between the success rate of the “most on, difference strategy” and the fuzzy logic system was only 0.7%. B. Fuzzy System Real-Time Analysis

and the inference rule base. The figure shows the input and output MBFs and the IRB with associated DOS for subject C. Several of these systems were generated for each subject, using 10, 15, 20, 25, 30, 50, and 100 cluster centers per motion to create the IRB. Fig. 5(a) shows, as expected, that as the number of cluster centers increased, the number of rules increased as well. This relation implies that there is more information in the data to be captured, and that more clusters do not produce redundancy in rule production. However, an increase in the number of rules does not necessarily imply an increase in system accuracy. Fig. 5(b) shows how the number of cluster centers affected the overall classification accuracy for each subject. Accuracy is defined as the percentage of correctly classified individual samples versus the total number of samples processed. These percentages include correct classification of the OFF state, which

The ability of the fuzzy logic system to perform real-time classification of the generated myoelectric patterns of independent motions is shown in Fig. 7(a). The system was very accurate in the recognition of wrist extension, ulnar deviation, finger flexion, and wrist flexion for subject . Regarding wrist extension, it is noted that the misclassification of one instance is a misclassification to the OFF state, and not a different active state. Regarding finger flexion, it is noted that the few errors shown again are misclassifications to the OFF state, and not to a different active state. There were some errors when the user returned to the rest state from finger flexion, as represented by the classification spike to wrist extension. With the current inference rule base, the system did not perform as successfully in the clean recognition of wrist flexion. There were several instances that were classified as ulnar deviation, particularly in the second trial. However, increasing the gain of the wrist flexors input relative to the

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from ulnar deviation to finger flexion, and from finger flexion to wrist extension. In most of these cases, the transition was seamless i.e., there were no misclassifications during the transition periods. In some cases such as the transitioning from ulnar deviation to finger flexion, there was one point of misclassification to the OFF state and two non-OFF misclassification points, both of which occurred during the subject’s transition from wrist extension to finger flexion. IV. DISCUSSION

Fig. 6. Success rate of fuzzy logic based recognition systems compared to various “first on, lockout strategy” and “most on, difference strategy” based systems. “Lockout (a, b)” implies a “lockout with hysteresis” strategy, where the hard lockout and unlock thresholds are “a” and “b” standard deviations above the respective signal quiescent mean. “Difference (a)” implies a “most on, difference” algorithm where the hard thresholds are set to be “a” standard deviations above the respective quiescent signal mean.

other input sites remedied much of this problem, and the classifier performed much better as shown in Fig. 7(b). While there still exist instances where the classifier returns an incorrect result, these are relatively few. The second trial of wrist flexion produced no errors in recognition, suggesting that with appropriate feedback and training, a subject could further reduce the number of misclassifications. It is important to realize that classification is done on a sample-by-sample basis, and the system has a 45.7 ms update rate. Hence, each “dot” in Figs. 7 and 8 is a classification of one sample every 45.7 ms. Fig. 8 reports the ability of the fuzzy logic system to handle seamless transitions from one active state to another. Specifically demonstrated is the system’s behavior during transition from wrist extension to ulnar deviation and back, from wrist extension to wrist flexion, from wrist flexion to ulnar deviation,

Fuzzy logic is simply a tool in the problem of multisignal pattern classification. Other researchers have reported, with varying degrees of success, different algorithms to accomplish the same goal. Many of these algorithms, however, assume a longer available window for data acquisition and decision making [11], [12] than we believe to be acceptable by the end user. While there is no standard in the literature addressing the issue of perceivable delay, our laboratory experience suggests that an acceptable delay is no greater than 100 ms, and even 50 ms for a highly responsive device. The fuzzy system presented in this paper has an update rate of 45.7 ms. From an implementation standpoint there is very little computation involved once the membership functions and rules have been established. The rules and membership functions are established at system setup. In operation the program fuzzifies each input, drops through a set of inference rules implemented as “IF… THEN” statements looking for the rules that are true, and defuzzifies the output. This process is something that microprocessors can do very quickly with minimal processing overhead. Such systems can be readily implemented on simple, low-power, 8 bit microprocessors. The simplicity and automation of generation of the membership functions and inference rule base through basic signal statistics and fuzzy -means clustering produces an easily generated fuzzy-system that is transparent to the prosthetist. The prosthetist does not have to be an expert in fuzzy-system design. The prosthetist does what he/she is trained to do, which is locate independent EMG sites, and acquire quiescent and active EMG data. The rest is taken care of by the system. The high accuracy of classification of the fuzzy systems is encouraging. This simple analysis performs better than current threshold based algorithms in terms of percent accuracy. It is on a par with other more complex and computationally intensive pattern recognition algorithms proposed in current literature [10]–[12], [14], [17], [18], with the advantage of a quicker response time. The recognition rates reported in Table II are given as a means of expressing how well a transradial prosthesis user would perform with such a controller. It has yet to be determined what rate of recognition is acceptable to be practical and therefore accepted. This issue, typically referred to as the “hot coffee problem” is stated as follows: Is sufficient for a practical prosthesis? Even if the proposed system was 99% accurate, a user picking up a hot cup of coffee would spill hot coffee on herself one time out of one hundred. This is unacceptable. This is a valid statement if the reported recognition rates are task oriented (i.e., how many times out of 100 will the given task be

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Fig. 7. (a) Real-time behavior of fuzzy logic system during wrist extension, ulnar deviation, finger flexion, and wrist flexion trials of normal-limbed subject . x axis is the sample number, with a 45.7 ms update rate between samples. All spikes in the data are representative of classification errors. (b) Real-time behavior of fuzzy logic system during wrist flexion trials of normal-limbed subject N after electrode gain adjustment. The x axis is the sample number, with a 45.7 ms update rate between samples. All spikes in the data are representative of classification errors.

successfully completed). In such a case, it is not unreasonable to require “four nines” accuracy (99.99%; even normal limbed individuals are not perfect in motor control), particularly when dealing with tasks where any error could result in harm to the end-user. However, the rates reported in Table II are sample oriented. The decision algorithm makes a classification decision on each sample of data read. Thus, if a given contraction lasts five seconds, the algorithm will make about 110 classifications of the motion within the contraction interval. The sample oriented system accuracies reported are thus what percentage of the total decisions made within this interval that were consistent with the user’s intentions. Each individual classification, as represented by each point in Figs. 7 and 8, is a command sent to operate the prosthesis motors. The argument has been made [12] that a single error in misclassification is a minor issue, since the motor dynamics would

act like a mechanical low pass filter to smooth out a single dropped point in a stream of classification commands, similar to how the motor dynamics are used to smooth a pulse width modulation stream [1]. This claim is true for the motor that was supposed to receive the misclassified pulse. All that will happen is that the intended motor will momentarily stop or slow down (depending on the update rate). It is not true for the motor that receives an unintended pulse. The type of misclassification is important. If the system misclassifies to OFF, a false negative, then the system effectively defaults to a “safe mode” since no other motor will be activated. However, if the system misclassifies to another motion, a false positive, then an ON pulse will be sent to the misclassified motion’s motor. In other work [30] it was discovered that a single full ON pulse of duration 50 ms was sufficient to open an Otto Bock Adult hand 20 out of a full range of 60 and open a Hosmer Dorrance Synergetic Prehensor

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Fig. 8. Real-time behavior of fuzzy logic system during transition periods between active states. x-axis is the sample number, with a 45.7 ms update rate between samples. Misclassifications occur at samples 56, 135, 155, 172, and 173.

60 out of a full range of 80 . Clearly, these examples highlight the need for high accuracy and, when misclassifications occur, that the incorrectly selected state is the OFF state. This would in effect implement a “safety” mode of operation. The entire process, from location of EMG sites, to initial data collection, to automatic system generation, to real-time analysis took less than one hour for subject , with the location of the EMG sites taking by far the most time. Automatic system generation took about one minute using a MATLAB script on a 500-MHz PC. The fuzzy based system proved successful in the real-time recognition of wrist extension and ulnar deviation contractions, as shown in Figs. 7 and 8. There was only one point of misclassification for the wrist extension exercise. Slight difficulties arose during the real-time recognitions of finger and wrist flexion. The misclassifications during wrist flexion were, however, misclassifications to the OFF state and not to a different action state. A false negative is more desirable than a false positive. However, the real-time misclassifications of wrist flexion did not default to OFF. The misclassifications are mainly to the ulnar deviation action state. Analysis of acquired EMG showed that the subject’s extensor carpi ulnaris became quite active at this time. Increasing the electrode gain over the flexor carpi ulnaris by a factor of two remedied the problem by effectively increasing the ON mean signal level, and the classifier performed much better, as shown in Fig. 7(b). While there still exist instances where the classifier returns an incorrect result, these are relatively few. Of note is that the second trial of wrist flexion produced no errors in recognition, suggesting that with practice and training users might be able to achieve perfect control. Tweaking of input signal gains to improve signal independence using visual displays of EMG levels is standard clinical practice during myoelectric prosthetic fittings. The real-time behavior of the classifier during transition states shows that the classifier can transition cleanly between action states (Fig. 8). In some cases, the system first transitions to the OFF state before transitioning to the next state. This behavior is acceptable because the transition time is minimal (one sample).

The ability of the classifier to perform this exercise successfully speaks to the ability of the system to actually perform “seamless” sequential control in real-time. The algorithm presented here currently only allows for one DOF to be active at a time. However, we believe the concepts demonstrated can be extended into recognizing combinations of motions, an advantage not realized by the algorithms based upon a “crisp threshold” or a “most on” scenario. This simultaneous classification is readily achieved through the addition of membership functions and the implementation of additional rules to cover the scenarios of simultaneous activity of multiple DOFs. The real power of using fuzzy logic in this application is the ability to write high-level language rules to describe EMG signal levels from multiple inputs. The automatic rule generation takes into consideration the rms voltage levels of each channel and generates a rule to classify this combination of signals as being associated with the desired function. In addition, it is easy to modify rules to handle exceptions. V. CONCLUSION The issue of multiple EMG pattern recognition for multifunctional prosthesis control is not a new problem. The algorithm presented in this paper is an application of fuzzy logic to this problem. The simple fuzzy systems described use membership functions based on basic signal statistics (mean and standard deviation) and an inference rule base that is generated automatically using fuzzy -means data clustering of the signal amplitudes. The result is a fuzzy system that requires little post-processing after data collection and has an update rate of 45.7 ms, an advantage not seen with many systems in the literature. Reported classification accuracies are on par or better with other investigated systems, showing that these accuracies are not compromised by the simplicity of the algorithm. Furthermore, our results demonstrate it is possible for the user to effect different control motions to control different functions using a relatively simple algorithm. While our current fuzzy controller does not

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yet do parallel control (i.e., multiple independent control motions), it does show success in real-time recognition of state transitions, providing for seamless sequential control. ACKNOWLEDGMENT The authors would like to thank C. W Heckathorne for his much needed expertise in the area of myo-site selection and testing, and for his assessment of and participation with subjects A and C during the experimental protocol. REFERENCES [1] R. Weir, “Design of artificial arms and hands for prosthetic applications,” in Standard Handbook of Biomedical Engineering & Design, M. Kutz, Ed. New York: McGraw-Hill, 2003, pp. 32.1–32.61. [2] D. Childress, “An approach to powered grasp,” in 4th Int. Symp. External Control Human Extremities: Adv. External Control Human Extremities, Dubrovnik, Yugoslavia, 1972. [3] Personal Communication with Mr. Pat Prigge (Upper Extremity Manager; Clinical Specialist, Prosthetics, Upper Extremity) of Otto Bock Health Care, P. Prigge and C. W. Heckathorne, Eds., Minneapolis, MN. [4] The Utah Arm 2: Fitting Procedures Handbook, vol. 1 910 004 – Rev. B, Motion Control Inc., Salt Lake City, UT, 1998. [5] D. Taylor and F. Finley, “Multiple axis prosthesis control by muscle synergies,” in Proc. Int. Symp. Control Upper Extremity Prostheses Orthoses, Göteborg, Sweden, 1971. [6] P. Lawrence and R. Kadefors, “Classification of myoelectric patterns for the control of a prosthesis,” in Proc. Int. Symp.Control Upper Extremity Prostheses Orthoses, Göteborg, Sweden, 1971. [7] R. Wirta and D. Taylor, “Development of a myoelectrically controlled prosthetic arm,” in 3rd Int. Symp. External Control Human Extremities: Adv. External Control Human Extremities, Dubrovnik, Yugoslavia, 1969. [8] P. J. Gallant, E. L. Morin, and L. E. Peppard, “Feature-based classification of myoelectric signals using artificial neural networks,” Med. Biol. Eng. Comput., vol. 36, pp. 485–489, 1998. [9] D. Graupe and W. K. Cline, “Functional separation of EMG signals via arma identification methods for prosthesis control purposes,” IEEE Trans. Syst. Man Cybern., vol. SMC5, pp. 252–259, 1975. [10] B. Hudgins, P. Parker, and R. N. Scott, “A new strategy for multifunction myoelectric control,” IEEE Trans. Biomed. Eng., vol. 40, no. 1, pp. 82–94, Jan. 1993. [11] K. Englehart and B. Hudgins, “A robust, real-time control scheme for multifunction myoelectric control,” IEEE Trans. Biomed. Eng., vol. 50, no. 7, pp. 848–854, Jul. 2003. [12] K. Englehart, B. Hudgins, and P. A. Parker, “A wavelet-based continuous classification scheme for multifunction myoelectric control,” IEEE Trans. Biomed. Eng., vol. 48, no. 3, pp. 302–311, Mar. 2001. [13] K. Farry, J. Fernandez, R. Abramczyk, M. Novy, and D. Atkins, “Applying genetic programming to the control of an artificial arm,” in Myoelectric Controls Conf.: Issues Upper Limb Prosthetics, Fredericton, New Brunswick, Canada, 1997. [14] F. H. Y. Chan, Y. S. Yang, F. K. Lam, Y. T. Zhang, and P. A. Parker, “Fuzzy EMG classification for prosthesis control,” IEEE Trans. Rehabil. Eng., vol. 8, no. 3, pp. 305–311, Sep. 2000. [15] L. A. Zadeh, “Outline of a new approach to analysis of complex systems and decision processes,” IEEE Trans. Syst. Man Cybern., vol. SMC3, pp. 28–44, 1973. , “Fuzzy sets,” Inf. Control, vol. 8, pp. 338–353, 1965. [16] [17] S. E. Hussein and M. H. Granat, “Intention detection using a neurofuzzy EMG classifier,” IEEE Eng. Med. Biol. Mag., vol. 21, pp. 123–9, Nov./Dec. 2002. [18] B. Karlik, M. O. Tokhi, and M. Alci, “A fuzzy clustering neural network architecture for multifunction upper-limb prosthesis,” IEEE Trans. Biomed. Eng., vol. 50, no. 11, pp. 1255–1261, Nov. 2003. [19] N. Petroff, K. D. Reisinger, and P. A. C. Mason, “Fuzzy-control of a hand orthosis for restoring tip pinch, lateral pinch, and cylindrical prehensions to patients with elbow flexion intact,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 9, no. 2, pp. 225–231, Jun. 2001.

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[20] S. Micera, A. M. Sabatini, P. Dario, and B. Rossi, “A hybrid approach to EMG pattern analysis for classification of arm movements using statistical and fuzzy techniques,” Med. Eng. Phys., vol. 21, pp. 303–311, 1999. [21] S. Mitchell, “Phantom limbs,” Lippincott Mag., vol. 8, pp. 563–563, 1871. [22] L. Friedmann, The Psychological Rehabilitation of the Amputee. Springfield, IL: Charles C. Thomas Publishers, 1978. [23] J. Basmajian and C. De Luca, Muscles Alive: Their Functions Revealed by Electromyography, 5 ed. Baltimore, MD: Williams & Wilkins, 1985. [24] S. Micera, G. Vannozzi, A. M. Sabatini, and P. Dario, “Improving detection of muscle activation intervals,” IEEE Eng. Med. Biol. Mag., vol. 20, no. 6, pp. 38–46, Nov./Dec. 2001. [25] C. von Altrock, Fuzzy Logic and Neurofuzzy Applications Explained. Englewood Cliffs, NJ: Prentice Hall, 1995. [26] T. Ross, Fuzzy Logic with Engineering Applications. New York: McGraw-Hill, 1995, pp. 371–401. [27] J. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum, 1981. [28] A. Ajiboye, “Investigation of fuzzy logic as a classification algorithm of EMG for the control of multifunctional myoelectric prostheses,” in Biomedical Engineering. Evanston, IL: Northwestern Univ., 2003, pp. 145–145. [29] R. Duda and P. Hart, Pattern Classification and Scene Analysis. New York: Wiley, 1973. [30] “Impulse Responses of Powered Prehensors: In-House Technical Note,” Dept. Biomed. Eng., Northwestern Univ., Chicago, IL, 2004.

Abidemi Bolu Ajiboye received the dual B.S.E. degree in biomedical and electrical engineering and a minor in computer science from Duke University, Durham, NC, in 2000, the M.S. degree in biomedical engineering under D. S. Childress, and R. F. ff. Weir, in 2003, from Northwestern University, Evanston, IL, where he is currently working toward the Ph.D. degree, under R. F. ff. Weir, in the Prosthetics Research Laboratory. His research interests lie in the areas of neuromuscular control of human movement and myoelectric control of upper-limb prostheses. He is currently a Kirschstein National Research Service Award Predoctoral Training Fellow of the National Institute of Health.

Richard F. ff. Weir was born in Dublin, Ireland. He received the B.A. degree in mathematics and the B.AI. degree in microelectronics and electrical engineering from Trinity College, Dublin, Ireland, in 1983, and the M.S. and Ph.D. degrees in biomedical engineering from Northwestern University, Evanston, IL. After working as a Control Engineer in England, he moved to the USA. He is currently a Research Scientist at the Jesse Brown Veterans Affairs Medical Center, Chicago, IL and holds appointments as a Research Assistant Professor in the Departments of Physical Medicine and Rehabilitation and Biomedical Engineering, Northwestern University. He has research interests in the area of neural control, biomechatronics and rehabilitation, specifically arm/hand systems, manipulators, robotics and their associated control. The current focus of this work is the development of a multichannel/multifunction prosthetic hand/arm controller system based on implantable myoelectric sensors (IMES), the development of an externally powered partial-hand prostheses the development of a multifunction externally-powered prosthetic hand, as well as an exploration of the use of series elastic actuators for use in prosthetic devices.

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The Optimal Controller Delay for Myoelectric Prostheses Todd R. Farrell, Member, IEEE, and Richard F. Weir, Member, IEEE

Abstract—A tradeoff exists when considering the delay created by multifunctional prosthesis controllers. Large controller delays maximize the amount of time available for EMG signal collection and analysis (and thus maximize classification accuracy); however, large delays also degrade prosthesis performance by decreasing the responsiveness of the prosthesis. To elucidate an “optimal controller delay” twenty able-bodied subjects performed the Box and Block Test using a device called PHABS (prosthetic hand for able bodied subjects). Tests were conducted with seven different levels of controller delay ranging from nearly 0–300 ms and with two different artificial hand speeds. Based on repeted measures ANOVA analysis and a linear mixed effects model, the optimal controller delay was found to range between approximately 100 ms for fast prehensors and 125 ms for slower prehensors. Furthermore, the linear mixed effects model shows that there is a linear degradation in performance with increasing delay. Index Terms—Box and Block Test, delay, myoelectric, myo-pulse control, prostheses, prosthesis, prosthetics.

I. INTRODUCTION HE ideal multifunctional prosthesis is one that will quickly and accurately respond to the commands of the user. Multifunctional prosthesis controllers have shown higher classification accuracies when electromyographic (EMG) feature extraction and pattern recognition are performed on time windows of longer duration [1]–[3]. Unfortunately, there is a limit to the time over which EMG data can be collected and analyzed before the controller delay (i.e., the amount of time between the user’s command and the actuation of the device) resulting from this collection and analysis causes the control of the prosthesis to become cumbersome.

In fact, Hogan [4] specifically described a problem with the control of prosthetic elbows that he attributed to large controller delays. While he did not specify the length of the delay, Hogan observed an oscillatory behavior that was created when a large controller delay caused users to repeatedly overshoot the desired elbow position and then have to compensate for this overshoot. Kyberd, et al. [5] found that, for high-speed devices, the controller delay made it very difficult to open a prosthetic hand partway. The large controller delay caused the hand to open fully by the time a “stop” command could be generated. Otto Bock’s (Duderstadt, Germany) new Sensor Hand Speed has a speed of opening and closing of 4 radians per second but also exhibits a similar lack of responsiveness due to the long filter time constants of the Otto Bock electrodes. The goal of this experiment was to define the “optimal” delay for a prosthesis controller. We define the optimal delay as the maximum amount of time that can be used by the controller for data collection and analysis (so as to maximize classification accuracy) without affecting quantitatively observed prosthesis performance.

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Manuscript received May 4, 2006; revised November 21, 2006; accepted December 6, 2006. This work was supported in part by the National Institutes of Health (NIBIB/NICHD) under Grant 1 R01 EB01672-01 and by the Department of Veterans Affairs, Rehabilitation Research and Development Service and is administered through the Jesse Brown Veterans Affairs Medical Center, Chicago, IL. This work was also supported in part by the National Institute on Disability and Rehabilitation Research (NIDRR) of the Department of Education under Grant H133E030030. The opinions contained in this paper are those of the grantee and do not necessarily reflect those of the Department of Education. T. R. Farrell is with the Department of Biomedical Engineering, Northwestern University Prosthetics Research Laboratory, Chicago, IL 60611 USA (e-mail: [email protected]). R. F. Weir is with the Jesse Brown VA Medical Center—Lakeside CBOC, Chicago, IL 60612 USA and with the Department of Physical Medicine and Rehabilitation in the Northwestern University Feinberg School of Medicine, Chicago, ILL 60611 USA, and also with the Department of Biomedical Engineering in the Northwestern University McCormick School of Engineering and Applied Science, Chicago, IL 60611 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TNSRE.2007.891391

II. BACKGROUND Whereas the effects of delays on performance in remote manipulation tasks and virtual environments have previously been examined [6]–[14], Paciga et al.’s work [15] is the only study the authors are aware of that objectively attempted to quantify the effect of a controller delay on prosthesis performance. Paciga, et al. examined the ability of users to produce five different levels of an EMG signal for a five-state prosthesis controller. It was shown that introducing a 200 ms delay into the visual feedback path provided to the subject would increase the measured errors six-fold from 1.1% to 6.6%. Whereas relatively little work has objectively examined the impact of controller delays on prosthesis performance, the length of controller delay that can exist before prosthesis control degrades has been debated. Childress and Weir [16] believe that controller delays should be no longer than 50 ms to optimize performance and ensure these delays are imperceptible to the user. This is based upon anecdotal evidence from users that felt as if their hands “were being operated in molasses” if larger controller delays were present. However, members of a group at the University of New Brunswick (UNB) state that delays as large as 300 ms are not perceivable by the user [17], [18] and are acceptable for prosthesis control. Graupe et al. made contradictory statements in two of their efforts . In an early work, they stated that delays of greater than 200 ms are unacceptable [19] and in a later paper they stated that delays of 100–300 ms are satisfactory [20]. Additionally, Hefftner [21] et al. stated that controller delays must be kept below

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Fig. 1. (a) Photograph of PHABS detailing the components of the device. (b) Photograph of an individual wearing PHABS.

300–400 ms to prevent a noticeable delay. Chu, et al., [22] designed a real-time controller and attempted to keep the controller delay below 300 ms so as to not affect performance. In summary, the existing literature shows that an eight-fold (50–400 ms) difference exists in the published estimates of the acceptable delays for prosthetic limb systems. The length of acceptable controller delay may affect what signal processing and pattern recognition algorithms are used by multifunctional prosthesis controllers and thus it would be beneficial to establish this value for future investigations. Therefore, experiments were designed to discover the longest period of controller delay that does not significantly affect prosthesis performance and can thus be dedicated to EMG collection and analysis. III. HARDWARE AND PROTOCOL A. PHABS A bypass prosthesis called “PHABS” (Prosthetic Hand for Able-Bodied Subjects) was created to allow able-bodied subjects to operate a prosthetic terminal device. PHABS consists of a plastic cuff with adjustable straps and two aluminum stays that connect the user to the terminal device (Fig. 1). Two Hosmer surface electrode units (Hosmer Dorrance Corporation, Campbell, CA) were placed on the proximal third of the forearm over the flexor and extensor muscle bellies. The Hosmer electrodes perform very little filtering while amplifying the signal. The electrodes use capacitive decoupling to eliminate any direct current component of the signal and have a low pass cutoff frequency of 1500 Hz. The electrodes were fixed in place using Compressogrip #21/2 (Knit-Rite, Inc., Kansas City, KS) compression bandage that was then covered in standard kitchen plastic wrap to keep the electrode contact areas moist. Fig. 1 shows PHABS

Fig. 2. Linear speeds of all commercially available prostheses sold in the U.S. [23], [24], as well as the measured speeds for both the “fast” and “slow” prehensors used in these experiments. There are three prehensors that are marginally slower than our “slow” prehensor and the Motion Control ETD (when operated at 14 V) is the only device that has a higher speed than the “fast” prehensor. Based on this data it is believed that the spectrum of commercially available prehensor speeds was fairly well represented in these experiments.

equipped with an Otto Bock System Electric Hand (Otto Bock Healthcare, Duderstadt, Germany). For these experiments, PHABS was equipped with the Hosmer NU-VA Synergetic Prehensor (Hosmer-Dorrance Corp., Campbell, CA). This prehensor was chosen because of its high speed of opening and closing. One of the goals of these experiments was to investigate the effect of prehensor speed on the optimal controller delay. The supply voltage to the Synergetic Prehensor was varied to adjust the speed of the device. Supply voltages of 6.5 and 11.5 V were used ( 2.5 V from the standard operating voltage). The time from full open to full close for the 6.5 V and 11.5 V supply voltages were 430 ms and 240 ms, respectively. The speeds of the prehensor were calculated to be 10.2 cm/s (2.15 radians/s, 123 degrees/s angular velocity) for the 6.5 V supply voltage and 36.7 cm/s (3.85 radians/s, 221 degrees/s angular velocity) for the 11.5 V supply voltage. For a comparison of these speeds against the speeds of the other prehensors that are commercially available in the U.S., see Fig. 2. The fastest prehensors on the market are the Sensor Hand Speed from Otto Bock (Otto Bock Healthcare, Duderstadt, Germany) and the Motion Control ETD (when run at 14 V) (Motion Control, Salt Lake City, UT) which are reported to have an average maximum speed of 30.0 cm/s [23] and 41.9 cm/s [24], respectively. The slowest commercially available prehensor is the RSL Steeper Multicontrol Plus Electric Hand (RSL Steeper, Leeds, U.K.) which has an average maximum speed of 8.75 cm/s [24]. The data in Fig. 2 shows that the prehensor speeds that were used in these experiments

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FARRELL AND WEIR: THE OPTIMAL CONTROLLER DELAY FOR MYOELECTRIC PROSTHESES

Fig. 3. Graphical illustration of myo-pulse control. Myo-pulse control provides proportional control of a motor by varying the pulse width and timing of a digital control signal. Whenever the EMG signal (bottom trace) is lies outside a predetermined threshold, the motor drive signal (top trace) is turned “on.” The ratio of motor “on” command time to motor ‘off’ time determine the velocity of the motor. Used with permission of the Northwestern University Prosthetics Research Laboratory (NUPRL).

are representative of the two ends of the spectrum of prehensor speed available in current commercial devices. B. Controller 1) Theory and Implementation: Myo-pulse control ([25], [26]) is a commercially available control strategy (Hosmer–Dorrance Corporation, Campbell, CA) and, while it is infrequently used in clinical practice, it was chosen as the control algorithm for these experiments because it provided an easy way to both minimize the delay inherent in the controller and to set the controller delay to any value above this minimum. Myo-pulse control can be thought of as a combination of both pulse width modulation (PWM) and pulse period modulation (PPM) because it provides proportional control of motor speed by varying the pulse width and timing of a digital control signal. The prehensor’s motor and the inertia of the fingers then act as a mechanical low-pass filter to smooth the pulse train and create a smooth movement. A myo-pulse controller compares the absolute value of the EMG signal to a predefined threshold. If the EMG is above the threshold the motor will be turned “on” and if it is below the threshold the motor will be turned “off.” A graphical example of one-channel myo-pulse control is shown in Fig. 3. If the EMG signal is treated as a Gaussian signal whose variance is related to the strength of the contraction, as the strength of a contraction increases so does the probability that the amplitude of the EMG will lie outside the thresholds and thus increases the amount of time the signal is “on.” Variable speeds of opening and closing are created by the ratio of “on” time to “off” time. In typical EMG processing, the EMG is rectified and lowpass filtered to provide the envelope of the EMG signal as the input to the controller. Low-pass processing methods introduce a substantial delay between EMG onset and controller output due to the long time constants of these enveloping filters. Myopulse modulation avoids these delays by allowing the inertia inherent in the prehensor mechanism to perform the filtering, which makes for a very responsive EMG control system. In fact, the delay introduced by the controller is limited to its sampling period. For our purposes, myo-pulse control allows the inherent

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controller delay to be kept as close to zero as possible to create an ideal baseline condition. For these experiments the controller was created in Matlab’s (The Mathworks, Inc., Natick, MA) Simulink and executed using Simulink’s Real Time and XPC Target Toolboxes. The myo-pulse controller was executed at 1 kHz and thus the inherent controller delay was only 1 ms when no additional artificial delay was added. The Simulink software allowed artificial controller delays to be added to the controller and variable myo-pulse thresholds to be implemented. 2) Myo-Pulse Creates the Ideal Baseline Condition: Fig. 4 shows the elements that could introduce a delay in a multifunctional prosthesis control system. These delays include: the amount of time it takes from the intent of movement to the development of EMG, the time constant of the analog filters contained in the EMG preamplifiers, the analog to digital sampling period, the time required to collect the EMG signal for feature extraction, the time required to perform the EMG feature extraction, the time required to execute the pattern recognition on the extracted features and the time required to actuate the component. By implementing a myo-pulse controller, the delays associated with analog low-pass filtering, EMG signal collection, feature extraction, and pattern recognition were eliminated. Additionally, the combination of the A/D sampling period and signal processing has been reduced to 1 ms. Therefore, for the baseline condition, our controller delay (time from EMG development to motor drive signal) is only 1 ms. In these experiments up to 300 ms of additional delay was artificially added to the myo-pulse controller. This additional delay can be thought of as representing any combination of the variables that are eliminated by using the myo-pulse controller (e.g., EMG signal collection, analog filter time constant). Admittedly there is some delay between the intent of movement and the development of EMG. For example, Bereitschaftspotentials, or very preliminary neurological precursors of movement, can appear up to 1.5 s prior to voluntary finger movement [27]. In these experiments, we are not investigating or attempting to control the neurological component shown in Fig. 4. Finally, as mentioned previously in the description of PHABS, we will be examining the effect of the time necessary for the actuator to produce a movement by varying the speed of the prehensor. C. Box and Block Test The Box and Block Test was used to quantify prosthesis performance. This test was chosen because it is quantitative, quick and easy to administer, sensitive [28], and normative data has been collected [29], [30]. It has been used frequently to quantify the effect of treatment on upper limb function for disorders such as cerebral palsy [31], multiple sclerosis [32], and stroke [33]–[35]. The testing apparatus for the Box and Block Test (Sammons Preston Inc., Bolingbrook, IL) consists of two adjacent compartments separated by a 6-in barrier (Fig. 5). The Box and Block Test is a 60-s timed test in which subjects are instructed to pick up blocks from one compartment, transport them across the barrier, and release them in the opposite compartment as quickly as possible. Several rules govern the scoring of the test, i.e., blocks thrown across the barrier do not count, if two blocks are moved

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Fig. 4. Elements composing the time from the intention of movement to the completion of the movement by the prosthesis.

Fig. 5. Photograph of a Box and Block apparatus. Subjects will pick up blocks from one side of the box, transport them over the barrier, and then release them on the other side of the box. The number of blocks transported over the barrier in 1 min is the score that the subjects receive.

across the barrier together they only count as one, etc. For more details on these rules and the test itself, see [30]. D. Testing Protocol 1) Pretest Procedures: Each testing session began with an explanation of the test procedures and the acquisition of informed consent from the subject. For simplicity, the two prehensor speeds will now be referred to as “fast” and “slow.” Half of the subjects were given the slow prehensor speed first and half were given the fast speed first. The first eighteen subjects flipped a coin to determine which prehensor speed would be used during the first set of trials. The last two subjects were simply assigned the speed that they would complete first to ensure that an equal number of subjects used each speed first. Two EMG sites were located on the forearm over the wrist flexor and extensor groups according to standard clinical prosthetics practice. This procedure involves having subjects repeatedly produce contractions of similar intensity and then iteratively moving a testing electrode around the flexor or extensor surface of the forearm. The different sites are examined in an effort to find the two sites that provide the strongest signal for the test movement (i.e., wrist flexion or extension) without substantial coactivation from the opposite movement or interference from the brachioradialis, which is used to support the weight of the PHABS. The subjects donned the PHABS with the electrodes placed at the previously identified locations. Threshold levels in the

myo-pulse controller were altered so that they were as low as possible without allowing the baseline noise contained in the EMG channels to elicit movement of the prosthesis. The subject was then allowed time to practice picking up several blocks and transporting them across the barrier. An Otto Bock Quick-Disconnect Wrist (Otto Bock Healthcare, Duderstadt, Germany) allowed the amount of pronation/supination of the terminal device to be altered to a position that was preferred by the subject to increase visibility, correlate movement of the anatomic wrist to the prosthetic finger, etc. Once the subject felt comfortable controlling the PHABS the instructions for the Box and Block Test were read to them and the subjects then completed two 1-min practice trails of the Box and Block Test. 2) Test Administration: Seven levels of additional controller delay (i.e., delay that was added to simulate EMG collection and processing) were investigated in this study, ranging from 0 to 300 ms in 50 ms increments. It was observed that there was a substantial improvement in the Box and Block scores during the first several trials as the subjects developed strategies as to how to best complete the Box and Block Test and became more comfortable controlling the PHABS. In all but one of the studies listed earlier, the Box and Block Test was only administered once per testing session. One study [28] had each subject perform the test three times per sitting but made no comments regarding any improvement in performance from the first to the third trials. As a result of this learning effect each subject performed seven trials at the beginning of testing (trials #1–7) that were timed and recorded but not included in the final analysis. Each of the seven delay levels was introduced once within the first seven “ignored” trials. The subject then performed three more groups of seven trials (trials #8–28) in which each delay level was randomized and presented once per group (three times total). The randomization of the trials was done to ensure that any further learning/fatigue effects were distributed equally across all conditions. Each of the first 28 trials was conducted using the hand speed that was determined by the coin flip. After trial #28 the speed of the hand was switched and the subject was allowed to do two practice trials to become familiar with the new prehensor speed (trials #29–30). After completing the first 28 trials, the subjects were found to adapt quickly to the new speed of the prehensor. The subject then performed another three sets of seven trials (trials #31–51) to complete the protocol. Subjects were required to take a 5-min break after every 10–12 trials to reduce the effects of fatigue.

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Fig. 6. Average Box and Blocks test scores (n = 20) when using the “fast” and “slow” prehensors. As the additional controller delay increases, the average scores on the Box and Block Test decreases. Additionally, as expected, subject performed better when using the “fast” prehensor.

IV. RESULTS A. Box and Block Scores Twenty subjects participated in the study and the average Box and Block scores for all subjects are shown in Fig. 6. As expected, the “fast” prehensor had higher scores, on average, than the “slow” prehensor. Also as expected, as the amount of controller delay increases the average Box and Block score tends to decrease. The only exception to this rule is the slight increase from 0 to 50 ms with the “fast” prehensor condition. B. Statistical Analysis 1) Repeated Measures ANOVA: A single-factor repeated measures ANOVA was used to compare statistical intrasubject differences in the average Box and Block scores for the various controller delays. The null hypothesis was that there was no difference between the delay conditions. Additionally, a Bonferoni correction for multiple comparisons was made. The data passed Mauchly’s Test of Sphericity for both the “slow” data and the “fast” data meaning that the variance of the data for each of the conditions can be considered equal and is, therefore, adequate for repeated measures ANOVA analysis. Additionally, the data for all of the conditions passed the Shapiro–Wilk test of normality , ensuring that the distribution of the data was appropriate for an ANOVA analysis. The results of the repeated measures ANOVA are presented in Fig. 7. Those comparisons that produced statistically significant differences are highlighted in gray. The most important comparisons to examine are those between the smallest controller delays, i.e., 0 and 50 ms and the larger delays. There is no statistically significant difference between the 0/50 ms delay conditions and the 100 ms condition but there is a difference between the 0/50 ms conditions and all controller delays of 150 ms or larger. These differences existed for both the “fast” and “slow” prehensors. All of the comparisons produced the same results for both prehensor speeds with the exception

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Fig. 7. Results of the repeated measures ANOVA analysis on the Box and Block data. Each cell represents the probability that there is no difference between the two conditions. Those combinations that produce a statistically significant result (p < 0:05) are highlighted in gray.

of the 100 ms versus 200 ms and 200 ms versus 250 ms levels. These differences were not statistically significant for the slow prehensor but were statistically significant for the fast prehensor. 2) Linear Mixed Effects Model: In addition to attempting to determine simply statistical differences between the different conditions, a linear mixed effects model was constructed to determine a clinically significant change in the Box and Block scores. This type of model does not attempt to determine the presence of differences between experimental conditions but instead attempts to create a model that best explains the observed data. From this model, the amount of controller delay necessary to produce a change of n blocks in the Box and Block Test can be calculated. Prior to beginning the study, we determined that a change of three blocks is a clinically significant change in a Box and Block score. This estimate was based off of the results from our pilot experiments, where a change in score of three blocks was equal to a 12.4% change from the overall average score of all trials. The linear mixed effects model includes both standard fixed effects (i.e., intercept, controller delay, prehensor speed, and an interaction term) as well as random effects to account for intersubject differences and takes the following form:

(1) Score Delay Speed

Score on the Box and Block test. The delay added to the controller [0, 50, 100, 150, 200, 250, 300]. Speed of the prehensor [10.2 or 36.7 m/s] Random effects, i.e., the expected differences of the intercept, delay, speed and interaction coefficients from the population means, given a particular subject j (1-20). Residual effects.

The null hypothesis was that each of the coefficients in (1) was equal to zero. All coefficients were found to be statistically significant ( , ; , ; , ; , ). If

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the calculated the form


values are entered into (1) the final model takes

The average Box and Blocks scores show that there is a decreasing trend in Box and Block score as the amount of controller delay increases. A linear relationship was observed which is consistent with similar linear trends between performance and controller delay observed by others [6], [7]. This relationship is monotonic for the “slow” prehensor and broadly monotonic for the “fast” prehensor results. The one exception for the fast prehensor is the small increase in the Box and Block scores for the 50 ms condition when compared to the 0 ms condition. However, this increase was not statistically significant . This “knee” may be due to the limitations in the human operator rather than the prosthesis controller. The average Box and Block scores also indicate that the subjects tended to score higher with the faster prehensor. This difference was shown to be statistically significant by the linear mixed effects model ( , ).

the controller delay increased, the difference between the delay conditions did not become statistically significant until the additional controller delays reached at least 150 ms. For both the “fast” and “slow” prehensors, there was a statistically significant difference between the two smallest controller delay increments (0 and 50 ms) and the 150 ms condition. Additionally, there was no difference between the 0 and 50 ms delay increments and the 100 ms delay condition. The conclusion that can be made from these ANOVA results is that, on average, a delay of 100 ms does not cause a statistically significant decrease in performance on the Box and Block Test. However, a delay of 150 ms will cause of statistically significant decrease in performance when compared to the 0 ms condition. These results indicate that the controller delays should be kept between 100 and 150 ms for the average subject to avoid producing a statistically significant decrease in performance. 2) Linear Mixed Effects Model: The disadvantage of the ANOVA analysis is that, while it does tell us which conditions statistically differ from one another, it does not permit calculation of user-defined clinically significant effects of controller delay on performance. Additionally, the ANOVA does not take advantage of the obvious relationship that exists between delay levels. The linear mixed effects model demonstrated that, depending on the speed of the prosthesis, a prosthesis controller should have a delay of less than 100–125 ms to avoid producing any clinically significant change in performance on the Box and Block Test for 90% of the population. Even though a statistically significant difference between the groups may not have been detected by the ANOVA until 150 ms was significant the linear mixed of delay was present, since effects model suggests that any delay will decrease the Box and Block Test score. Implications of this observation for single degree-of-freedom prosthesis performance is that smaller delays will improve performance on the Box and Block Test. However, in the case of pattern recognition based multifunctional prosthesis control, it has been shown that larger analysis windows (and thus larger delays) increase classification accuracy. Therefore, a balance must be struck between increased speed of response and increased classification accuracy when considering pattern recognition based multifunctional prosthesis controllers. The coefficient of the speed term was positive, indicating that as the speed of the prehensor increases the Box and Block scores tend to increase. This is not surprising since the “fast” prehensor opens and closes more quickly. The statistical significance of the interaction term indicates that the affect of controller delay on the Box and Block performance is a function of prehensor speed. Additionally, the interaction term was negative, which indicates that as the controller delay increases the difference in the scores for the fast and slow prehensors will decrease. The effect of the interaction term makes intuitive sense because as the controller delays are increased, the controller delay, and not the speed of the prehensor, will dictate the responsiveness of the device.

B. Statistical Analysis

C. Applicability to Other Forms of Controllers

1) Repeated Measures ANOVA: While there was a general trend of decreasing performance on the Box and Block test as

In these experiments, myo-pulse control was used to create a controller with minimal delay. Until the last decade or so

(2) A statistically significant interaction term implies that the amount of delay required to cause an n block change in the score will be dependent upon the prehensor speed. For a given prehensor speed, the change in delay that would be required to change the Box and Block Test score by n blocks can be determined by (3) For a fast prehensor (Speed cm/s), a three block change can be obtained with a delay of 138 ms. For the slow prehensor (Speed cm/s) a three block difference will be produced with a delay of 173 ms. These results show that users can tolerate more delay with slower devices but at the expense of lower overall performance. The 138 ms and 173 ms values are estimates of the delays that cause a three block change in the performance for an average subject i.e., 50% of the subjects show a three block change for a 138 ms (fast prehensor) or 173 ms (slow prehensor) controller delay. When designing a controller, it should be effective for the majority of users, rather than the average subject. To obtain an estimate of the optimal delay for 90% of the population a model was constructed for each individual subject. The delay required to create a change of three blocks for the fast prehensor was observed to range from 80 to 268 ms for the 20 subjects. Based on these data, we were then able to conclude that 90% of the population (mean + 1.282 SD) would show a change of less than three blocks when a delay of 99.8 ms (which we round up to 100 ms) was present. Likewise, for the slow prehensor, it was found that 90% of the population would show a change of less than three blocks with a 123 ms controller delay (which we round up to 125 ms). V. DISCUSSION A. Average Box and Block Scores

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most commercially available prehensors have been relatively slow and therefore did not require a responsive controller. As faster devices were created, more responsive signal processing techniques have been implemented to control these devices. For example, Hosmer Dorrance’s Synergetic Prehensor uses myopulse control whereas the Motion Control ETD uses an adaptive filtering technique developed by Park and Meek [36] that modifies the time constant of the EMG filter based upon the EMGs’ rate of change. These relatively new processing methods have been shown to be effective means of providing quick, responsive control of high-speed prehensors. The task that was performed in these experiments required the subject to open and close the terminal device as quickly as possible in order to move the maximum number of blocks in the allotted time. It is reasonable to assume that the terminal device was being operated in a bang-bang fashion with intense contractions being produced to drive the hand at top speed. Given this scenario, the authors perceive little advantage to using longer time constant filters to reduce signal variability because the input signals are all likely above the maximum velocity threshold. Therefore, we believe that our results using myo-pulse control with a pure delay are a good estimate of the results that would be obtained using a low-pass filter based controller and therefore these results are applicable to other forms of controllers. D. Applicability to Multiple Degree of Freedom Systems There is an apparent tradeoff when examining the results from this study in the context of currently evolving pattern recognition systems. Past research in pattern recognition systems has shown a clear advantage to using larger analysis windows to increase classification accuracies [1]–[3]. While no performance analysis has been done with one of these systems implemented in a clinical fitting on an amputee, one would infer that there would be an increase in prosthesis performance with increased classification accuracy. However, longer analysis windows also lead to increased controller delay, which should degrade performance. We have shown a linear decrease in prosthesis performance with increasing controller delay. Englehart, et al. [1] showed a nonlinear increase in classification accuracy with increasing window length. The “knee” in the error rate versus record length occurs somewhere below 100 ms. This curve also shows diminishing returns with respect to classification accuracy for record lengths longer than 100 ms. Additionally, Zardoshti–Kermani, et al. [37] showed that using window sizes greater than 100 ms did not substantially increase the separability of EMG signal features. These observations are encouraging when examined in the light of the results obtained in the preceding experiments. We have demonstrated that prosthesis performance can show a clinically significant decrease with a controller delays of 100 ms or greater and Englehart, et al., has shown that there is relatively little classification accuracy gained when more than 100 ms of EMG is collected for classification purposes. Therefore, while 100 ms may be a slightly conservative estimate of the optimal controller delay in light of the potential classification accuracy increases with larger analysis windows, we assume that the optimal controller delay for multiple degree-of-freedom devices

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utilizing pattern recognition will be similar to what we have reported here. Finally, when extending these results to multijoint devices, the speed of different prosthetic components must be considered. While a 100–125 ms delay was found to be the optimal controller delay for the range of commercially available prehensors speeds, this value may be higher for larger inertia components such as prosthetic elbows. However, even if slower devices are found to have a larger acceptable delay, one of the degreesof-freedom inevitably being controlled by the multifunctional controller would be the prehensor. Since there is no way to tell when an “elbow flexion” command would be given instead of a “hand open” command, we need to design for the most responsive component. Therefore the ideal controller delay for the prosthesis controller would still be 100–125 ms, unless separate controllers are used for each degree-of-freedom of the prosthesis. E. Other Observations The fact that delays of greater than 100 ms cause a decrease in performance is consistent with some clinical observations that have been made in our laboratory. When controller delays were greater than 50–100 ms users noted that it felt as if they were operating their prosthesis ‘in molasses.’ The data collected in these experiments reinforces our clinical experience that the delays should be kept at or below 100 ms. Keeping controller delays below 100 ms is a goal. If reliable control of a multifunctional prosthesis can be demonstrated but only by using larger controller delays, then users may choose to have a sluggish device that gives them robust control over several degrees of freedom. However, our results show that any additional delay results in decreasing performance and, therefore, an ideal multifunctional prosthesis would accurately respond to the users’ commands and do so as little time as possible. VI. CONCLUSION In an effort to define the “optimal controller delay,” (i.e., the maximum amount of time that can be used by the controller for data collection and analysis to maximize classification accuracy without affecting prosthesis performance) twenty subjects performed the Box and Block Test with a variety of controller delays. We have shown that both a repeated measures ANOVA analysis and a linear mixed effects model analysis give us estimates of the optimal controller delay that lie between 100 and 175 ms for the average user. However, if the controller is designed to accommodate the 90th percentile user, we show that the optimal controller delay lies in the neighborhood of 100-125 ms, depending on the prehensor speed. In addition we show a linear decrease in operator performance for any additional delay. REFERENCES [1] K. Englehart, B. Hudgins, and P. A. Parker, “A wavelet-based continuous classification scheme for multifunction myoelectric control,” IEEE Trans. Biomed. Eng., vol. 48, no. 3, pp. 302–311, Mar. 2001. [2] S. Du and M. I. Vuskovic, “Temporal vs. spectral approach to feature extraction from prehensile EMG signals,” in Proc. IEEE Int. Conf. Inf. Reuse Integration, Nov. 8–10, 2004, pp. 344–350. [3] M. Yamada, N. Niwa, and A. Uchiyama, “Evaluation of a multifunctional hand prosthesis system using EMG controlled animation,” IEEE Trans. Biomed. Eng., vol. 30, pp. 759–763, 1983.

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[4] N. Hogan, “A review of the methods of processing EMG for use as a proportional control signal,” Biomed. Eng., vol. 11, pp. 81–86, 1976. [5] P. J. Kyberd, O. E. Holland, P. H. Chappell, S. Smith, R. Tregidgo, P. J. Bagwell, and M. Snaith, “MARCUS: A two degree of freedom hand prosthesis with hierarchical grip control,” IEEE Trans. Rehabil. Eng., vol. 3, no. 1, pp. 70–76, Mar. 1995. [6] J. E. Conklin, “Linearity of the tracking performance function,” Perceptual Motor Skills, vol. 9, pp. 387–391, 1959. [7] W. R. Ferrell, “Remote manipulation with transmission delay,” IEEE Trans. Human Factors Electronics, vol. HFE6, pp. 24–32, 1965. [8] W. R. Ferrell and T. B. Sheridan, “Supervisory Control of Remote Manipulation,” IEEE Spectrum, vol. 4, pp. 81–88, 1967. [9] I. MacKenzie and C. Ware, “Lag as a determinant of human performance in interactive systems,” in Proc. ACM Conf. Human Factors Comput. Syst.—INTERCHI ’93, 1993, pp. 488–493. [10] T. B. Sheridan and W. R. Ferrell, “Remote manipulative control with transmission delay,” IEEE Trans. Human Factors Eng., vol. HFE4, pp. 25–29, Sep. 1963. [11] K. U. Smith, W. M. Smith, and M. F. Smith, Delayed Sensory Feedback and Behavior. Philadelphia, PA: W.B. Saunders and Company, 1962. [12] W. M. Smith, “Feedback: Real-time delayed vision of one’s own tracking behavior,” Science, vol. 176, pp. 939–940, 1972. [13] W. M. Smith and K. F. Bowen, “The effects of delayed and displaced visual feedback on motor control,” J. Mot. Behav., vol. 12, pp. 91–101, 1980. [14] R. Held, A. Efstathiou, and M. Greene, “Adaptation to displaced and delayed visual feedback from the hand,” J. Exp. Psychol., vol. 72, pp. 887–891, 1966. [15] J. E. Paciga, P. D. Richard, and R. N. Scott, “Error rate in five-state myoelectric control systems,” Med. Biol. Eng. Comput., vol. 18, pp. 287–290, 1980. [16] D. S. Childress and R. F. Weir, “Control of limb prostheses,” in Atlas of Amputations and Limb Deficiencies: Surgical, Prosthetic, and Rehabilitation Principles, D. G. Smith, J. W. Michael, and B. J. H. , Eds., 3rd ed. Rosemont, IL: J. H. Bowker, 2004, pp. 173–195. [17] K. Englehart and B. Hudgins, “A robust, real-time control scheme for multifunction myoelectric control,” IEEE Trans. Biomed. Eng., vol. 50, no. 7, pp. 848–854, Jul. 2003. [18] K. Englehart, B. Hudgins, and A. Chan, “Continuous multifunction myoelectric control using pattern recognition,” Technol. Disability, vol. 15, pp. 95–103, 2003. [19] D. Graupe, J. Salahi, and K. H. Kohn, “Multifunctional prosthesis and orthosis control via microcomputer identification of temporal pattern differences in single-site myoelectric signals,” J. Biomed. Eng., vol. 4, pp. 17–22, 1982. [20] D. Graupe, J. Salahi, and D. S. Zhang, “Stochastic analysis of myoelectric temporal signatures for multifunctional single-site activation of prostheses and orthoses,” J. Biomed. Eng., vol. 7, pp. 18–29, 1985. [21] G. Hefftner, W. Zucchini, and G. G. Jaros, “The electromyogram (EMG) as a control signal for functional neuromuscular stimulation—Part I: Autoregressive modeling as a means of EMG signature discrimination,” IEEE Trans. Biomed. Eng., vol. 35, no. 4, pp. 230–237, Apr. 1988. [22] J. K. Chu, I. Moon, and M. Mun, “A real-time EMG pattern recognition based on linear-nonlinear feature projection for multifunction myoelectric hand,” presented at the IEEE 9th Int. Conf. Rehabilitation Robotics (ICORR), Chicago, IL, 2005. [23] Myobock Arm Components Catalog. Duderstadt, Germany: Otto Bock Healthcare, 2004/2005. [24] C. W. Heckathorne, “Components for electric-powered systems,” in Atlas of Amputations and Limb Deficiencies, D. G. Smith, J. W. Michael, and J. H. Bowker, Eds., 3rd ed. Rosemont, IL: American Academy of Orthopaedic Surgeons, 2004, pp. 145–171. [25] D. S. Childress, “An approach to powered grasp,” in Advances in External Control of Human ExtremitiesFourth International Symposium on External Control of Human Extremities, M M. Gavrilovic and A B. Wilson, Jr., Eds., Belgrade, Yugoslavia, 1973, pp. 159–167. [26] R. F. Weir, “Design of artificial arms and hands for prosthetic applications,” in Standard Handbook of Biomedical Engineering and Design, M. Kutz, Ed. New York: McGraw–Hill, 2003, ch. 32, pp. 32.1–32.61. [27] L. Deecke, B. Grozinger, and H. H. Kornhuber, “Voluntary finger movement in man: Cerebral potentials and theory,” Biol. Cybern., vol. 23, pp. 99–119, 1976. [28] D. E. Goodkin, D. Hertsgaard, and J. Seminary, “Upper extremity function in multiple sclerosis: Improving assessment sensitivity with boxand-block and nine-hole peg tests,” Arch. Phys. Med. Rehabil., vol. 69, pp. 850–854, 1988.

[29] J. Desrosiers, G. Bravo, R. Hebert, E. Dutil, and L. Mercier, “Validation of the Box and Block Test as a measure of dexterity of elderly people: Reliability, validity, and norms studies,” Arch. Phys. Med. Rehabil., vol. 75, pp. 751–755, 1994. [30] V. Mathiowetz, G. Volland, N. Kashman, and K. Weber, “Adult norms for the Box and Block Test of manual dexterity,” Am. J. Occup. Ther., vol. 39, pp. 386–391, 1985. [31] G. Goodman and S. Bazyk, “The effects of a short thumb opponens splint on hand function in cerebral palsy: A single-subject study,” Am. J. Occup. Ther., vol. 45, pp. 726–731, 1991. [32] D. E. Goodkin, R. A. Rudick, S. VanderBrug Medendorp, M. M. Daughtry, K. M. Schwetz, J. Fischer, and C. Van Dyke, “Low-dose (7.5 mg) oral methotrexate reduces the rate of progression in chronic progressive multiple sclerosis,” Ann. Neurol., vol. 37, pp. 30–40, 1995. [33] J. H. Cauraugh and S. B. Kim, “Chronic stroke motor recovery: Duration of active neuromuscular stimulation,” J. Neurol. Sci., vol. 215, pp. 13–19, 2003. [34] J. R. Carey, T. J. Kimberley, S. M. Lewis, E. J. Auerbach, L. Dorsey, P. Rundquist, and K. Ugurbil, “Analysis of fMRI and finger tracking training in subjects with chronic stroke,” Brain, vol. 125, pp. 773–788, 2002. [35] J. Cauraugh, K. Light, S. Kim, M. Thigpen, and A. Behrman, “Chronic motor dysfunction after stroke: Recovering wrist and finger extension by electromyography-triggered neuromuscular stimulation,” Stroke, vol. 31, pp. 1360–1364, 2000. [36] E. Park and S. G. Meek, “Adaptive filtering of the electromyographic signal for prosthetic control and force estimation,” IEEE Trans. Biomed. Eng., vol. 42, no. 10, pp. 1048–1052, Oct. 1995. [37] M. Zardoshti-Kermani, B. C. Wheeler, K. Badie, and R. M. Hashemi, “EMG feature evaluation for movement control of upper extremity prostheses,” IEEE Trans. Rehab. Eng., vol. 3, no. 4, pp. 324–333, Dec. 1995.

Todd R. Farrell (M’02) received the B.S. degree in biomedical engineering from The Catholic University of America, Washington, DC, in 2000 and the M.S. degree in biomedical engineering, in 2003, from Northwestern University, Evanston, IL, where he is currently working toward the Ph.D. in the Northwestern University Prosthetics Research Laboratory. His research interests lie in the area of multifunctional prosthesis control, specifically the use of intramuscular EMG as well as the effect of delay and controller accuracy on prosthesis performance. Mr. Farrell was awarded the National Defense Science and Engineering Graduate Fellowship and the Kosciuszko Foundation Tuition Scholarship.

Richard F. Weir (M’91) was born in Dublin, Ireland. He received the B.A. degree in mathematics, BAI in microelectronics and electrical engineering from Trinity College, Dublin, in 1983. and the M.S. and Ph.D. degrees in biomedical engineering from Northwestern University, Evanston, IL. After working as a Control Engineer in England, he moved to the USA. He is currently employed as a Research Scientist by the Jesse Brown VA Medical Center, Chicago, IL and holds appointments as a Research Assistant Professor in the Departments of Physical Medicine and Rehabilitation and Biomedical Engineering at Northwestern University. He has research interests in the area of neural control, biomechatronics and rehabilitation, specifically arm/hand systems, manipulators, robotics and their associated control. The current focus of this work is the development of a multichannel/multifunction prosthetic hand/arm controller system based on implantable myoelectric sensors (IMES), the development of an externally-powered partial hand prostheses the development of a multifunction externally-powered prosthetic hand, as well as an exploration of the use of series elastic actuators for use in prosthetic devices.

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

TBME-00027-2007.R1

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User-Modulated Impedance Control of a Prosthetic Elbow in Unconstrained, Perturbed Motion Jonathon W. Sensinger and Richard F. ff. Weir, Member, IEEE

Abstract—Humans use the agonist-antagonist structure of their muscles to simultaneously determine both the motion and the stiffness of their joints. Designing this feature into an artificial limb may prove advantageous. To evaluate the performance of an artificial limb capable of modulating its impedance, the authors have created a compact series elastic actuator that has the same size and similar weight as commercially available electric prosthetic elbows. The inherent compliance in series elastic actuators ensure their safety to the user, even at high speeds, while creating a high-fidelity force actuator ideally suited for impedance control. This paper describes three serial studies that build on each other. The first study presents modeling of the actuator to ensure stability in the range of impedance modulation and empirically tests the actuator to validate its ability to modulate impedance. The actuator is found to be stable and accurate over a wide range of impedances. In the second study, four subjects are tested in a preliminary experiment to answer basic questions necessary to implement user-modulated impedance control. Findings include the superiority of velocity control over position control as the underlying motion paradigm and the preference for high stiffness and non-negative inertia. Based on the findings of the second study, the third study evaluates the performance of 15 able-bodied subjects for two tasks, using 5 different impedance paradigms. Impedance modulation, speed, and error were compared across paradigms. The results indicate that subjects do not actively modulate impedance if it is near a preferred baseline. Fixed impedance and viscosity modulation provide the most accurate control. Index Terms— Impedance Control, Series Elastic Actuator, prosthesis, artificial limb. Manuscript received January 7, 2007. This work was supported in part by the National Defense Science and Engineering Graduate Fellowship; the Department of Veterans Affairs, Rehabilitation Research and Development Service administered through the Jesse Brown VA Medical Center, Chicago; and the National Institute of Health under grant R01 EB001672. J. W. Sensinger is with the Rehabilitation Institute of Chicago, Chicago, IL 60611 USA (phone: 312-238-2088; e-mail: [email protected]). R. F. ff. Weir, is the Director of the Biomechatronics Development Laboratory at the Rehabilitation Institute of Chicago, and is also affiliated with the Jesse Brown VA Medical Center, Chicago, IL 60611 USA and the Departments of Physical Medicine & Rehabilitation & Biomedical Engineering, Northwestern University, Evanston, IL 60208 USA (e-mail: [email protected]). Copyright © 2007 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending an e-mail to [email protected]

I. INTRODUCTION

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for control of upper limb prostheses have always been high because of the standard established by able-bodied dexterity. Factors to be improved include the number of joints that may be manipulated, as well as the ability to simultaneously and accurately control motion of those joints. Another factor that plays an integral role in ablebodied movement and that is not implemented in prostheses is the control of impedance, or the relationship between forces and movements. The modulation of impedance in able-bodied persons may allow various optimization paradigms to be used, including reduction of power consumption, minimization of trajectory error in the presence of perturbations, and smooth movement [1]. Muscle architecture intrinsically modulates the impedance of joints based on position and speed, while allowing humans to change that impedance depending on the task [2]. As a result, Hogan [3] has suggested adaptive impedance control as a preferred paradigm for controlling prostheses. Impedance may be divided into three components that affect the interaction of force and movement: stiffness, viscosity, and inertia. Humans have a stiffness in their elbow joint (the joint the authors are studying) of 2-15 Nm/rad for most activities of daily living, although depending on the task they can increase the stiffness to 140-200 Nm/rad by cocontracting their muscles [4]. Viscosity of the human elbow ranges from 0.4-2.5 Nms/rad depending on the position of the joint and cocontraction level of the muscles [5], and is not independently modulated by humans [2]. Inertia is based on the mass of the limb segments as well as any external loads the hand may be carrying, combined with each limb’s position in space, and may be modulated by changing the position of the endpoint (hand) with respect to the base (chest) [6, 7]. To ensure safety, any technology used to modulate the impedance of a prosthesis must have low impedance above the controllable bandwidth of the actuator. Conventional electromechanical robots have high impedance above their controllable bandwidth, due to their large gear ratios coupled with the inertia of their rotors [8, 9]. Although impedance control has been advocated in the past for use in prostheses [3], physical limitations on robotic actuators have made modulating impedance difficult, especially while limiting impedance above the controllable bandwidth. One subset of electromechanical motors, series elastic actuators (SEAs) XPECTATIONS

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TBME-00027-2007.R1 [10], provides high fidelity force control within the controllable frequency bandwidth and low impedance above the controllable frequency bandwidth, due to a compliant spring that saturates the impedance of the system [8, 11]. Pratt et. al [12] and the authors [11] have demonstrated that an SEA can mimic the impedance range used by the human elbow. In addition, the authors have shown that, despite the addition of a long torsional spring, this technology may be used with an anthropomorphically appropriate size and weight [11]. This paper is divided into three studies, including technology modeling and validation (Sections II & III), preliminary investigation of foundational questions (Sections IV-VII), and subsequent testing of more impedance components in a more diverse experimental setup (Sections VIII-XI). The first study in this paper describes a compact SEA design used to implement user-modulated impedance control that may be practically implemented in prostheses using available technology. Towards this end a model of the design is presented and analyzed for stability within the range of desired impedance, and results from empirical testing of a physical prototype are presented to verify the actuator’s ability to modulate impedance. The second study in this paper addresses two questions related to user-modulated impedance control that must be answered before a robust analysis of the performance of impedance control may be undertaken. These two questions are: • What underlying motion paradigm should be used to implement impedance control? Specifically, should subjects directly control the position or velocity of the prosthetic elbow? • What default impedance should the prosthesis have? These questions are answered by a preliminary study involving four persons who used the physical prototype to complete an unconstrained, perturbed task under a variety of controller configurations. The third study in this paper uses the answers provided in the preliminary study to investigate more components of impedance using a larger sample population (n=15), while performing 2 tasks with and without the presence of an additional mental load II. CONTROL & MODELING A. Control Architecture Impedance control, as defined by Hogan [13], is a subset of position control. In impedance control, the user determines the desired position and the desired impedance, where the impedance is the relationship between position perturbations and resultant force. The desired position and impedance are fed to the controller, which calculates a torque based on the desired impedance and the difference between the actual position of the limb segment and the desired position. The actuator generates the calculated torque. The actual position of the limb segment is fed back to the controller. The generated torque is a function of the desired stiffness (K), viscosity (b) , and inertia (I):

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Tgen = K (θ − θ *) − bω − I α

(1)

where Tgen is the torque generated, θ is the actual position, θ* is the desired position, ω is the actual speed, and α is the actual acceleration. Using this paradigm, Popat et al. [14] have allowed the user to modulate a prosthetic elbow’s stiffness, but only for a small range of modulation (2-7 Nm/rad) and in a constrained state. In a constrained state, the endpoint of a single degree of freedom joint is fixed, whereas a system containing more than one degree of freedom is constrained to a particular path. In an unconstrained state the endpoint is free to move. It is considerably more difficult to implement impedance control in an unconstrained state than in a constrained state [11], and as a result, even high fidelity actuators can only achieve a position bandwidth of 3-4 Hz using unconstrained impedance control [8, 11, 12]. Humans track at a frequency of 1-2 Hz [15, 16], however, so a bandwidth of 3-4 Hz is sufficient for mimicking human joints. B. Plant Modeling Many controllers use internal current regulation to provide precise torques. In series elastic actuators, however, internal voltage regulation provides higher fidelity torque control than internal current regulation [12]. Internal voltage regulation enhances the precision of the motor’s movements. These precise movements are in turn converted into precise torques by the elastic element (F=kx). Using internal voltage regulation has large ramifications on the system dynamics. Previous models of series elastic actuators have either assumed torque regulation to simplify the model [17], or assumed a simplified motor model [18] in which those ramifications are not apparent. The authors have created a model that includes the electrical winding of the motor to preserve the dynamic effect of rotor inertia. The inertial portion of the rotor is a significant term when amplified by the high gear ratio. As a result, the model must include the resistance and inductance of the wire, along with the inertia and the viscosity of the rotor To preserve the effect of the rotor inertia on the dynamic response. Such a model is shown in Fig. 1 in bond graph form [19], which allows for the fact that each stage of the system is not necessarily a high impedance stage. The dynamic characterization is significantly different from that of a simplified model.

Fig. 1. Bond graph of series elastic actuator, controlled by internal voltage regulation. The motor wiring must be modeled To preserve the dynamic effect of the rotor inertia, because a voltage source is used to drive the motor The motor side of the gear box inertia has been lumped together with the rotor inertia.

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TBME-00027-2007.R1 To generate the motor’s input voltage (Vvoltage) shown in Fig. 1, rotary series elastic actuators sense the strain on the torsional spring and feed it back to a torque controller, as shown in Fig. 2. The lower stiffness of the torsional spring, compared to a stiff shaft, allows for a higher proportional gain (Ktorque), which increases the torque fidelity of the system. This desired torque may be determined by applying a desired impedance to the system. A decreased sampling time also allows for a higher proportional gain [20], but has no effect on the impedance above the controllable bandwidth .

3 It may be seen in Fig. 3 that the system is stable for the range of desired impedances (K=2-102 Nm/rad, b=0-10 Nm/(rad/sec), I=-0.08 - 0.08 kg m2). As expected, the system becomes underdamped as the stiffness increases (Fig. 3a), the viscosity decreases (Fig. 3b), or the inertia decreases (Fig. 3c). It should be noted that negative desired inertia in the controller is allowed. This decision was made based on literature regarding the IBM TrackPoint [22], which suggests that a negative inertia of the actuator, coupled with a positive inertia of muscle activation of the user, multiply together to create a system with little if any overall inertia. As this impedance controlled system remains stable for a negative desired inertial term, it seemed beneficial to explore the capability. III. PHYSICAL ACTUATOR

Fig. 2. Control system. The inner torque control loop senses the torque applied on the compliant torsional spring, and feeds the error between the desired and actual force into a proportional gain. The outer impedance loop creates an impedance for the actuator to mimic, consisting of stiffness K, viscosity b, and inertia I.

Due to the complexity of the modeled plant and control system, the transfer functions of control for this system are lengthy. Simplification does not adequately represent the dynamic response. As a result, it is more instructive to present a 2D projection of a 5-dimensional root locus [21] of the impedance terms, shown in Fig. 3. These overlaid figures provide a general feel for the impact that individual impedance variables have on the overall stability of the system.

Fig. 3. 2D projection of a 5D Root locus of impedance terms plotted using randomized values of stiffness K, viscosity b, and inertia I. Ktorque = 1. a) Red(K=100 Nm/rad), Green (K=2 Nm/rad) b) Red(b=0 Nm/(rad/sec)), Green (b=10 Nm/(rad/sec)) c) Red(I=-.08 kg m2) Green (I=.08 kg m2)

The authors designed and created an actuator, which contained a customized Emoteq1 HT02500 frameless brushless motor capable of producing 2.8 Nm stall torque and a 160:1 gear ratio Harmonic Drive LLC2 CSD 20 gear transmission. The motor was controlled by a Faulhaber3 BLD7010 servo amplifier capable of handling large currents, powered at 13.5 volts by an external power supply. A torsional spring with a stiffness of 327 Nm/rad was used to provide compliance. This design allowed the torsional spring to be passed back through the center of the actuator, due to the fact that a frameless motor and hollow gear transmission were used. This placement is illustrated in Fig. 4a-b. As a result, the actuator was compliant without being any larger than commercially available electric prosthetic elbows. The motor had both a rotor diameter and a rotor length of 25mm. The entire actuator had both a diameter and a length of 70mm. The prosthesis weighs 0.74 kg (1.6 lbs), similar to commercially available prosthetic elbows. It has a maximum full extension to full flexion speed of 2.5 rad/sec (140°/sec) and a calculated maximum torque in excess of 50 Nm (37 lb-ft). The speed is comparable to existing electric prostheses, and the torque is more than double that of the strongest commercially available prosthetic elbow. The torsional spring was instrumented with two Omega4 SG-4/350-TY31 rosette foil strain gauges with a 5-volt power supply to provide torque control. The strain gauges were configured in a Wheatstone bridge and fed through an instrumentation amplifier with a 1065 differential gain to use the full range of the data acquisition system. Position was measured using Hall effect sensors, which allow for discritization of 6 units per electrical commutation. 8 poles provided 4 electrical commutations per mechanical commutation, which coupled with a 160:1 gear ratio provided a digital encoder count of 3800 lines/revolution. Velocity was obtained by differentiating the position signal s    vel = 0.01s + 1 pos  and passing it through a 100 unit/sec   rate-limiter. Acceleration was likewise calculated by differentiating the non rate-limited velocity, and rate-limiting the acceleration at 100 units/sec.This method provides a clean and accurate signal at low speeds (such as those used with a prosthesis, which moves between 0 and 2.5 rad/sec).

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TBME-00027-2007.R1 Matlab’s5 Simulink XPc and Realtime toolboxes, coupled to a target computer with a hard sampling frequency of 10 kHz, were used to control the prosthetic elbow.

Fig. 4. SEA Prosthetic Elbow. a) Torsional spring passes back through the middle of the harmonic drive and frameless motor. b) CAD rendering of elbow c) Photograph of the elbow

The actuator accurately mimics various impedances at low frequencies, as illustrated by Fig. 5. The ability to mimic a stiffness (2Nm/rad) over two magnitudes of order removed from the actual stiffness of the system (327 Nm/rad) demonstrates the ability of series elastic actuators to provide high fidelity force control, and improves on the results of Pratt et. al [12], in which they successfully created a stiffness one order of magnitude less than the actual stiffness of their actuator. The actuator is not able to entirely mitigate the inherent effects of damping at that low stiffness level, but still provides effective impedance control.

Fig. 5. Empirical Test of Unconstrained Impedance Control. a) Commanded Stiffness = 100 Nm/rad. b) Commanded Stiffness = 2 Nm/rad. This stiffness is over 2 magnitudes of order smaller than the actual stiffness of 327 Nm/rad, yet the actuator still does a reasonable job of mimicking the low stiffness. It is not able to completely mitigate the inherent damping of the system at this low stiffness. Note axes are not the same in a and b.

IV. DECOUPLING CONFOUNDING VARIABLES The prosthetic elbow is capable of modulating impedance over the desired range of values. Two questions related to usermodulated impedance control must be answered prior to examining whether or not this capability is useful to subjects. These two questions are: what underlying motion paradigm should be used, and what should be the default impedance?

4 The remaining portion of this paper will address these questions. A. What motion paradigm should be used? In impedance control, two variables determine the output force generated by the actuator: the desired motion, and the desired impedance. Before analyzing desired impedance paradigms, it is necessary to select an underlying desired motion paradigm. Electromyographic (EMG) signals from a pair of angonist/antagonist muscles are often used clinically to control the motion of electric prostheses. EMG signals are created as a byproduct of muscle contraction and are broadly proportional to the amplitude of contraction [23]. The velocity of the joint has conventionally been proportional to the amplitude of the rectified, 3 Hz -3dB low-pass filtered EMG signals [24]. This relationship between speed and EMG signals is called proportional velocity control (PVC). A different motion control paradigm, proportional position control (PPC), sets the position of the joint proportional to the amplitude of the rectified, 3 Hz -3dB low-pass filtered EMG signals. PPC has been found to be better than PVC [25, 26] in pursuit tracking tasks, but these studies used force transducers as opposed to EMG signals as inputs. The high level of noise present in EMG signals may mitigate any inherent advantage in PPC. Popat et. al [14] used PVC for their conventional paradigm and PPC for their impedance modulation paradigm. Thus the effects of the impedance paradigm and motion paradigm were confounded. To decouple the motion paradigm from the impedance paradigm, each impedance paradigm used in this study was tested using both PVC and PPC to determine which motion paradigm is better for impedance control. B. Identifying default impedance Able bodied subjects typically have minimal stiffness in their elbow joint [5], most likely because it requires less energy expenditure than continuously cocontracting their muscles. Using computer based impedance control, however, the relaxed state of the subject may be set to an arbitrary impedance: either low if subjects prefer low impedance most of the time, or high if subjects prefer high levels of impedance most of the time. Although cocontracting muscles to lower stiffness does not mimic human physiology, it may provide better control with less energy expenditure than mimicking human physiology. Although exact values are not necessary for further experiments, an understanding of whether low or high impedances are preferred would aide future experiments. To answer this question, it is necessary to decouple the subject’s preferred cocontraction level from subject’s preferred impedance of the prosthesis. The stiffness and inertial component of independence were independently tested in this experiment while the other components of impedance remained fixed, in addition to an impedance paradigm in which all components of impedance remained fixed. Each of these impedance paradigms was tested for two cocontraction states to decouple these two variables. If the subject’s cocontraction level changes when the cocontraction state changes, then it may be inferred that the subjects were willing to change their cocontraction level to maintain a preferred

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impedance. If the cocontraction level does not change when the cocontraction state changes, it may be inferred that the subject is either incapable of changing their cocontraction state, or that the subject does not have a preferred impedance. V. EXPERIMENTAL APPARATUS The protocol was approved by the Northwestern University Institutional Review Board, and all patients signed informed consent forms. Four able bodied subjects (mean age 28 +/- 3 years) including two males and two females were enrolled in this preliminary study. Subjects remotely controlled the prosthesis by tensing a pair of agonist and antagonist muscles. Individual components of impedance, including stiffness and inertia, were individually set proportional to the cocontraction of the subject, while the other impedance components remained constant. The amount one muscle was contracted more than the other was set proportional to motion. Otto Bock6 13E200 electromyography (EMG) sensors were used to record EMG signals. For the remainder of the paper, these will be referred to simply as electrodes, although it is important to note that they contain both a pair of electrodes and an amplification and processing circuit. Otto Bock’s 13E200 electrodes use a 100400 Hz bandpass filter and a 60 Hz notch filter. The resulting signal is rectified and low-pass filtered. The electrodes were located on the lateral head of the triceps brachii and the long head of the biceps brachii, over the center of the muscle belly. Subjects wore an elbow orthosis to maintain 90 degrees of elbow flexion, and held onto a fixed pole to allow for the use of isometric contractions. Subject’s EMG signals were used to calibrate eight thresholds, shown in Fig. 6. The first four thresholds involved the maximum and minimum levels of the agonist and antagonist muscles. The final four thresholds involved the maximum and minimum values of the motion signal and impedance signal. The voltages corresponding to minimum and maximum muscle contraction were proportionally scaled to 0-1 for both muscles. The scaled muscle signals were then sent to the motion and impedance blocks, where the maximum and minimum motion and impedance were each proportionally scaled to 0-1. Subjects were asked to exert moderate contractions with each muscle to calibrate the maximum setting of each muscle, To avoid fatigue. To determine the minimum thresholds for each muscle, subjects were asked to alternate between a moderate contraction of one muscle and a moderate contraction of the other muscle. The level they contracted the relaxed muscle was set as the minimum threshold, so that impedance wouldn’t be activated by involuntary antagonist muscle contraction.

Fig. 6. Calibrating Signal thresholds. Maximum and Minimum thresholds were set for each muscle. These thresholds were scaled to 0-1, and then fed into Impedance and speed blocks, where maximum and minimum thresholds were again calibrated. These thresholds were likewise scaled to 0-1.

To ensure that the thresholds were correctly set, subjects were asked to track a moving target on a computer screen while exerting three levels of cocontraction: minimum, medium, and maximum. In addition, subjects were asked to cocontract at two different levels shown on the screen. The maximum impedance threshold was adjusted to allow subjects to accurately but easily control their impedance value without affecting their performance. Impedance maximum thresholds ranged from 20 to 40% of the maximum cocontraction range. The maximum velocity threshold was set to 80% of the maximum velocity signal, allowing subjects to obtain maximum cocontraction at maximum velocity. The minimum velocity threshold was set to 0. To decouple the motion paradigm from the impedance paradigm, each impedance paradigm was tested using both PVC and PPC to determine which motion paradigm is better for impedance control. For PVC, the desired velocity was set proportional to the EMG signals. This velocity signal was then integrated to obtain the desired position necessary to implement impedance control. Integration served the added function of inherently low-pass filtering the signal, such that no additional filtering was required. For PPC, a position range double that of the range of the elbow was set proportional to the range of the EMG signals. This position signal was then rate limited to 0.6 rad/sec to ensure stability. Rate limiting provided more responsive control than implementing a low pass filter. Without rate limiting, the elbow could not be accurately controlled using proportional position control, due to the high noise levels inherent in the EMG signals. Each impedance paradigm was tested for two cocontraction states. In the first cocontraction state, the default impedance corresponded to low impedance, with cocontraction raising the impedance. In the second cocontraction state, the default impedance corresponded to high impedance, with cocontraction lowering the impedance.

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TBME-00027-2007.R1 The task was designed to mimic real life situations, in which the majority of tasks are unconstrained, but where perturbations may be encountered. Subjects remotely controlled the prosthetic elbow while trying to position its endpoint on stationary projected targets, as shown in Fig. 7. Subjects were asked to arrive at the targets as accurately and quickly as possible. A compliant perturbation in the middle of the target space impeded movement. The experimental apparatus is shown in Fig. 7.

6 paradigms and both cocontraction states, as illustrated in Table 1. Subjects were blinded to all paradigm variations. Table 1 Combinations of Motion, Impedance, and Physiology Paradigms tested

PPC = proportional position control PPV = proportional velocity control F = Fixed Impedance S = Stiffness modulation I = Inertia modulation L = Default Low impedance H = Default High impedance

VI. RESULTS

Fig. 7. a) Experimental Apparatus. A projector projects targets onto the display board. The compact SEA elbow is mounted to the display board, and remotely controlled by the subject’s EMG signals. A fixed compliant perturbation impedes movement. Subjects are fitted in an orthosis and grasp a weighted pole to exert isometric contractions. The position of the target changes with each trial. b) A picture showing the actual setup c) Schematic of the compliant perturbation, including an inertial mass and spring, that may be randomly retracted by a linear actuator.

The computer displayed a new target at a different location when the subject’s velocity reversed direction or stopped near the target. The computer also recorded the time taken to arrive from the previous target, the angular error between desired and actual endpoint position (based on where the subject stopped or reversed direction), and the average impedance throughout the entire movement. Average angular velocity was calculated based on the time required to reach the target and the actual distance covered. Subjects were given a practice run for each motion paradigm. Subjects completed the task for 50 targets for each combination of paradigms. Only the last 40 targets were analyzed for each trial. Subjects were encouraged to try to modulate their cocontraction level during the first 10 targets to see if it helped or hurt their performance. Subjects were independently tested for stiffness modulation and inertia modulation, as well as a control paradigm in which the impedance was fixed regardless of cocontraction levels. These impedance paradigms were tested using both motion

A. Performance of Underlying Motion Paradigm Speed, endpoint error, and cocontraction levels are compared between proportional position control (PPC) and proportional velocity control (PVC) in Fig. 8. There is a significant increase in speed using PVC (p0.19). The addition of the mental load task decreased mean speed across paradigms from 0.74 rad/sec to 0.69 rad/sec (p=.04)), but had no statistically significant effect on error (p=0.28). With the additional mental load task, the spread of cocontraction levels for a given trial of a given subject increased dramatically. As a result, any statistical comparisons had p values of around 0.9, since the cocontraction levels effectively became white noise. As a result, only the results for the no-mental load condition are presented below, since the addition of a mental load effectively prevented subjects from having any control over their cocontraction levels.

Fig. 13. Impedance Modulation, compared by paradigm. p = 0.27 for pointing task and 0.50 for tracking task. Subjects did not have a consensus for the optimal impedance

A significant difference in the cocontraction levels between the two tasks is expected if subjects modulate impedance levels based on the particular task. The difference between the median cocontraction levels of both tasks for each impedance paradigm is shown in Fig. 14. There was no statistical significance between the tasks using a paired student’s t-test, except for the negative inertia modulation paradigm (p=0.01), in which subjects cocontracted more during the tracking task than during the pointing task.

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Fig. 14. Impedance Modulation, compared by task. There was no difference in the level of impedance modulation between the two tasks, except for negative inertia modulation, in which subjects cocontracted more in the tracking task, providing more negative inertia.

Cocontraction levels were also analyzed within three movement regions for each movement: movement initiation, free swing, and termination, as illustrated in Fig. 15. Subjects cocontracted more at movement initiation (0.182) and termination (0.210) than during free swing (0.088), regardless of paradigm (p=0.011), even when cocontraction had no influence on motion control.

Fig. 16. Impedance paradigm effect on performance.

The cocontraction level corresponding to the optimum performance (minum error, maximum speed) is shown in Fig. 17. Linear regressions were done between optimum performance and the cocontraction level corresponding to it across subjects. There was no significant correlation between cocontraction levels and performance, except for the error of the Fixed Impedance paradigm (Error ~ .05* Cocontraction) and the speed of positive inertia (Speed ~ 0.91* Cocontraction).

Fig. 15. Average impedance was recorded for three movement regions: Movement initiation, free swing, and movement termination. Subjects cocontracted more during the start and stop of each movement than in the middle, regardless of the impedance paradigm.

B. Performance From the results of section IX.A, it may be inferred that subjects did not actively modulate their impedance to improve their performance. The level that they did modulate their impedance, however, may have had an effect on their performance. As a result, median performance metrics were compared across impedance paradigms to see if subjects performed better using a particular impedance paradigm. A linear regression was also done between optimum performance metrics and their corresponding cocontraction levels for each paradigm, to see if impedance values affected performance. Median performance metrics are shown in Fig. 16. There was a significant difference between the paradigms for both error (p=