Control and Intelligent Systems, Vol. 39, No. 4, 2011
A NOVEL APPROACH TO PATH PLANNING FOR AUTONOMOUS MOBILE ROBOTS Yun-Qian Miao,∗ Alaa M. Khamis,∗∗ Fakhri Karray,∗ and Mohamed S. Kamel∗
Abstract
objective. Beside this, the necessity of considering collisions avoidance and path smoothness makes the problem becoming more challenging. Different conventional approaches have been developed to solve the path planning problem [4], such as A* [5], [6], the Rapidly Exploring Random Trees (RRT) [7], and the Distance Transform approach [8]. These conventional approaches are grid-based and usually computationally expensive especially in case of high resolution. When lowering problem space’s resolution, their precision is degraded. Other algorithms such as potential field (PF) approach and probabilistic roadmap methods [9] have been proposed to deliver more faster and practical solutions to this problem, and to generalize it as possible for any robot with many degrees of freedom. The PF method [10] is based on gradient of PF that is built through a fitness function of considering both traveling cost and obstacles avoidance. The performance of PF method is largely associated with the initial setup, and may easily be trapped at local minima. Genetic algorithm (GA) has been recognized as one of robust searching techniques for complex optimization problems [11–13]. There are several reports of applying GA to solve the path planning problem [14–18]. The most challenging problems of these GA approaches include needing domain specific operators (such as shortcutting and smoothening for local disturbance), which add extra computational load and can only achieve near optimal solutions. This paper examines the strengths and constraints of PF and GA algorithm, and proposes a hybrid approach that combines both algorithms to solve the path planning problem. In this novel integrated framework, the PF method is used to exploit local optimal solutions and the GA is designed to explore the whole problem space. Different implementation strategies are examined and analysed through simulations at different complexity environments. It is demonstrated that the combining approach can effectively achieve global optimal in various situations when properly implemented. The rest of this paper is organized as follows. Section 2 introduces theoretical background on potential field method and genetic algorithm for path planning. Section 3 describes the details of the proposed hybrid approach. Section 4 presents our experimental setup, simulation results,
Path planning is considered as one of the core problems of autonomous mobile robots. Different approaches have been proposed with different levels of complexity, accuracy, and applicability. This paper presents a hybrid approach to the problem of path planning that can be used to find global optimal collision-free paths. This approach relies on combining potential field (PF) method and genetic algorithm (GA) which takes the strengths of both and overcomes their inherent limitations. In this integrated frame, the PF method is designed as a gradient-based searching strategy to exploit local optimal, and the GA is used to explore over the whole problem space. In this work, different implementing strategies are examined in different complexity scenarios. The conducted experiments show that global optimal paths can be achieved effectively using the proposed approach with a strategy of high diversity and memorization.
Key Words Mobile robotics, path planning, potential field, genetic algorithm
1. Introduction Autonomous mobile robot path planning is an interesting problem that has been studied extensively over the last two decades. This problem addresses how to find a collision-free path for a mobile robot from a start position to a given goal position, amidst a collection of obstacles. Efficient algorithms for solving problems of this type have important applications in areas such as mobile robotics, intelligent transportation, computer animation, drug design, and automated surveillance [1]. Path planning can be seen as an optimization problem which aims at improving some system objectives with several constraints [2], [3]. System objectives may be the traveling distance, traveling time, and consuming energy. However, the traveling distance is the most common ∗
Pattern Analysis and Machine Intelligence (PAMI) Research Group, Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada; e-mail: {mikem,karray,mkamel}@pami.uwaterloo.ca ∗∗ Faculty of Petroleum and Mining Engineering, Suez Canal University, Egypt; e-mail:
[email protected] Recommended by Prof. Fakhri Karray (DOI: 10.2316/Journal.201.2011.4.201-2312)
235
• Oscillations in the presence of obstacles. • Oscillations in narrow passages. The most significant problem of PF method is the problem of trapping in local minima. There are some recovery methods for remedying the trap situation to find feasible solution, such as the randomized PF approach [4], which uses random walks to attempt to escape trapping of local minima. However, in most cases this approach is likely to result in non-optimal solutions [21], [22]. Thus, more intelligent heuristics are worthy to be studied to explore the problem space and guide the selection of initial routines of the PF methods.
and analysis. Finally, conclusions and future directions are summarized in Section 5. 2. Background 2.1 Potential Field (PF) PF methods are rapidly gaining popularity in obstacle avoidance applications for mobile robots and manipulators. The idea of virtually forces acting on a robot has been suggested by Andrews and Hogan [19] and Khatib [10]. In these approaches obstacles exert repulsive forces onto the robot, while the target applies an attractive force to the robot. The sum of all forces determines the subsequent direction and speed of travel. One of the reasons for the popularity of this method is its simplicity and elegance. Simple PF methods can be implemented quickly and initially provide acceptable results without requiring many refinements. Krogh and Thorpe [20] had applied the PF method to off-line path planning.
2.2 Genetic Algorithm (GA) GA has been recognized as a robust searching algorithm to optimize complex problem with the concept of evolution strategy. To use GA for solving the path planning problem, there are three steps to consider: • Representing the problem and generating the initial population. • Genetic operators for reproduction. • Domain specific operators for considering constraints such as obstacles avoidance and path smoothness.
2.1.1 Problem Formulation The problem of collision-free path planning may be treated as an optimization problem with two objectives. One objective is avoiding collision with obstacles. Another objective is to minimize the traveling distance. To integrate these two factors, we can formalize a path’s fitness function that is comprised of two parts, energy function of distance and obstacles penalty function, respectively, as: F (P ath) = ωl El + ωo Eo
2.2.1 Representation and Initial Population Initialization: Create an initial population with a predefined population size. The population contains number of individuals (i.e., chromosomes). Each individual represents a solution for the problem under study. In our case, each solution is in fact a path between the start and end point in the search space. The initial population with size N can be presented as:
(1)
where El represents energy function of path distance, Eo represents collision penalty function, ωl and ωo are weights of the two parts. The path planning problem is formalized as to minimize the path’s fitness based on (1). It means that the optimal solution should avoid collision with obstacles and keep the traveling distance as short as possible at the same time.
Initial Population =< S1 , S2 , . . . , SN >
(2)
Each structure Si is simply a float string of length M , in general. This structure represents a vector of node numbers in the space which contains “x” and “y” coordinates of a point in the search space. Normally, GA individuals can contain any point value between the starting and ending point. Thus, the individual generated by GAs is in the form of:
2.1.2 Demos Figure 1 demonstrates the process by using the PF method to optimize paths to get collision-free solutions. As we can observe from Fig. 1(a) and (b), the PF method will produce different solution paths when starting at different initial routines. The choice of initial settings is beyond the classical PF methods, and the most heuristic best-first try is the straight line that connects the start position and the goal position. However, this best-first search may easily become struck because of local minima trapping [9], [21].
Si =
(3)
where M is the number of visited node in the search space. To include the starting and ending point, we need to make some modification to the individual structure so that we can add the starting point as the first point, Pi1 , and ending point as the last point, PiM . Fitness function: Fitness function represents an important part of any evolutionary process using GA. Appropriate selection of the fitness function will lead the search towards the optimal solution. The optimal path, in our case, is the shortest collisionfree path between the starting and ending point. Thus, the fitness function is responsible for finding this path.
2.1.3 Limitations of PF Methods From observation of our experiments and also revealing by Koren’s research [21], the PF method has the following inherent limitations as: • Trap situations due to local minima. • No passage between closely spaced obstacles. 236
Figure 1. Collision-free path planning using PF method, (a) and (b) show the different resulting paths with different initials. Equation (5) results in that the shorter the path is, the higher possibility it is selected.
Consequently, the fitness value for a complete solution Si will be computed as: F itness(Si ) = Li =
M −1
ds
Crossover: This operator combines two selected paths (parents) to generate two offspring’s as follows: a random mating position node is selected on each parent. Then, this node splits the path into two sections. The first offspring is generated by combining the first fraction of the first parent with the second fraction of the second parent. And, the second offspring is generated by combining the first fraction of the second parent with the second part of the first parent. Figure 2 illustrates the crossover operation.
(4)
s=1
where ds is the Euclidean distance between points Pis and Pi(s+1) , i.e. ds = ||Pis − Pi(s+1) ||. 2.2.2 Genetic Operators Selection: The selection procedure is applied to choose the individuals that participate in the reproduction process to give birth to the next generation. To make the whole population evolution towards good solutions, selection is executed probabilistically based on its fitness function, which is the probability of being chosen: F itness(Si ) P rob(Si ) = 1 − N j=1 F itness(Sj )
Mutation: This operator changes the node’s coordinates of the selected path, except the start point and end point keep unaffected. The mutation happens at given level of possibility with a predefined range. Immigration: In case of further increasing population diversity, immigration operator is introduced, which creates
(5) 237
Figure 4. Smooth operator. segment such that makes the path with smooth segments connections, as illustrated in Fig. 4.
Figure 2. Crossover operator.
3. Hybrid Approach The PF method has advantages of finding a collision-free smooth solution effectively, but with a main drawback of easy trapping in local minima. The GA algorithm with a proper strategy can explore complex problem space to search for global optimal, but in most case, the solution is only near best. Furthermore, when applying pure GA algorithm to the problem of path planning, some extra domain specific operators are needed such as repair, shortcut, and smooth, as described in the previous section. These operations will degrade the usability of GA because of their extra computational burden. In this section, a combining PF+GA approach for path planning is described, which takes the advantages of both methods and makes up the shortages of them.
Figure 3. Shortcut operator.
some random individuals and injects them into the next generation directly during the evolution progress.
3.1 Structure of PF+GA Path Planner
Memory: This operator stores the best solution from the population of present generation, and clones it directly to the next generation. This operation is used to keep the evolution consistently converging towards the direction of better fitness, and avoid interference that comes from crossover and mutation.
The structure of PF+GA combining approach is described in Algorithm 1. The algorithm is terminated when a predefined number of generations is reached, or the results converge to a predefined level. Algorithm 1. PF + GA algorithm for path planning 1. Initialize the environment (setup parameters, obstacles representation, start point, goal point). 2. Initialize the first generation by randomly generating paths as individuals. 3. Applying PF method to each individual to make each becoming a collision-free local optimal solution. 4. Loop until termination condition reached: a. evaluate the fitness of each solution, b. applying GA operators: Selection, Mutation, Crossover, Immigration, Memory, c. next generation produced, d. applying PF method to individuals of new generation.
2.2.3 Domain Specific Operators Repair: This operation executes when infeasible path detected, which refers that there exists a segment of the planned path going across an obstacle. In [16], the repair operator is to generate a set of random points around the intersecting obstacle and connects these points to pull the segment around the obstacle. Shortcut: This operator removes the intermediate points between two points if the direct connection line is collisionfree, as illustrated in Fig. 3. Smooth: This operator is applied to a path with two connected segments with sharp turn around, which is not executable for actual mobile robots. The connection node is removed and replaced with two new nodes on each
5. Loop end. 6. Output the solution. 238
3.2 Implementing Strategies
Table 1 Implementing Strategies and Their Parameters
3.2.1 Diversity Methods
Strategy Description
While selection is an operator to lead the population converge to better fitness, diversity operations are intend to explore the problem space. Crossover, mutation, and immigration operators and their different combinations are candidates for increasing diversity. Obviously, low level of diversity will make GA easily being trapped at a region, and GA is showing converging quickly to some sub-optimal prematurely. Among these diversity operations, mutation is used to search locally. Because the proposed approach combining PF method for digging locally using gradient-based method, the functionality of mutation is then duplicated and can be taken out from GA operation’s pool, which reduces algorithm’s computation cost. The later experimental results also prove the idea of unnecessary mutation operation in this hybrid approach. 3.2.2 Memory Strategy On one hand, we need diversity for broad exploring. On the other hand, high level of diversity will lead the population oscillating and good solutions are easy to be disturbed by diversity interference. In [15] and [16], authors introduced the concept of memory operator to GA, which memorizes the best solution so far and clones it directly to the next generation. So, applying memory strategy can effectively avoid good solutions being disturbed by the diversity operations of GA. Therefore, the memory strategy is adopted in our combining PF+GA approach to keep the evolution progress stable.
Parameters
A0
Low diversity, Cross_Rate = 0.1 no memory Mutation_Rate = 0.1 Immigrate_Rate = 0.0 Memory = 0
A1
Low diversity, Cross_Rate = 0.1 has memory Mutation_Rate = 0.1 Immigrate_Rate = 0.0 Memory = 1
A2
High diversity, Cross_Rate = 0.2 no memory Mutation_Rate = 0.2 Immigrate_Rate = 0.2 Memory = 0
A3
High diversity, Cross_Rate = 0.2 has memory, Mutation_Rate = 0 no mutation Immigrate_Rate = 0.2 Memory = 1
A4
High diversity, Cross_Rate = 0.2 has memory, Mutation_Rate = 0.2 has mutation Immigrate_Rate = 0.2; Memory = 1
4.2 Experimental Results 4.2.1 Simple Scenario In the simple scenario, there are three obstacles in a 2-D environment as shown in Fig. 5. When using low diversity strategy (A0, see Table 1), Fig. 5 demonstrates the situation of prematurely converging to a sub-optimal solution. On the other hand, Fig. 6 demonstrates the situation of achieving global optimal solution in the case of using high diversity with memory strategy (A4). As shown in Table 1, A0 (Low diversity, without memory) and A4 (High diversity, with memory, with mutation) represent the two extremes of the implementation strategies. Furthermore, to investigate the effect of “memory” strategy, Fig. 7 gives us an inside look about the fitness evolving process as evolution progress by comparing strategy A0 and A1, which the only difference is “no memory” and “has memory”. It can be observed that the fitness of population is oscillating for “no memory” strategy, and the fitness of population decreases monotonically for “has memory” strategy. This can be justified that the memory strategy is effective to avoid evolution disturbance caused by diversity.
3.2.3 Strategies Composition The performance of GA algorithm is affected by different level of each operator and different kind of combination of these operators. When using in PF+GA approach, the implementing strategies become more complex and their related performance will be studied by experiments in the next section. 4. Experimental Results 4.1 Experimental Setup The experiments were conducted in 2-D environments with different number of obstacles of different sizes. For each experimental setting, the results are collected by 5 runs to avoid randomness. Both the average and standard deviation are reported accordingly. The composition strategies of implementation to be examined are listed in Table 1.
4.2.2 Complex Scenario In the complex scenario, there are 10 obstacles in a 2-D environment, as shown in Fig. 8. 239
Figure 5. In the simple scenario, an example shows the situation of prematurely converging to sub-optimal path due to low diversity (A0).
Figure 6. In the simple scenario, an example demonstrates the situation of achieving global optimal solution through PF+GA approach with high diversity and memory strategy (A4). 4.2.3 Performance Comparison of Different Strategies
Figure 8 illustrates the situation of prematurely converging to sub-optimal solution in the case of using low diversity approach (A0, see Table 1). On the contrary, Fig. 9 demonstrates the situation of achieving global optimal solution in the case of using high diversity with memory approach (A4, see Table 1).
The performance evaluation for each implementation strategy is determined by the best solution (the shortest path) of the final population. Table 2 reports the average and standard deviation according to 5 runs of each settlement. Results in Table 2 clearly indicates that strategies without memory operator perform worst (A0 and A2), while strategies with high diversity and with memory perform best (A3 and A4). Comparing A3 and A4 (“no mutation” and “has mutation”), there is no distinguishable performance gap. Furthermore, when no mutation injected, the results are showing more consistent (the standard deviation is smaller).
Comparing strategy of “no memory” and “has memory”, the dynamic feature of solution’s convergence along the evolution progress in the complex scenario is shown in Fig. 10. Similar to the simple scenario, the fitness of population suffers from oscillation for “no memory” strategy, and this fitness decreases monotonically for “has memory” strategy. 240
Figure 7. Comparison of convergence property along the evolution progress in simple scenario (A0 vs. A1).
Figure 8. In the complex scenario, an example shows the situation of prematurely converging to sub-optimal path due to low diversity (A0).
Figure 9. In the complex scenario, an example demonstrates the situation of achieving global optimal solution through PF+GA approach with high diversity and memory strategy (A4). 241
Figure 10. Convergence property along the evolution progress in complex scenario (A0 vs. A1). Table 2 Performance Comparison of Different Implementing Strategies Strategy
Simple Scenario
Complex Scenario
Average of Best Standard Deviation Average of Best Standard Deviation A0
121.92
±0.95
131.42
±4.43
A1
119.54
±0.74
122.12
±0.70
A2
123.25
±4.42
124.93
±2.78
A3
119.03
±0.13
122.14
±0.69
A4
119.08
±0.35
120.51
±1.86
lution through evolution strategy. But, when applying pure GA to the path planning problem, the individuals of populations are in most probably infeasible, especially in complex scenarios with high number of obstacles. To overcome this challenge, some specific domain operators can give a hand with extra computation load. And the final solutions are only near optimal. The proposed hybrid approach is showing effective and global optimal to accomplish path planning with benefits that come from both PF and GA. Even so, for the specific problem of path planning, different implementation strategy affects the algorithm’s performance a lot. The interesting findings are: • In general, high diversity with memory strategy performs better than any other combinations. • Diversity plays a key role for exploring problem space to avoid prematurely converging to sub-optimal solution. The diversity of population can be achieved by the operations of crossover and immigration. • Mutation operator is a common strategy in GAs for increasing searching diversity. However, the mutation operator has no contribution in this case, because the PF method executes local optimal searching and replaces the functionality of the mutation operator.
5. Discussion The PF method is a gradient-based approach that demonstrates ability to find a local optimal path and avoid obstacles in a harmony way. The solution path of PF method is heuristically smooth and suitable for mobile robot navigation. However, the result of PF-based path planning is largely decided by its initialization, and is lack of ability to find global optimal solutions. Different meta-heuristic optimization [22], [23], fuzzy [24], and neural network [25] techniques have been used to improve the performance of PF-based path planning. Most of these methods focus on solving the local minima problem associated with PF or generating a smoother path. For example, Zhu et al. [22] suggested the use of simulated annealing as a trajectory-based meta-heuristic optimization method to get out of the local minima and continue moving towards the goal. The simulated annealing search is invoked when the local search algorithm gets stuck at a local minimum. Vadakkepat et al. [23] proposed an evolutionary artificial PF method by combing PF with GA to derive optimal PF functions. GA as a population-based meta-heuristic optimization method owns the ability of searching global optimal so242
• Memory is another important operator in this problem, which colons the best solution so far to the next generation directly. It keeps the fitness of each generation decreasing monotonically. On the contrary, the solutions generated through “no memory” lead to oscillate along evolution progress because of possible interference by crossover.
[12] Fakhreddine O. Karray and Clarence W. De Silva, Soft computing and intelligent systems design: theory, tools, and applications (Boston, USA: Pearson/Addison Wesley, 2004). [13] C. Hsu and C. Yu, Robust control of interval plants using genetic algorithms, Control and Intelligent Systems, 35(2), 2007, 140–148. [14] M. Gerke, Genetic path planning for mobile robots, Proc. of the American Control Conf. 4, 1999, 2424–2429. [15] K. Trojanowski, Z. Michalewicz, and J. Xiao, Adding memory to the evolutionary planner/navigator, Proc. of the 4th IEEE ICEC, 1997, 483–487.
6. Conclusion
[16] A. Elshamli, H.A. Abdullah, and S. Areibi, Genetic algorithm for dynamic path planning, Proc. of Canadian Conf. Elect. and Comput. Eng., Niagara Falls, 2, May 2–5, 2004, 677–680.
This paper proposed a hybrid approach to autonomous mobile robots path planning problem combining PF methods and GA algorithms. This approach takes the advantages of PF and GA methods and overcomes their inherent limitations. By studying different implementation strategies, it was revealed that the PF+GA combining framework with high diversity and memorization strategy is effective to find global optimal solutions. In the future, we plan to extend this work to dynamic environments with moving obstacles and goal positions.
[17] Ismail AL-Taharwa, Alaa Sheta, and Mohammed Al-Weshah, A mobile robot path planning using genetic algorithm in static environment, Journal of Computer Science, 4(4), 2008, 341– 344. [18] D. Vrajitoru, P. Konnanur, and R. Mehler, Genetic algorithms for a single-track vehicle autonomous pilot, Control and Intelligent Systems, 36(1), 2008, 47–56. [19] J.R. Andrews and N. Hogan, Impedance control as a framework for implementing obstacle avoidance in a manipulator, in D.E. Hardt and W. Book (Eds.) Control of manufacturing processes and robotic systems, (Boston: ASME, 1983), 243–251.
Acknowledgments
[20] B.H. Krogh and C.E. Thorpe, Integrated path planning and dynamic steering control for autonomous vehicles, Proc. of the 1986 IEEE Int. Conf. on Robotics and Automation, San Francisco, California, April 7–10, 1986, 1664–1669.
This work has been supported through the Collaborative Research and Development (CRD) project “DIScrimination of Critical Objects and EVents in PErvasive Multimodal SuRveillance Systems (DISCOVER)” funded by Natural Sciences and Engineering Research Council of Canada (NSERC) and Thales Canada Inc.
[21] Y. Koren and J. Borenstein, Potential field methods and their inherent limitations for mobile robot navigation, Proc. of the IEEE Int. Conf. on Robotics and Automation, 2, 1991, 1398– 1404. [22] Q. Zhu, Y. Yan, and Z. Xing, Robot path planning based on artificial potential field approach with simulated annealing, Proc. of the Sixth Int. Conf. on Intelligent Systems Design and Applications (ISDA’06), Jinan, China, October 16–18, 2006.
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Biographies Yun-Qian Miao received the B.Eng. (Southwest Jiaotong University, Chengdu, China) and M.ASc. (University of Waterloo, Waterloo, Canada) degrees both in Computer Engineering. Currently, he is working toward the Ph.D. degree at the Department of Electrical and Computer Engineering, University of Waterloo. Since September 2008, he has been a research assistant at the Pattern Analysis and Machine Intelligence Laboratory at University of Waterloo. His research interests include autonomous and intelligent system, machine learning, and related applications. 243
Alaa M. Khamis received the B.Sc. degree with “Distinction with Honor’s Degree” in Electrical Engineering from Alexandria University, Egypt, in 1993, the M.Sc. degree in Electrical Engineering from Suez Canal University, Egypt in 1998, and the Ph.D. degree in Systems Engineering from Carlos III University of Madrid in 2003. In 2001, he was selected as distinguished scholar in the DAAD-Programme “International Quality Network” (IQN) to share in research projects related to remotely controlled experiments at Faculty of Applied Science, FH Ravensburg-Weingarten, Germany. During the academic year 2003–2004, he worked as a postdoctoral fellow in the RoboticsLab, Department of Systems Engineering and Automation, Carlos III University of Madrid, Spain. During the academic year 2004–2005, he was postdoctoral fellow and coordinator of Autonomous Systems and Real Time Distributed Design (ASRTDD) Focus Group, Pattern Analysis and Machine Intelligence Lab (PAMI), Department of Electrical and Computer Engineering, University of Waterloo, Canada. During the academic year 2005–2006, he was a visiting professor in Department of Systems Engineering and Automation, Carlos III University of Madrid, Spain. From 2006 to 2008 he was an assistant professor at Suez Canal University and German University in Cairo (GUC), Egypt. From 2008 to 2010 he was a research assistant professor at University of Waterloo, Canada. He is currently working as assistant professor at Suez Canal University and in the Mechatronics Engineering Department at German University in Cairo. His research interests include sensor and actor networks, distributed surveillance and monitoring, swarm robotics, multiagent systems, cooperative intelligent systems, and human–robot interaction. He published a book, three book chapters, three technical reports, and more than 45 papers in refereed journals and international conferences. He is a senior member in the IEEE, an associate editor for the International Journal of Robotics and Automation and founding program chair of International Conference on Autonomous and Intelligent Systems (AIS).
is the co-author of a textbook on Soft Computing and Intelligent Systems Design (Addison Wesley, 2004). He serves as associate editor for the IEEE Transactions an Mechatronics, the IEEE Transactions Systems Man and Cybernetics – Part B, the IEEE Computational Intelligence Magazine, the International Journal of Robotics and Automation, the International Journal of Control and Intelligent Systems, and the International Journal of Image Processing. He has served as Chair/Co-chair of more than 12 international conferences and technical programs, was the General Co-chair of the IEEE Conference on Logistics and Automation, China, in 2008 and the General Co-chair of the International Conference on Systems, Circuits and Signals, Tunisia, 2009. He is the local Waterloo Chapter Chair of the IEEE Control Systems Society, and the IEEE Computational Intelligence Society, respectively. Mohamed S. Kamel received the B.Sc. (Hons) degree in Electrical Engineering from the University of Alexandria, Egypt, M.Sc. degree in Computation from McMaster University, Hamilton, Canada, and Ph.D. degree in Computer Science from the University of Toronto, Canada. He joined the University of Waterloo, Canada in 1985 where he is at present professor and director of the Pattern Analysis and Machine Intelligence Laboratory at the Department of Electrical and Computer Engineering. He currently holds University Research Chair and held Canada Research Chair in Cooperative Intelligent Systems (2001–2008). His research interests are in Computational Intelligence, Pattern Recognition, Machine Learning and Cooperative Intelligent Systems. He has authored and co-authored over 400 papers in journals and conference proceedings, 11 edited volumes, 2 patents, and numerous technical and industrial project reports. Under his supervision, 84 Ph.D. and M.A.SC. students have completed their degrees. He is the editor-in-chief of the International Journal of Robotics and Automation, associate editor of the IEEE SMC, Part A, Pattern Recognition, Pattern Recognition Letters, Computational Intelligence, and Cognitive Neurodynamics journal. He is also member of the editorial advisory board of the International Journal of Image and Graphics and the Intelligent Automation and Soft Computing journal. He is member of ACM, PEO, Fellow of IEEE, Fellow of the Engineering Institute of Canada (EIC), Fellow of the Canadian Academy of Engineering (CAE), and Fellow of the International Association of Pattern Recognition (IAPR). He is co-founder of Virtek Vision Inc. of Waterloo (now part of Gerber Technology Co.). He served as member of the board from 1992 to 2008 and VP research and development from 1987 to 1992.
Fakhri Karray received his Ing. Dipl. degree in Electrical Engineering from the University of Tunis, Tunisia in 1984, and his Ph.D. degree from the University of Illinois, Urbana-Champaign, in 1989. He is a professor of electrical and computer engineering with the University of Waterloo, Waterloo, ON, Canada, and the associate director of the Pattern Analysis and Machine Intelligence Laboratory. His research interests are autonomous systems and intelligent man–machine interfacing, on which he has extensively authored. He is the holder of 13 US patents in the areas of Mechatronics and Intelligent Systems. He 244
