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Proceedings of ASME-IMECE 2006: 2006 ASME International Mechanical Engineering Conference and Exposition November 5-10 2006, Chicago, Illinois, USA

IMECE2006-13435 COOPERATIVE CONTROL OF AUTONOMOUS MOBILE ROBOTS IN UNKNOWN TERRAIN Laura E. Ray, Devin Brande, John Murphy, James Joslin Thayer School of Engineering Dartmouth College

ABSTRACT This paper presents a distributed control framework for groups of wheeled mobile robots with significant (nonnegligible) vehicle dynamics driving on terrain with variable performance characteristics. A dynamic model of a high-speed robot is developed with attention to representation of wheelterrain performance characteristics. Using this model, aspects of distributed, cooperative control on unknown terrain are investigated. A potential function path planning and cooperative control algorithm is combined with a local slip controller on each robot to provide high-speed control of vehicle formation. Local slip control is shown to reduce sensitivity of the distributed path planning and control method to tire-terrain performance variation and its resulting effect on dynamic behavior of the robots. Computationally efficient methods for real-time assessment of force-slip characteristics are presented to provide slip setpoints for this control architecture. INTRODUCTION The problem of cooperative control of multi-robot systems has resulted in a multitude of control schemes to produce various behaviors. In general, control laws and strategies have been developed using point-mass vehicles, or vehicles operating at speeds in which a point-mass or linear model holds. The exception to this is the control of vehicle platoons on a highway, or that of airborne vehicles, whose nonlinear dynamics cannot be neglected [1-3]. This paper incorporates a dynamic model of a four-wheel drive (4WD), differential steered, high speed mobile robot within an existing cooperative control method and summarizes control issues encountered during formation control from arbitrary initial conditions. The model assumes that tires exhibit nonlinear behavior at high slip or slip angle. Thus, the vehicle dynamics are described by the

rigid-body equations of motion, while the external tire forces and moments are analytic or semi-empirical functions of sliding velocities and terrain parameters. Issues encountered when introducing a dynamic vehicle within a cooperative control scheme are illustrated using a potential function control method studied extensively for pointmass robots. Because existing methods address the general problem of cooperative control and path planning well, it is useful to modify these methods for dynamic robots in a manner that allows for robust or adaptive operation for a range of terrains, operating conditions, speeds, and initial conditions. We introduce a local wheel slip controller for each robot that serves this purpose. In order to implement slip control, wheel slip estimates and an appropriate slip setpoint are required. We develop a computationally efficient method for estimating force-slip characteristics at the terrain-tire interface. Slip estimates can then be used with the potential function path planning and control approach to provide robust, high speed operation during cooperative formation control. The paper summarizes the mathematical model of the robot, describes the control framework, presents the force-slip estimation methodology and results, and demonstrates the performance of the cooperative control framework by computer simulation. NOMENCLATURE R

σ α Mz

vx vy

1

wheel radius wheel slip wheel slip angle Tire restoring moment longitudinal velocity of robot center-of-mass lateral velocity of robot center-of-mass

Copyright © 2006 by ASME

r yaw rate about z-axis through the center-of-mass (fl), (fr), (rl), (rr) designate one of four wheels in the following: ω() wheel angular velocity Fx()

net longitudinal tire force along body-fixed Cartesian

Fy ()

coordinate axes net lateral tire force along body-fixed Cartesian

T()

coordinate axes applied torque

Tr ()

resistive torque

ROBOT DYNAMIC MODEL The robot model is based on a prototype suspensionless, differential-steered robot fabricated and tested in-house. The prototype robot is part of an experimental facility under development comprised of seven 10-13 kg robots with maximum speed of up to 10 m/s. The prototype, shown in Fig. 1, is configurable for either two-wheel drive (2WD) or fourwheel drive (4WD). A hard rubber caster is mounted on a common two-wheel plastic molded chassis in 2WD. To reconfigure to 4WD, a two wheel unit mounts on a hollow bushing joint in the middle of the back end. This joint allows two wheels to pivot passively 60 degrees in either direction in order to maintain ground contact on uneven terrain. 24-volt brushless DC motors with 3:1 planetary gearheads deliver 0.27 N-m of torque to each wheel @ 1275 RPM at peak efficiency, providing a predicted maximum speed of 10.1 m/s. The peak drivetrain efficiency is over 70%. The wheels are 6” x 3” monster truck, non-inflatable rubber tires with foam inserts and plastic hubs. Two 24-volt 3.3-Ah NiMH batteries provide at least 1.5 hours of operation on average. A Z-World Jackrabbit 3100 microprocessor provides control functions and data collection. Sensors include GPS, three-axis angular rates and

accelerations, wheel speeds, and motor currents. Wireless communication is employed. A combination of commercial and in-house developed electronics provides signal conditioning and input-output. The measured hard surface acceleration of the prototype is up to 7 m/s2, with a maximum speed of 10-12 m/s and yaw rate of up to one rev/sec. The vehicle dynamic model incorporates nonlinear tireterrain models and a seven degree-of-freedom rigid-body model. For off-road terrain, the semi-empirical theory of [4,5] provides a relationship between terrain parameters (friction angle, cohesion, pressure-sinkage constants, and shear deformation modulus) and shear and normal stress under wheels that behave rigidly in deformable terrain. Stress distributions are integrated to provide net force or drawbar pull (traction force minus resistance) and resisting moment on each wheel as a function of wheel slip. Reference [6] provides empirical models for vehicle tires on hard surfaces. We scale parameters from the model in [6] to our lightweight mobile robot to provide the longitudinal and lateral adhesion coefficient developed at the contact patch between the rubber tire and hard driving surface in terms of wheel slip and slip angle. An example of tire-terrain forces resulting from these terrain models for a 10 kg vehicle is shown in Figure 3. Figure 3 depicts the potential range of tire performance for on- and off-road terrain and shows the need to determine slip setpoint required to maximize traction on various terrains. Future experimental studies using the prototype robot will estimate actual tire force characteristics on a variety of surfaces. The robot model is given here for the 4WD configuration. The net forces from each driven wheel combine to exert net forces and moments on the vehicle, which is modeled using a three degree-of-freedom rigid-body model. Including the wheel degrees of freedom, the equations of motion are

(

)

1 (1) Fxfl + Fxfr + Fxrl + Fxrr m 1 (2) v& y = −v x r + Fyfl + Fyfr + Fyrl + Fyrr m tw ⎡ ⎤ + F yfr + F yfl L f 1 ⎢ Fxfr + Fxrr − Fxfl − Fxrl ⎥ (3) r& = 2 ⎥ I zz ⎢ − F yrl + F yrr Lr + M z − M res r ⎥⎦ ⎢⎣ 1 ω& fl = T fl − Trfl − bω fl (4) Iw v&x = v y r +

(

)

(

(

(

)

( )

)

)

ω& fr = T fr − Trfr − bω fr

(

) I1

(5)

ω& rl = (Trl − Trrl − bωrl )

1 Iw

(6)

w

ω& fl = (Trr − Trrr − bωrrl )

1 Iw

(7)

Figure 1 Robot design model and prototype in two configurations -2WD, 4WD

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α

Fxfl

⎧ ⎛ ⎪α d ⎜ ln(rij ) + ⎪⎪ ⎜ Vd = ⎨ ⎝ ⎪ ⎛ ⎪α d ⎜⎜ ln(d1) + ⎪⎩ ⎝

x

Fyfl Lf

y

d o ⎞⎟ rij ⎟⎠

0 < rij < d1

do ⎞ ⎟ d1 ⎟⎠

rij ≥ d1

(10)

is the inter-vehicle potential and ⎧ ⎛ h ⎞ ⎪α h ⎜⎜ ln(hik ) + o ⎟⎟ h ⎪ ⎝ ik ⎠ Vh = ⎨ ⎛ ho ⎞ ⎪ ⎜ ⎪α h ⎜ ln(h1) + h ⎟⎟ 1⎠ ⎩ ⎝

Lr

0 < hik < h1

(11) hik ≥ h1

is the potential associated with a real or virtual leader. rij and hik are distances between robot i and j and robot i and leader k, respectively. d o , ho , d1 , and h1 are scalar parameters governing

tw Figure 2 Definition of tire forces and slip angle. TABLE I: Vehicle Model Parameters

20

Symbol

Value

Track width

tw

0.44 m

Wheel radius Vehicle mass

R m

0.075 m 10 kg

Yaw moment of inertia

I zz

0.24 kg-m2

Wheel moment of inertia

Iw

0.005 kg-m2

dry surface wet surface

10

Fx (N)

Description

0 −10 −20 −1

−0.5

0 slip ratio

0.5

1

20

Damping terms bωl , bωr and M res r represent the drivetrain mechanical resistance and yaw damping force. Other constants are defined in Table I. Figure 2 defines body-fixed coordinate axes, slip angle and tire forces.

Fy (N)

−20 −30

where

−20

−10

0 10 slip angle (deg)

20

30

(a) hard surface

x

Net F (N)

25

(8)

where r and r& are the generalized position and velocity of the robot, d (r , r& ) is a dissipative function, and T (r , r&) is a control input [8]. The instantiation of this method using a radial potential function described in [11] is used here to provide dynamic path planning and global control as the robots move with respect to each other. The field contains both physical vehicles and real or virtual leaders. Each entity has a potential function defined by V = Vh + Vd

0 −10

COOPERATIVE CONTROL METHOD The artificial potential function approach provides path planning and navigation along a path [8-10]. Given a suitable potential function V, the control law takes the form T (r , r& ) = −∇V ( r ) + d (r , r& )

dry surface wet surface

10

20 15 10 5

Resistive Torque Tr (N−m)

0 0

(9)

Lean clay Dry sand

0.2

0.4

0.6

0.8

1

0.6

0.8

1

slip ratio 2 1.5

Lean clay Dry sand

1 0.5 0 0

0.2

0.4 slip ratio

(b) deformable terrain Figure 3 Tire-terrain characteristics for a 10-kg robot on (a) hard surface and (b) deformable terrain. Soil parameters for (b) from [7].

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k

acts opposite to

ik

the direction of the velocity vector, where vi is the speed of robot i, and f dis is a scalar gain. This functional form promotes robust overdamped responses during formation control on varied terrain. Eq. 8 provides a commanded force vector for each robot along the gradient of the potential function, comprised of distance-dependent contributions from each robot and leader, and a dissipative term opposite the robot’s velocity vector. The leader potential shepherds the vehicles either to flock to within a distance ho of the leader while maintaining an inter-vehicle distance d o , or to follow a moving virtual leader at a distance ho , while maintaining inter-vehicle distances. Obstacles found by any robot or known a priori can be accommodated by including an obstacle potential term. Potential function approaches were originally developed for point mass robots, though they have been used in vehicle control, e.g., for lane keeping and stability augmentation [3]. Here, we consider potential functions for formation control of robots with nonlinear tire-terrain performance positioned arbitrarily on a two-dimensional surface at t = 0. The maximum velocity achieved along a trajectory for point masses depends heavily on the scalar control gains, e.g., α d and α h in the instantiation of eq. 8-11. For particle dynamics, it is straightforward to choose these scalar gains and a corresponding linear dissipative force that targets a certain peak velocity and provides an over-damped response; given sufficient actuator bandwidth and power, arbitrary bandwidth is achieved for a point mass. When the control method is applied to a dynamic vehicle, as the control bandwidth increases demanding higher vehicle velocities and accelerations, tires can saturate causing loss of traction. On low adhesion surfaces or deformable terrain with low cohesion soil, net traction is limited. Thus, for a wheeled robot on an arbitrary surface, a change in tire-terrain performance has the same effect as changing the potential function scalar gains and thus would require modification of the dissipative term to avoid oscillatory or unstable behavior. Alternatively, sufficient dissipation would need to be provided in eq. 8 to avoid tire saturation given tire-terrain performance, which would limit vehicle performance (maximum velocities achieved) during cooperative control. The relationship between the dynamics and dissipation requires an additional control component, i.e., sensing and accommodating terrain characteristics for each individual robot, in order to avoid a performance tradeoff. Figure 4 demonstrates behaviors exhibited for a robot with a fixed potential function and varying adhesion on a hard

100

15

high adhesion low adhesion

80

10

velocity (m/s)

n

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time (s)

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time (s)

Figure 4 Distance from virtual leader and speed vs. time for a single robot on high and low adhesion surfaces, slip setpoint control inactive. 100

15

high adhesion low adhesion

80

10

velocity (m/s)

v

∑ f dis h i m

distance (m)

nonlinear dissipative function

surface using the model of Fig. 3a. Figure 4 shows two time histories of distance from virtual leader for a single robot (i.e., α h > 0 and α d = 0). Potential function parameters ( α d , α h , n, m, and f dis ) are set such that the maximum force command is approximately equal to the maximum traction force available on the high adhesion surface, and avoiding tire saturation. The robot is pointed directly towards a virtual leader at t=0 (i.e., no steering). With high adhesion and a sufficiently large dissipative force, well-damped motion results and the robot achieves a peak velocity of 10 m/s (solid line). Holding the potential function parameters constant, a loss in adhesion results in poorly damped motion, with a 10 meter overshoot and longer settling time (dashed line), which, if active in a field of multiple robots, could induce poor group dynamics. The poorly damped motion is due to the fact that, on the lower adhesion surface, slip increases and tires saturate, thus the ability to control longitudinal acceleration and deceleration is compromised. The nominal damping added by the potential function controller is sufficient to stabilize the vehicle, but insufficient to reduce overshoot and settling time. Overshoot could induce collisions within a group or collision with a real leader. Increasing the potential function dissipative force could easily recover the well-damped behavior on the low adhesion surface; however, mapping the dissipative force parameters to surface condition would be difficult and costly to establish and would effectively provide only open-loop adaptation to surface condition. Instead, a local slip-based traction controller is designed to maintain stability and robust performance on varying terrain. Slip control is triggered when the potential

distance (m)

the domain of repulsion and attraction between vehicles. α d , α h are scalar control gains governing the gradient of the potential function associated with other robots and leaders. A

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time (s)

Figure 5 Distance from virtual leader and speed vs. time for a single robot, slip setpoint control active.

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Copyright © 2006 by ASME

function commands a force that exceeds the maximum traction capability of the robot. Slip is then controlled at a setpoint just below the peak of the tire force curves using a PID controller, such that the linearized model of the vehicle about that operating point is stable. In practice, the slip setpoint selected and setpoint controller can be realized by a suitable force-slip estimator, discussed in the following section. Figure 5 shows the motion of a single robot on high and low adhesion surfaces, with the same potential function and disspative force parameters as in Fig. 4, and slip control active. On the high adhesion surface, slip control is triggered only briefly during the trajectory, as the potential function parameters are set to largely avoid force commands that saturate the tires. Thus, there is no noticeable difference in performance on the high adhesion surface. On the low adhesion surface, overshoot is halved and settling time is comparable to that of the vehicle on the high adhesion surface. Thus, the local slip control increases damping significantly, allowing the vehicle to perform the maneuver in approximately 15 seconds on either surface. Eq. 8 provides a vector force (magnitude and direction) to be applied to each robot. However, non-point-mass robots generally have nonholonomic constraints and cannot accommodate an arbitrary commanded force direction. Here, a steering control law provides total wheel torques that are directly proportional to the commanded force magnitude up to the adhesion limit, while the error between the vehicle heading and force direction (e.g., the bearing error) proportions the total torque between the wheels on two sides. There are an infinite number of ways to proportion the torque in a differentially steered vehicle. One could turn the vehicle around a vertical axis through its center-of-mass until the vehicle is pointed in the correct direction, and then proceed forward, or one could turn with a finite radius to achieve a desired heading. In order to generalize this study to Ackerman steered robots, the proportioning scheme is based on bearing error. The magnitude of the total applied torque, T, is from eq. 8, and the torques on each side of the vehicle are (1 − p)T and (1 + p)T , respectively. p is a proportioning parameter normalized to +1 and derived using a PID control law based on bearing error, φ d − φ , where φ d is the direction of the force vector from the potential function and φ is the current bearing of the robot . When the commanded force resulting from steering proportioning exceeds the maximum traction capability of the vehicle, slip control mode is triggered, and individual torque commands are scaled accordingly, so as not to exceed the slip setpoint. SLIP ESTIMATION In order to implement slip setpoint control, slip estimates are required at each wheel. Reference [12] develops a tire force and slip estimation method for automotive vehicles on hard surfaces. This method uses a standard sensor set and nonlinear filtering to determine per-wheel net longitudinal and

per-axle lateral forces from sensor data as a means of off-line empirical modeling of tire forces. The method, based on the five-step extended Kalman-Bucy filter (EKBF), treats unknown tire forces as state elements and requires integration of the rigid-body equations of motion, augmented with tire force state elements modeled as random walk processes. An associated covariance matrix is also integrated at each time step. A filter gain is computed based on covariance matrix propagation, and this gain combines the state estimate propagated through integration of dynamic equations with sensor measurements. Through this process, the filter estimates the vehicle state and tire forces. Slip and slip angle estimates at each wheel are derived kinematically from v x , v y , r, and the vehicle geometry. The original derivation and evaluation of this method was intended to accommodate data collected through field tests and processed off-line to determine tire force solicitations for various controlled maneuvers, e.g., steady turns or longitudinal acceleration. Here, we investigate the potential of a constant gain EKBF for real-time implementation of slip and tire force estimation during arbitrary maneuvers. The EKBF derivation for vehicle state and tire force estimation is detailed in [12]. The constant gain filter implementation requires two steps: t + Δt

xˆk ( −) = xˆk +

∫ f (xˆ(τ ), u(τ ))dτ

(16)

t

xˆk +1 = xˆk (−) + K ( zk − h( xˆk (−)))

(17)

where f (xˆ (τ ), u (τ ) ) are the nonlinear vehicle dynamics augmented with random walk models for each tire force to be estimated, K is the steady-state filter gain found by propagating the state covariance matrices to steady state off-line, zk = [r ω fl ω fr ωrl ωrr a x a y V ] is the measurement vector comprised of measurement of yaw rate, four wheel angular velocities, two accelerations, and vehicle speed V, h( xˆk ) is the nonlinear measurement equation for the measurement vector, and xˆk is the augmented state vector comprised of the robot state and a second-order random walk model for teach tire force estimated. For hard surfaces, the longitudinal forces at the contact patch contribute to resistive torque at each wheel, i.e., Tr () = Fx() R , and thus per-wheel longitudinal forces and per-axle lateral forces are estimated. For deformable terrain, the four resistive torques, per-side longitudinal forces, and peraxle lateral forces are estimated. Performance of the constant gain estimator is evaluated by computer simulation of longitudinal and lateral maneuvers. Sample results are presented here for a high adhesion hard surface and for a deformable surface (lean clay). Measurement noise variances for the measurement vector are reported in Table II for a 100 Hz sample frequency, with the exception of a GPS-based speed measurement at 1 Hz. Variance estimates are

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Table II Noise variance of sensors

Sensor Yaw rate Wheel speed acceleration Ground speed

variance 1.35e-4 (rad/s)2 0.351 (rad/s) 2 6e-4 (m/s2) 2 0.8 (m/s) 2

based on a combination of measurements taken from sensors on the prototype robot and manufacturer’s specifications. Figure 6 shows time histories of applied torque and actual and estimated vehicle speed, front-left wheel slip and front-left longitudinal tire force for longitudinal acceleration on a hard, dry surface. First, a constant torque input is applied to each wheel and the steady-state filter gain is computed for this maneuver. The gain is stored and subsequently applied for all longitudinal maneuvers. The steady-state gain is computed for 0.65 N-m torque inputs, and in Fig. 6, the inputs vary from 0 to 0.85 N-m per wheel. The estimated force vs. slip trajectory in Fig. 6 compares well to the true force vs. slip trajectory, and the important features of the tire force characteristics - peak force and slip corresponding to peak force – are clearly visible. Figure 7 shows estimation results for a turning maneuver. The applied torques, velocity magnitude, yaw rate, and slip and force estimates for the front wheels are provided. As for the

0.8 0.6 0.4 0.2 0

10

Velocity magnitude (m/s)

applied torque (N−m)

1

longitudinal case, first, a constant torque input is applied to wheels on each side to elicit differential wheel speeds, and the steady-state filter gain is computed. The gain is stored and subsequently applied to all maneuvers involving turning. The steady-state gain is found using 0.85 N-m input torque to the left wheels and 0.55 N-m to the right wheels. In Fig. 7, the steering inputs are varied as shown, with both left and right turns solicited during the maneuver. The estimates track true values well, even during transients elicited by step changes in wheel torques. For off-road maneuvers where wheel performance is governed by semi-empirical theory of [4,5], the EKBF is formulated to estimate per-side longitudinal forces and per-axle lateral forces. Figure 8 summarizes results of applying a constant-gain EKBF to estimation of tire forces and slip for lean clay soil parameters given in [7] (solid line, Figure 3b). As with previous results, the steady-state filter gain is found by performing a maneuver with constant torque of 0.65 N-m applied to each wheel. The constant-gain filter is applied during a maneuver where torque constant (0.55 N-m) for two seconds, and then is ramped up to 1.75 N-m over six seconds. Again, the estimated force-slip and resistive torque-slip solicitations trace the shape of the actual solicitations well.

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40 60 Front left slip estimate %

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Figure 6 Results of state and force estimation for front left wheel during longitudinal acceleration.

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left right 0.5

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4 6 time (sec)

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true estimate 0

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front left slip angle (rad)

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F

xfl

(N)

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(Fxfl + Fxrl)/2 estimate (N)

Figure 7 Results of state and force estimation for front left and front right wheels during steering maneuver. 20 15 10 5 0 −5

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slip 1 Trfl estimate (N−m)

Trfl (N−m)

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slip

Figure 8 Estimated net longitudinal forces (left and right) vs. slip estimate, actual net longitudinal forces (front left and right) vs. slip, and estimated and actual resistive torque vs. slip for one wheel, for simulation of longitudinal acceleration on lean clay (parameters from [7]).

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Figure 9 shows the trajectories of each robot during global formation control on the high adhesion surface of Fig. 3a, with and without slip control active. The vehicles start parallel to each other, thus the two flanking vehicles start with a bearing error and must execute a turn, with net force applied to the vehicle being a result of both the potential function force, and the steering control law. The solid circle represents the well of the virtual leader’s potential function, or the “stopping point” for the robots, and the dashed circles represent the domain of repulsion of the individual robots at the end of the simulation. For the high adhesion surface, potential function control gains and dissipative force were tuned for a single vehicle to avoid slip setpoint control (Fig. 5). When these parameters are retained for group control, slip setpoint control is triggered infrequently, though there is modest improvement in overshoot for the center vehicle due to slip setpoint control and a decrease in settling time for each vehicle. All vehicles proceed smoothly to the potential well around the virtual leader.

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Y (m)

PERFORMANCE OF COOPERATIVE PATH PLANNING AND FORMATION CONTROL The performance of the global potential function and local slip control in a cooperative path planning and control task is demonstrated here for a group of three robots moving on a low adhesion surface. As indicated in eq. 8-11, the robots interact with each other via the inter-vehicle potential, and the degree of interaction is adjusted by scalar gain α d . d o and ho affect the way robots arrange themselves relative to each other and around the leader at steady-state. The inter-vehicle potential also reduces the potential for collision. The task is for robots to arrange themselves on a circle around a virtual leader or target, starting from a distance of roughly 100 m from the target. Here, ho = 10 m and d o = d1 = ho 3 to target a symmetric radial configuration of the robots around the leader. The potential function parameters are tuned for high adhesion surface (Fig. 3a), thus the simulation is a test of robustness of the cooperative control framework to adhesion conditions.

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Figure 9 Group dynamics on high adhesion surface of Figure 3a. Left: slip control is inactive, right: slip control is active. 60

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Figure 10 Group dynamics on low adhesion surface of Figure 3a. Left: slip control is inactive, right: slip control is active.

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Copyright © 2006 by ASME

Figure 10 shows the trajectories of each robot on the low adhesion surface of Fig. 3a., holding the potential function parameters constant at the values tuned for the high adhesion surface. With slip control inactive, the commanded forces from the potential function cause the tires forces on both sides of the robots to saturate. This causes the flanking robots to lose directional control during the high velocity maneuver. While lateral stability is retained due to sufficiently high lateral forces, the robots cannot achieve forces commanded by the potential function controller and thus fail to turn towards the potential well. With slip control active, directional control is retained. Table III summarizes peak velocity achieved and settling time for each robot in the simulations of Figures 9 and 10. Table III Performance summary for cooperative control of three robots on high and low adhesion surface with slip setpoint control inactive and active

Settling time (sec) High adhesion Flanking robot Center robot Low adhesion Flanking robot Center robot

Peak speed (m/s)

Overshoot (m)

Inactive Active Inactive Active Inactive Active 32 19 10 10 18 16 11.2 11.2 8.8 5.0

22

32 18

8.5 10.8

15.7 12.5

8.3

4.5

Future research will focus on experimental validation of the vehicle dynamic model, slip estimation, and control framework with the robotic testbed. CONCLUSION This paper presents a cooperative control framework for high-speed robots driving on varied terrain. Varied terrain presents a range of force-slip characteristics that must be known a priori or estimated in real-time in order to retain vehicle directional control and maximize traction. The control framework, comprised of a global, dynamic path planning and motion controller and a local slip-based traction control, is shown to provide robust formation control on low adhesion terrain when the global controller is tuned for high adhesion terrain. A constant-gain EKBF is proposed for implementing a local slip-based traction controller. The estimator is demonstrated for longitudinal acceleration and steering maneuvers showing good tracking of tire forces, slip, and slip angles during high acceleration and transients.

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ACKNOWLEDGMENTS This research was supported by the National Institute of Standards under Grant No. 60NANB4D1144, by the Institute for Security Technology Studies, through Grant No. 2005-DDBX-1091 awarded by the Bureau of Justice Assistance, and by the Army Research Office under contract No W911NF-06-10153.

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