The Design and Control of a Prototype Quadruped Microrover GAURAV S. SUKHATME.

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1 ??,??, 1{10 (??) c?? Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. The Design and Control of a Prototype Quadruped Microrover GAURAV S. SUKHATME gaurav@robotics.usc.edu Robotics Research Laboratory, Department of Computer Science, Institute for Robotics and Intelligent Systems, University of Southern California, Los Angeles, CA Received??. Revised??. Abstract. We describe the design, construction and control of a quadruped robot which walks on uneven terrain. A control system which produces a statically stable gait has been implemented; results showing a straight and turning gait are presented. The control of quadruped robots poses interesting challenges due to a small stability margin (when compared to hexapods for example). For this reason most implemented systems for outdoor walking on uneven terrain have been hexapods. The system described here has the added virtue of using very few inexpensive sensors and actuators. One of the aims of this work is to build a reduced complexity (low power, low mass and direct drive) walking robot for statically stable walking. The other aim is to compare the performance of this robot with a wheeled robot roughly the same size and weight. In this paper we report on progress towards the rst of these two goals using a traverse across an obstacle eld as an example. Keywords: quadruped robot, static stability, microrover, walking robot 1. Introduction The advantages that walking robots possess have been extolled for many years. An important example is the ability to reduce the mechanical coupling between the payload and the terrain thereby enabling irregular terrain traversal. Several successful walking robots have been built that have walked on uneven terrain; (Song & Waldron 1989), (Bares & Whittaker 1993) are examples. Almost all of them have either been hexapods or eight legged frame walkers. The notable exceptions are the family of quadrupeds built by Hirose et al. (Hirose 1984), (Hirose, Kikuchi & Umetani 1986) and (Hirose & Kunieda 1991). In this paper we propose a design for a quadruped robot (called MENO 1 ) which walks on uneven terrain using a small number of inexpensive sensors and actuators. A quadruped has the disadvantage of being less stable but it is lighter than comparably sized eight legged and hexapod designs. This makes it better suited for applications where lightweight robots are preferable. One such application is planetary exploration. The forthcoming missions to Mars, planned by NASA (Matthies, Gat, Harrison, Wilcox, Volpe & Litwin 1995), all use wheeled robot rovers but in the future it is conceivable that a legged rover may prove preferable for exploring planetary surfaces. We have constructed two rovers (one wheeled and the other legged) and a mockup of a Martian surface. Experiments are in progress to evaluate the performance of the two robots using a multicriteria approach (Sukhatme & Bekey 1996). In this paper we describe the design and construction of MENO and its control system as well as results on walking, turning and navigation. The control system is a set of interacting sensor and actuator processes which maintain balance while moving the robot forward (or turning it in place). A preprogrammed, open-loop gait fails frequently due to uneven terrain, mechanical and calibration errors and slippage on the ground. However with the control system operational we are able to demonstrate stable walking and turning. We are also

2 2?? able to demonstrate robust navigation using dead reckoning. 2. Previous Work The study of walking robots goes back some four decades. The literature is largely divided into two approaches: a. based on static stability and b. based on dynamically stabilized machines. The larger body of work is in the former category due to the complexity of implementation of dynamic methods. The Phony Pony built by McGhee et al. (McGhee 1967) is an early example of using a nite state machine to control a quadruped. All statically stable walking machines have been based on some measurement of static stability such as the stability margin; (Messuri & Klein 1986) and (Nagy, Desa & Whittaker 1994) are examples of applying stability measures to evaluate gait quality. Once a criterion function for stability is decided upon the next challenge is the gait design. Gait is a temporal sequence of joint positions (and by consequence footplacement) that cause locomotion. Obviously any arbitrary sequence will not produce a gait since at all times the stability criterion must be met and locomotion must result. One approach is to calculate the gait `on the y' - by this we mean that the onboard controller is used to solve the problem of footplacement during locomotion using sensory input, a navigation goal and the stability criterion at every move. The `gait' is a side eect of such a computation. The second method is to predesign a (few) `xed' gait(s) based on the stability measure with assumptions made about the terrain and the nature of the foot contact. If sensory input leads the controller to believe that the system will be destabilized as a result of the next preplanned step then the controller reacts and plans an alternate footplacement sequence. An example of the second approach is (Nagy et al. 1994); this approach is also used in the current work. The problem of xed gait design is rendered intractable in general due to the large size of the conguration space of a typical multilegged walking machine. The conguration space of a quadruped robot with 3 DOF on each limb is 12 dimensional. To nd a gait in this space even by intelligent search is inecient. The alternative is to reduce the size of this space using certain assumptions. The rst assumption that is typically made is that of symmetry. By symmetry we mean that the joint congurations on one side of the robot mirror the joint congurations on the other (with a phase delay). Essentially the C-space has been halved in dimensionality. The second assumption that is typically made is that the footplacement strategy is assumed to be periodic. This reduces the original problem to nding a small number of (preferably short) footplacement sequences that cause stable locomotion. Examples of research that uses these two assumptions and a variety of stability measures are the body of research at CMU (Bares & Whittaker 1993), (Krotkov & Homan 1994) and (Simmons 1994); work by Hirose et al. (Hirose 1984), (Hirose et al. 1986) and (Hirose & Kunieda 1991); research at OSU on the OSU hexapod (Song & Waldron 1989) to name a few. Signicant recent work on quadrupeds has been done by Jimenez et al. (de Santos & Jimenez 1995). Several biologically motivated walking robots have been built; all are statically stable walkers. Examples can be found in (Brooks 1989), (Beer, Chiel & Sterling 1990) and (Ferrell 1995). The study of dynamically stabilized locomotion is not of immediate interest here. Excellent references are Raibert et al. (Raibert 1986). and (Hodgins & Raibert 1991). An additional challenge in dynamic locomotion is that footplacement has to happen quickly - this is not a problem with statically stable gaits and we shall not consider it further. 3. Robot Design MENO is a 12 DOF statically stable quadruped. Each leg is a rotary-rotary-prismatic (RRP) design. The body of the robot and the rst two links of each leg are in the horizontal plane and the prismatic joints (the most distal joint of each limb) are in the vertical plane. This orthogonal design was inspired by the design of Ambler (Bares & Whittaker 1993). The main advantages of such a design are ease of motion planning and energy eciency. The robot chassis and limbs are constructed out of aluminum tubing. The robot is actuated by 12

3 ?? 3 o-the-shelf servomotors. A lead-screw is used to convert the rotation of the motor to translation of the foot in the case of the prismatic joints. By retracting/extending the prismatic joints the chassis height above the ground is varied. Figure 1 shows the robot and the table below gives some of its mechanical parameters. The robot is equipped with the following sensors Foot switches: Measure contact (on/o) with the ground. There is one on each of the 4 feet. Two-axis inclinometer: Measures the roll and pitch of the robot chassis with respect to the local gravitational vertical. Resistive potentiometers: One on each of the 8 rotational joints, to measure the joint angle. Foot retraction microswitch: To measure when a foot is fully retracted (on/o). There is one on each leg. Compass: Measures yaw of the chassis. Foot obstacle contact switch: To measure when a foot comes into contact with an obstacle during its swing phase. There are four (in parallel) on each foot. Sonar: Measures distance to obstacles. One forward looking transducer in the current implementation. Fig. 1. MENO in a simulated Martian environment source of information for navigation; as we shall see in the next section navigation is done by dead reckoning using information measured by onboard sensors only. The sand surface is nominally at but not excessively so. No attempt is made to smooth out the surface which is usually uneven as a result of people walking in the sandbox, depressions left by rocks that are constantly moved around and other disturbances. It should be noted that we are not dealing with excessive slopes or terrain that is likely to fail. Experiments and an analysis of the kinematics shows that the maximum slope that the robot is able to navigate successfully is approximately 25 o. Onboard computing is all done on a custom board built around a Motorola microcontroller. A tether is used to supply oboard power for extended testing and for gathering telemetry. The testing is all done in a 3:5 m 3:5 m sandbox. This same environment is also used for experiments with the wheeled robot we have built. A single camera suspended 3 m above the center of the sandbox is used for tracking the robot's position. We do not use the overhead camera as a Table 1. Mechanical parameters Quantity total mass chassis length chassis width proximal limb link length distal limb link length minimum height maximum height Value 5 kg 0.18 m 0.15 m 0.09 m 0.11 m 0.14 m 0.29 m 4. The Control System 4.1. The Straight and Turn Gaits The control system for MENO operates about a nominal gait. In order to generate the nominal gait the combined mass of the limbs, the chassis and the control electronics was measured. Since these are the most massive parts of the robot the calculation of the center of mass uses only these values lumped at their geometric centers. For convenience they are shown on one limb only, as partially lled circles in Figure 5. Additional sensors that were added later were not used in making center of mass calculations for the nominal gait generation. The assumption was also made that the chassis and the rst two links of each leg always lie in the horizontal plane. Further, the nominal gait generation also assumes ideal actuators

4 4?? 10 cm (a) (b) (c) (d) (e) (f) (g) Fig. 2. A plan view of the straight gait (forward is towards the top of the page, numbers indicate stability margin in cm) 10 cm (a) (b) (c) (d) (e) (f) (g) (h) Fig. 3. A plan view of the turn gait (forward is towards the top of the page, numbers indicate stability margin in cm) and no slippage between the feet and the sand. The gait generation imposes the constraint that under the idealizations described above the projection of the center of mass of the robot onto the horizontal plane should lie in the support polygon formed by the stance feet (Messuri & Klein 1986). The term straight gait is used to denote a gait where the yaw of the robot chassis is constant. A turn gait serves to change the yaw of the chassis. The nominal straight gait generation was done as part of another project in our lab which investigates biologically inspired cerebellar approaches to quadruped and hexapod walking. It may be noted that the nominal straight gait is similar to the intermittent crawl gait presented in (Tsukagoshi, Hirose & Yoneda 1996). The nominal straight gait is shown pictorially in Figure 2. The rst two phases (Figures 2a, 2b and 2b, 2c) are with 3 legs on the ground and are used to recover the 4th leg to a forward position. The 3rd phase (Figure 2c, 2d) is with all four legs on the ground and is used to move the center of mass of the robot forward with respect to the ground. The next three phases are mirror images of the rst three. The nominal turn gait example shown in Figure 3 uses small rotations to achieve a 10 o clockwise turn. The rst phase of the turn gait shown in Figure 3 is 3a, 3b which rotates the chassis clockwise by 5 o while keeping all four feet on the ground. The second phase 3b, 3c is the recovery of the rear right leg to its new position. The third phase 3c, 3d is the recovery of the front right leg to its new position. In the fourth phase 3d, 3e the body of the robot is translated forward with all legs on the ground. Phase ve shown in 3e, 3f is a clockwise rotation of the chassis by 5 o. Phase six is shown in 3f, 3g and is the recovery of the rear left leg to its nal position. The nal phase is the movement of the front left leg to its nal position. In both Figures 2 and 3 the numbers denotes the stability margin (in cm) prior to a swing phase. The + is the center of mass of the robot and the o is the geometric center of the support polygon. The robot is thus designed to walk in a stable gait which can be modeled as a state graph. The straight gait is the sequence of congurations labeled S1 through S6 in Figure 4. Forward motion of the robot is achieved by cycling from left to right in this graph. Moving from right to left causes the robot to move backward in a straight line. Every state shown as a rectangle in Figure 4 encapsulates a turn sequence composed of 8 states (7 phases) as described in the previous paragraph. The eect of transitioning through a rectangular box once is to turn the robot by 10 o (either to the

5 ?? 5 TR1 6 TR6 1 TR4 3 Right Backward TR3 4 S6 S1 S2 S3 S4 S5 S6 TL3 4 Forward TL4 3 Left TL6 1 TL1 6 left or right). Composition of turns leads to larger turn angles. Notice that it is not possible to turn from states S2 and S5; to turn from one of these states we translate to a neighboring state and initiate a turn. It may be noted that the following correspondence exists between the state graph and the straight gait shown in Figure 2: S1-2a, S2-2b...S6-2f. It may also be noted that the conguration shown in Figure 3a is the same as the conguration shown in Figure 2a which we call S1 in the state graph. Figure 3h is the same conguration as Figure 2f; both are denoted by S6 in the state graph. The example turn gait shown in Figure 3 is therefore the rectangle denoted TR1-6 in Figure 4. The other rectangles contain similar sequences which cause the robot to turn Attitude and Gait Control Fig. 4. The state graph The center of mass location is quite sensitive to the conguration as shown below. We show a sample sensitivity calculation to estimate the amount of error xcm in the x position of the center of mass as a function of a small error 1 of the proximal joint angle. The center of mass along the local x axis (attached to the chassis) depends on the mass at locations A through E (Figure 5) and the mass of the chassis. The mass at A is the proximal servo motor which is xed to the chassis. The conguration dependent mass moments are due to the mass at points B through E. We write only those terms (for one leg) explicitly below. xcm = 1 M ( m B a 2 cos 1 + mc acos 1 + md(acos 1 + b 2 cos( ))+ me(acos 1 + bcos( )) + : : :) (1) When the nominal gait is implemented on the robot with no feedback it fails almost immediately. Often before the robot completes one gait cycle it is destabilized enough to fall over while recovering a leg. The stability margin under which the nominal gait operates is small - see Figures 2 and 3. where M = 5kg is the total mass of the robot, xi denotes the x position of the point i in the chassis frame, mi is the mass at point i, 1 and 2 are the proximal and distal joint angles as shown in Figure 5 and a = 0:09m and b = 0:11m are the link lengths. By dierentiating the above with

6 6?? respect to 1 and bounding the sine and cosine values we conclude for small 1, jxcmj 1 M ( a 2 m B + amc + amd+ b 2 m D + ame + bme) j 1 j (2) Using measured values for the masses from MENO and the appropriate link lengths we have jxcmj 0:024 j 1 j (3) The measured errors in 1 on MENO are on the order of 10 o. Substituting into the equation above we have the following error estimate jxcmj 0:0041 m (4) There are 8 rotational joints - if we assume that all of them are in error by 10 o then we have an upper bound on the error estimate xcm 8 0:0041 = 0:0328m. This is an overestimate since the center of mass is not as sensitive to the distal angle 2 as it is to the proximal angle 1 but it serves as a good order of magnitude estimate. The above calculation was for the x component of the center of mass, a similar number for the y component may be assumed and the resultant error estimate in the center of mass position may be calculated as p 2 0: = 0:0469m. This estimate exceeds the best stability margin available (see Figures 2 and 3). In light of the above calculation we may expect destabilization quite routinely when a leg recovery is attempted if the nominal gait is used without feedback. The reason for this Y D X Global frame C B A E b = 0.11 Y X a = 0.09 P O 1 Fig. 5. MENO parameters (plan view) O2 T is the play in the rotational joints. Further consider that there is unmodeled mass in the system in the form of new sensors, connectors etc. This mass is rigidly connected to the chassis and its moment does not depend on the conguration of the joints. However it can serve to introduce destabilization into the nominal gait which was derived without modeling it. Redesign of the robot with lighter materials for the legs and an indirect drive mechanism can be used to move mass closer to the chassis thus increasing the stability margin. This introduces both cost and complexity into the design which we try to avoid. Further, simulation results show that with the current RRP design and conventional materials there is no substantial gain in stability with an indirect drive mechanism. A second solution lies in making small corrections to the nominal gait at every leg recovery if the inclinometers show excessive roll and pitch. This results in a slower walk but is much more reliable than the situation discussed above. This heuristic approach is discussed below. The magnitude of the correction to the nominal gait that needs to be made at each leg recovery is calculated using the inverse kinematics of each leg. The objective is to shift the center of mass away from the leg being recovered since the robot tilts towards the leg being lifted when the stability margin is exceeded due to joint errors. The assumption made is that the unmodeled mass is attached rigidly to the chassis. Hence if the chassis is moved away from the recovering leg the objective will be achieved. In Figure 6 we see two locations of the chassis and a leg. While the foot (point T) remains in contact with the ground the leg and chassis are moved from the solid line to the dashed line. Using the inverse kinematics it is possible to calculate appropriate nal values for the two angles 1 and 2 given a desired shift in the geometric center of the robot S = (x; y) and a desired chassis rotation. The same shift S and rotation is used for all four legs and the two angles are calculated for each leg separately. The new joint angles are then commanded to each rotational joint and the leg recovery is attempted again. If it fails the leg is lowered until contact and another shift is commanded. The leg is not recovered until it is safe to do so. It is worth pointing out here that this solution is not guar-

7 ?? 7 ated. The shift is executed with all legs on the ground and the leg recovery is attempted again. On completion of a shift or a successful leg recovery the level() process is executed. Y O O P P y T The level() process tries to achieve two objectives: a. To level the plane of the robot, and b. To keep the centroid of the plane of the robot a certain (predened) height above the ground in order to keep the operating region of the prismatic joints near the center of their region of travel. The level() process nishes when the roll and pitch values are below some preset thresholds. X Global frame x 4.3. The Navigation Algorithm Fig. 6. A shift maneuver (plan view) anteed to succeed; it may happen that in some congurations the commanded shift cannot be executed due to physical limits, singularities etc. In our experiments to date this has happened rather infrequently. We are now ready to describe the complete control system as a set of interacting processes (see Figure 7). The sensor processes run at the fastest rate and may be considered as the lowest level processes. There is one process for each sensor and each updates a corresponding global data structure. The main control ow proceeds using an executive process that receives a command from a navigator. The navigator produces a nominal target sequence for the executive process to implement. It is described in the next subsection. No real time constraint is placed on the navigator which awaits a successful return from the executive process to advance its internal clock and produce the next target sequence. When attempting a leg recovery the executive process treats it as a guarded motion and lifts the appropriate leg by a small amount until contact is lost with the ground. The resulting roll and pitch values are thresholded to estimate whether the robot is tipping or whether the leg can be recovered safely. In the latter case the leg is raised higher and the inclination is monitored. At any stage in the leg raise phase if the inclination exceeds a preset threshold the leg is lowered and a shift command is gener- MENO navigates using dead reckoning interspersed with reactive obstacle avoidance. The basic strategy is to dead reckon using the kinematics of the robot and the appropriate transition along the state graph. The onboard compass is used to measure the direction of the chassis. Dead reckoning assumes that the chassis is horizontal and does not take into account the roll and pitch values. The robot is given a goal in world coordinates and is told its start location in the same world coordinate system. If an obstacle is encountered on the foot bumper switches the robot attempts to Sequence complete Unbalanced Adjust (shift/rotate) Navigator Command sequence Executive State? Check Balance level() Balanced Move Data Flow Control Flow Blackboard Sensor Processes incline() compass() jointangles() footswitch() legup() sonar() footbump() Fig. 7. The control system architecture

8 8?? roll pitch Power (W) Pitch/Roll (degrees) (a) (b) (c) (d) Phase Phase Fig. 8. Energy consumption and pitch/roll regulation (a) (b) (c) (d) (e) (f) (g) Fig. 9. Straight gait sequence (`forward' is to the right of the page) lift the leg higher to avoid the obstacle. If the leg is fully retracted and the obstacle is still in the way the robot backs up and turns. The front sonar is arranged so that it is triggered by large rocks which are insurmountable. The strategy used to avoid these large obstacles is to turn as soon as they are detected. If no obstacles are detected (either by the sonar or by the foot bumper switches) then the robot will attempt to walk forward provided the goal is in within an angular range of 30 o of the current forward direction as measured by the compass. If that is not the case a reorient procedure is initiated which turns the robot (essentially in place) thereby aligning it with the goal direction. The algorithm is essentially the same as the one employed on other reactive systems; (Gat 1995), and (Sukhatme & Bekey 1996) are examples. This algorithm is resident in the box labeled Navigator in Figure Results In Figure 8 we show the pitch and roll regulation imposed by the control system. The absolute value of the chassis pitch is seen to never exceed

9 ?? 9 4 o and the chassis roll never exceeds 4 o in magnitude either. The cost of maintaining the system attitude is the time spent in re-leveling. The inclinometers used in the current system are slow (settling time is approximately 0.25 s) and cause a signicant slowing in the overall performance. In Figure 8 we show the energy consumed by the robot as it walks on sandy terrain. The samples were taken at approximately 2 Hz. Figure 8 illustrates the fact that the power budget is relatively low (approximately 12 W on the average and no more than 16 W maximum). The peaks in Figure 8 correspond to the motion of the legs. The dotted lines correspond to the congurations shown in Figure 2. In Figure 9, we show a sequence of steps taken by the robot in the sandbox while executing a straight walk. In Figure 9 the robot translates forward approximately 20 cm in one complete gait cycle. The last frame of Figure 9 is the same conguration as the rst. Note that in Figure 9 the `forward' direction is to the right of the page and in Figures 2 and 3 the `forward' direction is towards the top of the page. In Figure 10 a sample traverse across an obstacle eld of rocks is shown. The robot is started at the position denoted by S and is commanded to the goal denoted by G. The nal position of the robot is shown by an x and the intermediate positions are shown by + signs. The circles represent rocks. The cluster of + signs near the center of the gure is due to the obstacle detected and a turn maneuver. The error in navigation is 0:28 m which is approximately 12% of the length of the traverse. This is fairly representative of our system. Multiple trials show dead reckoning errors which vary between 10 and 15% of the length of the traverse. 6. Conclusion We have described here the design, construction and control architecture for a quadruped robot which walks on uneven terrain. Experiments with the robot and our control approach show encouraging results. While it is premature to advocate the use of quadruped robots for expensive missions (such as planetary exploration), it is not out of the realm of possibility in the future. The current implementation is shown to perform satisfactorily using the shift heuristic described in the paper. The system described here has now been used for approximately 50 hours. The main cause of destabilization is play in the rotary joints due to the plastic gears used in them. A major mechanical renement is to replace these gears (and shafts) by metals gears (and shafts) which will align better and wear out less easily thereby reducing the play. The main sensor improvement that is planned is to replace the inclinometer with a faster device - it is currently heavily used and is extremely slow. The foot contact switches measure contact with the ground using one bit. We plan to replace these switches with pressure sensors so footplacement can be improved. In previous work (Sukhatme & Bekey 1996) we have described a statistical benchmarking technique for robot rovers which measures performance over a large number of obstacle placements drawn from the same statistical distribution. To make a comparison between the wheeled robot that we have already tested and MENO is one of the main thrusts of future work. Acknowledgments The author would like to thank S. Hayati, G. Rodriguez, R. Volpe, C. Weisbin and B. Wilcox (all at JPL) for stimulating discussions over the past few months. The author also thanks Scott Brizius, Scott Cozy and Steve Goldberg for their help with the experiments and robot construction. The author thanks Prof. Tony Lewis (now at UIUC) for the design inspiration for MENO. This work was done under the supervision of Prof. George Bekey and beneted greatly from his suggestions and advice. This work is supported in part by Jet Propulsion Labs, California Institute of Technology under contract # and the Oce of Naval Research under contract #N

10 10?? Notes 1. The mechanical design of MENO was strongly inuenced by an earlier quadruped machine built in the USC Robotics Research Laboratory by M. Anthony Lewis in This robot, also named MENO, had a 2 degree of freedom rotary-prismatic joint structure for each leg, but none of the sensor-based control features of the current model References Bares, J. & Whittaker, W. (1993), `Conguration of autonomous walkers for extreme terrain', International Journal of Robotics Research 12(6), 535{559. Beer, R. D., Chiel, H. J. & Sterling, L. S. (1990), `A biological perspective on autonomous agent design', Robotics and Autonomous Systems 6, 169{186. Brooks, R. A. (1989), `A robot that walks: Emergent behaviors from a carefully evolved network', Neural Computation 1(2), 365{382. de Santos, P. G. & Jimenez, M. A. (1995), `Generation of discontinuous gaits for quadruped walking vehicles', Journal of Robotic Systems 12(2), 599{611. Ferrell, C. (1995), `Global behavior via cooperative local control', Autonomous Robots 2(2), 105{125. Gat, E. (1995), `Towards principled experimental study of autonomous mobile robots', Autonomous Robots. Hirose, S. (1984), `A study of design and control of a quadruped walking vehicle', International Journal of Robotics Research 3(2), 113{133. Hirose, S. & Kunieda, O. (1991), `Generalized standard foot trajectory for a quadruped walking vehicle', The International Journal of Robotics Research 10(1), 3{ 12. Hirose, S., Kikuchi, H. & Umetani, Y. (1986), `The standard circular gait of a quadruped walking vehicle', Advanced Robotics 1(2), 143{164. Hodgins, J. K. & Raibert, M. H. (1991), `Adjusting step length for rough terrain locomotion', IEEE Transactions on Robotics and Automation 7(3), 289{298. Krotkov, E. & Homan, R. (1994), `Terrain mapping for a walking planetary rover', IEEE Transactions on Robotics and Automation 10(6), 728{739. Matthies, L., Gat, E., Harrison, R., Wilcox, B., Volpe, R. & Litwin, T. (1995), `Mars microrover navigation: Performance evaluation and enhancement', Autonomous Robots. McGhee, R. B. (1967), `Finite state control of quadruped locomotion', Simulation pp. 135{140. Messuri, D. A. & Klein, C. A. (1986), `Automatic body regulation for maintaining stability of a legged vehicle during rough terrain locomotion', IEEE Journal of Robotics and Automation 1(3), 132{141. Nagy, P., Desa, S. & Whittaker, W. L. (1994), `Energybased stability measures for reliable locomotion of statically stable walkers: Theory and application', The International Journal of Robotics Research 13(3), 272{287. Raibert, M. H. (1986), Legged Robots that Balance, The MIT Press, Cambridge. Massachusetts. Simmons, R. (1994), `Structured control for autonomous robots', IEEE Transactions on Robotics and Automation 10(1), 34{43. Song, S. & Waldron, K. J. (1989), Machines that Walk: The Adaptive Suspension Vehicle, The MIT Press, Cambridge, Massachusetts. Sukhatme, G. S. & Bekey, G. A. (1996), Multicriteria evaluation of a planetary rover, in `Proc. Workshop on Planetary Rover Technology and Systems, 1996 IEEE Int. Conf. on Robotics and Automation'. Tsukagoshi, H., Hirose, S. & Yoneda, K. (1996), Maneuvering operations of the quadruped walking robot on the slope, in `Proc IEEE/RSJ Int. Conf. on Intelligent Robots and Systems', pp. 863{869. Gaurav S. Sukhatme is a Ph.D. candidate in the Department of Computer Science at the University of Southern California in Los Angeles. He received a B. Tech. in Computer Science and Engineering from the Indian Institute of Technology, Bombay in 1991 and a M.S in Computer Science from the University of Southern California in He is interested in articial intelligence, robotics and dynamic modeling of physical systems. m S robot position rock final position m Fig. 10. A sample traverse (S is the start position, G is the desired goal) G