Towars bipeal running of a six-legge robot N. Neville an M. Buehler neville@cim.mcgill.ca, buehler@cim.mcgill.ca Ambulatory Robotics Laboratory Centre for Intelligent Machines, McGill University Montreal, Quebec, H3A 2A7, Canaa www.cim.mcgill.ca/~arlweb, www.rhex.net Abstract This paper presents preliminary bipeal running experiments with our Robotic Hexapo, RHex. The robot an the bipeal gait are uner-actuate, using only one actuate egree of freeom per compliant leg. We ouble up the hin legs by attaching a uplicate set of hin legs at 180 egrees, forming S shape hin legs. This reuces the actuator spee requirements uring noncontact, while preserving the bipeal ynamics an control challenges. Stable running at an average 1.08 m/s with a success rate of 59% (100% without steering failures) over ten runs is obtaine with only leg angle an boy pitch angle feeback. The average specific resistance (cost of transport) of 1.2 is lower than previously reporte numbers for pronk an boun gaits at similar spees. research on cockroach locomotion [3,4] with its sprawle posture, low center of gravity, passive compliant legs, an clock-riven tripo gaits. These biologically motivate ieas, combine with soun scientific an engineering principles, have enowe RHex with a large repertoire of gaits, incluing walking over highly broken an irregular terrain [9], pronking [6], stair climbing [7,8], swimming [11], flipping [10] an quarupeal bouning [2]. 1 Introuction Many application omains of robots require mobility. Such applications inclue fire fighting, support for emergency first response teams, mobile monitoring, inspection an surveillance, planetary exploration, antiterror an homelan security, to name just a few. To aress these nees, engineers have esigne a huge array of evices with wheels, tracks, an various numbers of legs, as well as articulate wheels an tracks, an combinations of legs an wheels. Of all these evices, legge robots resemble animals most. Thus, in aition to the potential for the kin of breathtaking mobility many animals are capable of, two more application omains exist for legge robots. First, entertainment robotic evices (toys, theme park versions of movie creatures) an robots esigne to be human helpers require biological resemblance. Secon, since legge robots must solve similar ynamic challenges in terms of legge mobility as humans an animals, but are much easier to stuy, they may serve as vehicles of scientific stuy to postulate or test hypotheses about animal or human locomotion. Naturally, legge robots may also benefit from inspiration from millions of years of biological evolution. This is the case with RHex, a hexapo robot inspire by Figure 1: RHex in outoor rock fiel In this paper we introuce the first steps towars aing a new behavior to RHex s alreay large behavioral repertoire: running on its hin legs. Just as the overall robot esign was inspire by Full s research on cockroach locomotion, so is this particular behavior. Full an Tu [4] reporte that the American cockroach, Periplaneta americana (mass < 1 g) can run bipeally on its hin legs at high spees. At the highest attainable spees, the bipeal gait may even inclue an aerial phase (short perios with no measurable groun forces). Why create a bipeal gait for a hexapo robot? We are intereste in expaning RHex s behavioral repertoire an investigating an exploiting possible mobility, spee or energetic avantages. For example, we expect an immeiate mobility improvement in terms of step an pipe traversal heights, ue to the raise center of mass of a bipeal RHex. Furthermore, the reporte behavior is a proof of concept an an important step towars an unmoifie bipeal RHex, which will be the simplest autonomous running bipe, in terms of sensing, computation an mechanical esign. 1
Report Documentation Page Form Approve OMB No. 0704-0188 Public reporting buren for the collection of information is estimate to average 1 hour per response, incluing the time for reviewing instructions, searching existing ata sources, gathering an maintaining the ata neee, an completing an reviewing the collection of information. Sen comments regaring this buren estimate or any other aspect of this collection of information, incluing suggestions for reucing this buren, to Washington Heaquarters Services, Directorate for Information Operations an Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Responents shoul be aware that notwithstaning any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it oes not isplay a currently vali OMB control number. 1. REPORT DATE 2003 2. REPORT TYPE 3. DATES COVERED - 4. TITLE AND SUBTITLE Towars bipeal running of a six-legge robot 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Defense Avance Research Projects Agency,3701 North Fairfax Drive,Arlington,VA,22203-1714 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR S ACRONYM(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approve for public release; istribution unlimite 13. SUPPLEMENTARY NOTES The original ocument contains color images. 14. ABSTRACT see report 15. SUBJECT TERMS 11. SPONSOR/MONITOR S REPORT NUMBER(S) 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT unclassifie b. ABSTRACT unclassifie c. THIS PAGE unclassifie 18. NUMBER OF PAGES 7 19a. NAME OF RESPONSIBLE PERSON Stanar Form 298 (Rev. 8-98) Prescribe by ANSI St Z39-18
2 Platform RHex is an untethere hexapo with a very simple mechanical esign featuring compliant legs with one actuate egree of freeom per leg at the hip. Leg retraction is accomplishe by rotating the leg over the hip to avoi toe stubbing an to clear obstacles. The simplicity of the system has resulte in a robust platform for stuying legge locomotion that is also a promising caniate for many practical applications. Some key physical characteristics of RHex are given in Table 1, together with the iagram in Figure 2 showing RHex in upright running moe. Boy Mass M B 8.4 kg Leg Mass M L 0.08 kg Boy Length L B 0.51 m Boy Height H B 0.14 m Leg Length (unloae) L L 0.17 m Leg Spring Constant (linear approximation) K L 1700 N/m Maximum Hip Torque τ max 5 Nm (intermittent only) Maximum Hip Spee ω max 5 rev/s For the basic hexapeal tripo gait, open loop target trajectories are shown in Figure 3, parameterize by four variables: the cycle time t c, the stance time t s, the stance angle φ s, an the leg offset wrt the boy, φ 0. The uty factor t / t etermines the ouble support s c uration, t, where both leg sets are in their slow phases, but possibly not all of them touching the groun. In a single cycle, both tripos go through their slow stance phase an fast swing phase, covering φ s, an 2π φs, respectively. During bipeal running, the front four legs are not use. The rear two legs alternate in a similar fashion as the two tripo leg sets alternate in tripo gait, prescribe by the motion profiles in Figure 3. To maintain stable running, we continuously ajust the trajectories parameters, as escribe in the subsequent section. Table 1: Basic RHex Data Figure 3: Motion profiles for left an right tripos for normal tripo gait Figure 2: Bipe running variables We moifie the hin legs as follows: we attache an aitional, ientical half-circle shape leg to each of the two hin legs, with a 180 eg offset, as shown in the iagram in Figure 2 an the photo in Figure 4. This S shape moification reuces the actuator spee requirements when not in stance, but otherwise oes not funamentally change the ynamics or control of the system. However, this change accommoates the current motor-gear spee capabilities an has facilitate this first bipeal operation. Any result reporte here coul be implemente with unmoifie legs were higher leg spees available. As we unerstan the ynamic an control better, an are able to operate at lower forwar spees, we plan to emonstrate bipeal operation without this leg moification. 2
control an leg trajectory tracking. The elements of the overall block iagram in Figure 5 are escribe below. Figure 4: High spee still photo uring single support phase in a 1 m/s bipeal run. 3 Sensing The control strategy uses minimal feeback leg angles wrt the boy, φ lr,, an boy pitch (lean) angle, θ. The two angles of the rear legs are measure by incremental optical encoers attache to the hip actuators. The boy pitch angle is measure via integrating the pitch rate from a fiber optic laser gyro. The biggest sensing challenge is the absence of a forwar velocity sensor. Instea we use a low pass filtere version of the esire leg velocities as an estimate of the actual forwar velocity. Actual forwar velocity, boy COM coorinates, leg lengths an angles after bening, leg forces, leg touchown an liftoff events, are all not easily measurable an were not available. Boy roll an yaw were available also from integrate gyro rate ata, but as yet were not use for control. 4 Control The controller is hierarchical, with three levels of PD controls for spee control, inverte penulum balance Figure 5: Control block iagram 3
Spee PD Control The input to the spee control is the esire forwar spee, x, which is converte to a esire leg stance velocity via the effective average leg length uring stance, l leg = 0.15m. The PD controller θ = x φ + sat kθp k φ θv (1) lleg generates esire pitch angles, θ, for the inverte penulum PD balancing controller. We limit this term to +/- 3.5 egrees. Commaning positive pitch angles will increase the robot spee an vice versa. Since both spee an boy pitch nee to be controlle simultaneously, but only one control input to the robot is available via the esire leg spee, φ, the spee PD control is set such that it respons more slowly than the more important inverte penulum balancing controller. Inverte Penulum PD Control The robot balancing problem is equivalent to the inverte penulum on cart problem. The linear PD control φp ( θ θ θ ) + k ( θ θ ) φ = k 0 (2) φv is use in the pitch plane. It commans leg stance accelerations, φ. A constant pitch offset angle, θ, 0 captures the ifference between the pitch angle where the robot is balance an vertical. θ is calculate online as the erivative of the esire pitch angle commans from the Spee PD Control, θ. pitch of the robot, φ 0 = θ + C 1, where C 1 is a constant. Together, the sweep angle an offset etermine the angle of the legs when the assume touchown an liftoff events occur. The fraction of the cycle that ouble leg support is assume is given by ( 2 f 1). Here, the uty factor is calculate so that a esire constant single leg support time is achieve. The uration of single leg support is a key factor that etermines the roll oscillation amplitue. The clock riven leg trajectories are upate in a 1 khz (nominal) control loop. The commane leg positions an velocities are base on a normalize time, which maps a cycle perio onto the unit interval. The cycle perio is given by φs tc =. (4) φ f Four phases are create base on the normalize time. In the case of a constant sweep velocity comman there is a stance phase, followe by a stanar three part trapezoial velocity profile as shown in Figure 6. The constant high velocity phase is characterize by the maximum leg velocity an exists only when the leg trajectory requires it. The trajectory parameters are upate uring each sampling perio. The resulting trajectories are smooth by virtue of the fact that the rate at which the trajectories are recalculate is sufficiently high. The two legs are kept 180 out of phase by having the cycle time offset of 0.5 between the legs. Integration The esire leg stance spee is obtaine via integration of the esire leg stance acceleration an the current leg stance spee estimate, via φ = φ + φ t. (3) Leg Trajectory Generator Four leg trajectory parameters are use: φ 0, φ s, φ, an f. These are irectly relate to the four stanar tripo trajectory parameters mentione previously. The sweep angle, φ s, is set to be a linear function of the esire stance velocity, φ. The offset is a function of the Figure 6: Leg trajectories for a constant sweep velocity comman Leg Trajectory PD Control The esire left an right leg trajectories are tracke with a PD controller uring stance an flight phases. 4
Low Pass Filter The leg velocities uring stance are estimate by simply passing the esire leg velocities through a 0.75 s low pass filter, ( α ) φ, 1 φ, (5), k = αφ + 1 k an the accelerations are the first orer ifference of the leg velocity estimates: ( φ, k φ, k 1 ) φ =. (6) t Roll The main failure moe currently is roll instability. For relatively small isturbances a (passively) stable small amplitue rolling oscillation is present. Larger isturbances can cause the rolling oscillations to amplify until failure. A small roll amplitue is obtaine by controlling the time that the robot is supporte by only one leg. Stability in the roll plane was primarily aresse by appropriate uty factor values an by choosing appropriate leg trajectory tracking gains. Actuator Saturation If the robot veers off to hit the wall (more than 1 m lateral travel) before the 4 m istance is traverse, this event is note as a steering failure, since active steering control has not yet been implemente. The effect of the variation in istance travele over the 4 m test track (a slight increase in actual average spee vs the quantity reporte) is neglecte. We repeat the runs until ten successful runs are obtaine. A run where the robot traverses both the start an the en tape upright without touching the walls is counte as a successful run. Results We performe 17 successive runs, to obtain 10 successful runs. All 7 iscounte runs were unsuccessful ue to steering failures the robot ran into the wall before completing the 4 m istance. Thus the success rate is 59% if we count the steering failures. None of the 17 runs faile ue to spee or boy pitch instabilities. Thus the success rate is 100% if we iscar the steering failures. The mean velocity of the ten runs was 1.08 m/s with a stanar eviation of 0.0247 m/s. Figure 7 shows stable run ata over a 5 s (approx. 5m) run. The top plot shows esire an actual boy pitch angles, with pitch errors limite to +/- 2 egrees most of the time, with occasional +/- 4 egree error spikes. Roll angles (mile plot) remain limite to +/- 5 egrees. Leg stance spee ata are relatively constant with an average error of about +/- 100 eg/s. Another major limitation in performance is actuation saturation in the retraction phase where high leg velocities are require. In orer to facilitate controller tuning two legs were attache 180 apart on each hip. In this way the istance the leg has to rotate in retraction was reuce. Once the controller stability an spee range is optimize ouble legs will be remove. Since we are only limite in spee, but not torque, a ifferent gear selection coul help solve this shortcoming. 5 Experiments Metho The robot is run repeately on a stanar linoleum floor over a 4 m istance which is emarke by start an en reflective tape. The robot is starte manually in upright posture at a istance of approximately 2 m before the start tape. The robot senses the start an en tapes via a mounte IR (infrare) sensor an stores the traversal time for average spee calculation. The with of the hallway is 2 m, an the robot is starte in the mile. Figure 7: Typical pitch, roll an leg velocity plots uring 1 m/s runs. Lighter lines inicate esire quantities ( subscripte values). Figure 8 shows the esire an actual leg angles. The trajectories are offset by 90 egrees (an not by 180 egrees as the regular tripo gait in Figure 3) ue to the S shape legs. The esire trajectories are not as simple an 5
smooth as in Figure 3 because the gait parameters are upate continuously to achieve stable bipe running. where P is the average total electrical power consume, m is the mass of the robot, g is the gravitational constant, an v is the spee of locomotion. A sample instantaneous total electrical power uring a 1 m/s run is shown in Figure 10. The power spikes occur aroun touchown an liftoff where the moment ue to gravity an inertia forces about the foot is largest. Over our ten runs it averages 107.31 W with a stanar eviation of 3.428 W. This results in a specific resistance average of 1.20 with a stanar eviation of 0.052. Figure 11 shows that this energetic performance compares very favorably with previously reporte results. Figure 8: Desire (ash) an actual (soli) hin leg trajectories. Figure 9 shows the corresponing esire an actual leg velocities (top plot) an the associate motor currents (bottom plot). Figure 10 Total electrical robot power consumption Figure 9: Top: typical esire (ash) an actual (soli) leg velocities. Bottom: motor currents. Darker/lighter lines ifferentiate left an right legs. Energy efficiency is particularly important in power autonomous mobile robot applications. As a measure of energetic efficiency the specific resistance is use [5]. The measure of the energetic cost of locomotion is calculate as P ε =, m g v Figure 11 Comparison of bipe specific resistance with other RHex gaits. Conclusion an Future Work We have shown the first stable bipeal running of RHex, an autonomous, simple, one actuate DOF per leg hexapo, with S shape, compliant hin legs an minimal sensing. Encourage by this initial success we are now 6
focusing on implementing RHex bipealism with unchange legs, implementing steering an yaw stabilization, further improving the spee range an stability through better moeling an control. In aition, we are eveloping behaviors that will permit RHex to stan up autonomously to transition from six to two legs. Acknowlegements This work was supporte by DARPA/SPAWAR contract N66001-00-C-8026. The authors woul like to thank the other RHex project s Principal Investigators an their local university teams for making this research possible, an for proviing a stimulating an supportive research environment Dr. D. E. Koitschek at University of Michigan, Dr. A. A. Rizzi at Carnegie Mellon University an in particular Dr. R. J. Full at University of California at Berkeley for proviing the inspiration for RHex an its bipeal gait, an for many relate fascinating iscussions an tutorials about animal locomotion. Furthermore we gratefully acknowlege the help the team members at McGill s Ambulatory Lab, in particular to D. McMorie, M. Smith, C. Prahacs, an D. Campbell for help with various aspects of robot esign, maintenance, sensing, logging or coing. N. Neville was supporte by the Natural Sciences an Engineering Research Council of Canaa (NSERC). [6] D. McMorie an M. Buehler, Towars Pronking with a Hexapo Robot, 4 th Int. Conf. Climbing an Walking Robots, p. 659-666, 2001. [7] E.Z. Moore an M. Buehler, Stable Stair Climbing in a Simple Hexapo, 4 th Int. Conf. Climbing an Walking Robots, p. 603-610, 2001. [8] E.Z. Moore, D. Campbell, F. Grimminger an M. Buehler, Reliable Stair Climbing in the Simple Hexapo RHex, IEEE Int. Conf. Robotics an Automation, p. 2222-2227, 2002. [9] U. Saranli, M. Buehler an D.E. Koitschek, RHex: A Simple an Highly Mobile Hexapo Robot, Int. J. Robotics Research, 20(7):616-631, July 2001. [10] U. Saranli an D.E. Koitschek, Back flips with a hexapeal robot, IEEE Int. Conf. Robotics an Automation, p.2209-2215, 2002. [11] vieo of 1999 swimming implementation at www.cim.mcgill.ca/~arlweb an www.rhex.net 231. References [1] R. Blickhan an R.J. Full, Similarity in multilegge locomotion: bouncing like a monopoe, J. Comparative Physiology, vol. A. 173, p. 509-517, 1993. [2] D. Campbell an M. Buehler, Preliminary Bouning Experiments in a Dynamic Hexapo, In B. Siciliano an P. Dario, ets, Experimental Robotics VIII, in "Lecture Notes in Control an Information Sciences, Springer-Verlag, p. 612-621, 2003. [3] R.J. Full, K. Autumn, J.I. Chung, an A. Ahn, Rapi negotiation of rough terrain by the eathhea cockroach, American Zoologist, vol. 38, p. 81A, 1998. [4] R.J. Full an M.S. Tu,. Mechanics of a rapi running insect: two-, four-, an six-legge locomotion. J. exp Biology, 156:215-231, 1991. [5] G. Gabrielli an TH. von Karman, What Price Spee?, Mechanical Engineering, 775-781, Oct 1950. 7