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Abstract

A motion planning algorithm is described for bounding over rough terrain with the LittleDog robot. Unlike walking gaits, bounding is highly dynamic and cannot be planned with quasi-steady approximations. LittleDog is modeled as a planar five-link system, with a 16-dimensional state space; computing a plan over rough terrain in this high-dimensional state space that respects the kinodynamic constraints due to underactuation and motor limits is extremely challenging. Rapidly Exploring Random Trees (RRTs) are known for fast kinematic path planning in high-dimensional configuration spaces in the presence of obstacles, but search efficiency degrades rapidly with the addition of challenging dynamics. A computationally tractable planner for bounding was developed by modifying the RRT algorithm by using: (1) motion primitives to reduce the dimensionality of the problem; (2) Reachability Guidance, which dynamically changes the sampling distribution and distance metric to address differential constraints and discontinuous motion primitive dynamics; and (3) sampling with a Voronoi bias in a lower-dimensional “task space” for bounding. Short trajectories were demonstrated to work on the robot, however open-loop bounding is inherently unstable. A feedback controller based on transverse linearization was implemented, and shown in simulation to stabilize perturbations in the presence of noise and time delays.

Keywords

Legged locomotion rough terrain bounding motion planning LittleDog RRT reachability-guided RRT transverse linearization

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References

Altendorfer R. , Moore N. , Komsuoglu H. , Buehler M. , Brown HB , McMordie D. , et al. (2001) RHex: A biologically inspired hexapod runner . Autonomous Robots 11: 207-213.

Berges P. and Bowling A. ( 2006) Rebound, slip, and compliance in the modeling and analysis of discrete impacts in legged locomotion. Journal of Vibration and Control 12: 1407-1430.

Byl K. , Shkolnik A. , Prentice S. , Roy N. and Tedrake R. ( 2008) Reliable dynamic motions for a stiff quadruped . In Proceedings of the 11th International Symposium on Experimental Robotics (ISER), Athens, Greece.

Byl K. and Tedrake R. ( 2009) Dynamically diverse legged locomotion for rough terrain . In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 09), Kobe, Japan.

Chan N. , Kuffner J. and Zucker M. ( 2008) Improved motion planning speed and safety using regions of inevitable collision. In 17th CISM-IFToMM Symposium on Robot Design, Dynamics, and Control (RoManSy’08), Tokyo, Japan.

Cheng P. ( 2005) Sampling-based Motion Planning with Differential Constraints. Ph.D. thesis, University of Illinois at Urbana-Champaign , IL.

Chestnutt J. , Lau M. , Cheung KM , Kuffner J. , Hodgins JK and Kanade T. ( 2005) Footstep planning for the honda asimo humanoid . In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 05), Barcelona .

Chevallereau C. , Abba G. , Aoustin Y. , Plestan F. , Westervelt ER , Canudas-De-Wit C. , et al. (2003). Rabbit: a testbed for advanced control theory. IEEE Control Systems Magazine 23: 57-79.

Collins SH , Ruina A. , Tedrake R. and Wisse M. ( 2005) Efficient bipedal robots based on passive-dynamic walkers . Science 307: 1082-1085.

10.

Fraichard T. ( 2007) A short paper about motion safety. In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 07), Rome, Italy, pp. 1140-1145.

11.

Fraichard T. and Asama H. ( 2003) Inevitable collision states. a step towards safer robots? In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 03), Volume 1, Las Vegas, NV, pp. 388-393.

12.

Frazzoli E. , Dahleh M. and Feron E. ( 2005) Maneuver-based motion planning for nonlinear systems with symmetries. IEEE Transactions on Robotics 21: 1077-1091.

13.

Frazzoli E. , Dahleh MA and Feron E. ( 2002) Real-time motion planning for agile autonomous vehicles . Journal of Guidance, Control, and Dynamics 25: 116-129.

14.

Gilardi G. and Sharf I. ( 2002) Literature survey of contact dynamics modelling . Mechanism and Machine Theory 37:1213-1239.

15.

Hahn W. ( 1967) Stability of Motion. Berlin : Springer-Verlag.

16.

Hale JK ( 1980) Ordinary Differential Equations. New York: Robert E. Krieger Publishing Company.

17.

Harada K. , Hattori S. , Hirukawa H. , Morisawa M. , Kajita S. and Yoshida E. ( 2007) Motion planning for walking pattern generation of humanoid . In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 07), pp. 4227-4233.

18.

Hauser J. and Chung CC ( 1994) Converse Lyapunov functions for exponentially stable periodic orbits. Systems and Control Letters 23: 27-34.

19.

Hauser K. ( 2008) Motion Planning for Legged and Humanoid Robots . Ph.D. thesis, Stanford.

20.

Hauser K. , Bretl T. , Latombe J-C. , Harada K. and Wilcox B. ( 2008) Motion planning for legged robots on varied terrain . The International Journal of Robotics Research 27: 1325-1349.

21.

Hirose M. and Ogawa K. ( 2007) Honda humanoid robots development. Philosophical Transactions of the Royal Society 365: 11-19.

22.

Hunt KH and Crossley FRE ( 1975) Coefficient of restitution interpreted as damping in vibroimpact . Journal of Applied Mechanics Series E 42: 440-445.

23.

Kajita S. , Kanehiro F. , Kaneko K. , Fujiware K. , Harada K. , Yokoi K. , et al. (2003) Biped walking pattern generation by using preview control of zero-moment point. In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 03), Taipei, Taiwan, pp. 1620-1626.

24.

Kaneko K. , Kanehiro F. , Kajita S. , Hirukawa H. , Kawasaki T. , Hirata M. , et al. (2004) Humanoid robot HRP-2. In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 04), New Orleans, LA, pp. 1083-1090.

25.

Kavraki L. , Svestka P. , Latombe J. and Overmars M. ( 1996) Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Transactions on Robotics and Automation 12(4): 566-580.

26.

Kolter JZ , Rodgers MP and Ng AY ( 2008) A control architecture for quadruped locomotion over rough terrain. In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 08), Pasadena, CA, pp. 811-818.

27.

Kuffner JJ , Kagami S. , Nishiwaki K. , Inaba M. and Inoue H. ( 2002) Dynamically-stable motion planning for humanoid robots . Autonomous Robots 12: 105-118.

28.

Kuffner JJ , Nishiwaki K. , Kagami S. , Inaba M. and Inoue H. ( 2003) Motion planning for humanoid robots. In Dario P and Chatila R (Eds), ISRR (Springer Tracts in Advanced Robotics , volume 15). Berlin: Springer, pp. 365-374.

29.

LaValle S. and Branicky M. ( 2002) On the relationship between classical grid search and probabilistic roadmaps. In Proceedings of the Workshop on the Algorithmic Foundations of Robotics, Nice , France.

30.

LaValle SM ( 2006) Planning Algorithms. Cambridge : Cambridge University Press.

31.

LaValle SM and Kuffner JJ ( 2001) Randomized kinodynamic planning. The International Journal of Robotics Research 20: 378-400.

32.

Manchester, IR ( 2010) Transverse dynamics and regions of stability for nonlinear hybrid limit cycles. arXiv:1010.2241 [math.OC].

33.

Manchester IR , Mettin U. , Iida F. and Tedrake R. ( 2009) Stable dynamic walking over rough terrain: Theory and experiment. In Proceedings of the International Symposium on Robotics Research (ISRR), Lucerne, Switzerland.

34.

Marhefka D. and Orin D. ( 1996) Simulation of contact using a nonlinear damping model . In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 96), Vol. 2, Minneapolis, MN, pp. 1662-1668.

35.

Pongas D. , Mistry M. and Schaal S. ( 2007) A robust quadruped walking gait for traversing rough terrain . In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 07).

36.

Pratt JE and Tedrake R. ( 2005) Velocity based stability margins for fast bipedal walking . In Proceedings of the First Ruperto Carola Symposium on Fast Motions in Biomechanics and Robotics: Optimization and Feedback Control , Vol. 340, pp. 299-324.

37.

Raibert M. , Blankespoor K. , Nelson G. , Playter R. and the BigDog Team (2008) Bigdog, the rough-terrain quadruped robot. Proceedings of the 17th World Congress of the International Federation of Automatic Control .

38.

Raibert M. , Chepponis M. and Brown H. ( 1986) Running on four legs as though they were one. IEEE Journal of Robotics and Automation 2: 70-82.

39.

Raibert MH ( 1986) Legged Robots That Balance. Cambridge, MA: The MIT Press.

40.

Ratliff N. , Zucker M. , Bagnell JAD and Srinivasa S. ( 2009) Chomp: Gradient optimization techniques for efficient motion planning. In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 09), Kobe, Japan.

41.

Rebula J. , Neuhaus P. , Bonnlander B. , Johnson M. and Pratt J. ( 2007) A controller for the littledog quadruped walking on rough terrain. Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 07).

42.

Sakagami Y. , Watanabe R. , Aoyama C. , Matsunaga S. and Fujimura NHK ( 2002) The intelligent ASIMO: system overview and integration . In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 02), Vol. 3, Switzerland, pp. 2478-2483.

43.

Shiriaev AS , Freidovich LB and Manchester IR ( 2008) Can we make a robot ballerina perform a pirouette? Orbital stabilization of periodic motions of underactuated mechanical systems . Annual Reviews in Control 32: 200-211.

44.

Shkolnik A. and Tedrake R. ( 2009) Path planning in 1000+ dimensions using a task-space Voronoi bias. In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 09), Kobe, Japan.

45.

Shkolnik A. , Walter M. and Tedrake R. ( 2009) Reachability-guided sampling for planning under differential constraints. In Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 09), Kobe, Japan, pp. 2859-2865.

46.

Song G. and Zefran M. ( 2006) Stabilization of hybrid periodic orbits with application to bipedal walking. In Proceedings of the 2006 American Control Conference, Minneapolis, MN.

47.

Sugihara T. ( 2004) Mobility Enhancement Control of Humanoid Robot based on Reaction Force Manipulation via Whole Body Motion. Ph.D. thesis, University of Tokyo.

48.

Westervelt ER , Grizzle JW , Chevallereau C. , Choi JH and Morris B. ( 2007) Feedback Control of Dynamic Bipedal Robot Locomotion . Boca Raton, FL: CRC Press.

49.

Westervelt ER , Grizzle JW and Koditschek DE ( 2003) Hybrid zero dynamics of planar biped walkers. IEEE Transactions on Automatic Control 48: 42-56.

50.

Yershova A. , Jaillet L. , Simeon T. and LaValle S. ( 2005) Dynamic-domain RRTs: Efficient exploration by controlling the sampling domain. Proceedings of the IEEE/RAS International Conference on Robotics and Automation (ICRA 05), pp. 3856-3861.

51.

Zucker M. ( 2009) A Data-Driven Approach to High Level Planning. PhD thesis, Carnegie Mellon University, available at http://www.cs.cmu.edu/mzucker/mz-thesis-proposal.pdf.

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