Approximate Perturbation Stance Map of the SLIP Runner and Application to Locomotion Control

doi:10.1016/S1672-6529(11)60138-8

Abstract

Abstract:

This paper presents a novel method of perturbation to obtain the analytic approximate solution to the Spring-Loaded Inverted Pendulum (SLIP) dynamics in stance phase with considering the effect of gravity. This perturbation solution achieves higher accuracy in predicting the apex state variables than the typical existing analytic approximations. Particularly, our solution is validated for non-symmetric trajectory of hopping in a large angle range. Furthermore, the stance controller of the SLIP runner is developed to regulate the apex state based on the approximate apex return map. To compensate the energy variation between the current and desired apex states, a stiffness adjustment of the leg spring in stance phase is presented. The deadbeat controller of the angle of attack is designed to track the regulated apex height and velocity. The simulation demonstrates that the SLIP runner applying the proposed stance controller reveals higher tracking accuracy and more rapidly converges to the regulated apex state.

Key words: legged locomotion, spring-loaded inverted pendulum, perturbation, apex return map, stiffness adjustment

Haitao Yu, Mantian Li, Pengfei Wang, Hegao Cai. Approximate Perturbation Stance Map of the SLIP Runner and Application to Locomotion Control[J].J4, 2012, 9(4): 411-422.

References

[1] Raibert M H. Legged Robots that Balance. MIT Press, Cambridge, USA, 1986.

[2] Gregorio P, Ahmadi M, Buehler M. Design, control and energetics of an electrically actuated legged robot. IEEE Transaction on Systems, Man and Cybernetics, 1997, 27, 626–634.

[3] Altendorfer R, Longman R W, Buehler M. Rhex: A biologically inspired hexapod runner. Autonomous Robots, 2001, 11, 207–213.

[4] Poulakakis I, Papadopoulos E, Buehler M. On the stability of the passive dynamics of quadruped running with a bounding gait. International Journal of Robotics Research, 2006, 25, 669–687.

[5] Buehler M, Playter R, Raibert M. Robots step outside. Proceedings of the 5 th International Symposium of Adaptive Motion of Animals and Machines (AMAM), Iimenau, Germany, 2005.

[6] R. Blickhan. The spring-mass model for running and hopping. Journal of Biomechanics, 1989, 185, 27–40.

[7] Ghigliazza R M, Altendorfer R, Holmes P. A simply stabilized running model. SIAM Journal of Applied Dynamical Systems, 2003, 2, 187–218.

[8] Schwind W J, Koditschek D E. Approximating the stance map of a 2-DOF monoped runner. Journal of Nonlinear Science, 2000, 10, 533–568.

[9] Geyer H, Seyfarth A, Blickhan R. Spring-mass running: simple approximate solution and application to gait stability. Journal of Theoretical Biology, 2005, 232, 315–328.

[10] Arslan Ö, Saranli U, Morgül Ö. An approximate stance map of the spring mass hopper with gravity correction for nonsymmetric locomotion. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Kobe, Japan, 2009, 2388–2393.

[11] Seyfarth A, Geyer H, Herr H. Swing-leg retraction: a simple control model for stable running. Journal of Experimental Biology, 2003, 206, 2547–2555.

[12] Schmitt J, Clark J. Modeling posture-dependent leg actuation in sagittal plane locomotion. Bioinspiration & Biomimetics, 2009, 4, 1–17.

[13] Saranli U, Arslan Ö, Ankarh M. Approximate analytic solutions to non-symmetric stance trajectories of the passive spring-loaded inverted pendulum with damping. Nonlinear Dynamics, 2010, 62, 729–742.

[14] Holmes P. Poinca?e, celestial mechanics, dynamical-systems theory and ‘chaos’. Physics Reports, 1990, 193, 137–163.

[15] Closkey R, Burdick J. Periodic motions of a hopping robot with vertical and forward motion. International Journal of Robotics Research, 1993, 12, 197–218.

[16] Nayfeh A H. Introduction to Perturbation Techniques. John Wiley & Sons Press, Canada, 1981.

[17] Seyfarth A, Geyer H, Gunther M. A movement criterion for running. Journal of Biomechanics, 2002, 35, 649–655.

[18] Uyanik ?, Saranli U, Morgül Ö. Adaptive control of a spring-mass hopper. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, 2011, 2138–2143.

[19] Kalveram K T, Haeufle D, Seyfarth A, Grimmer S. Energy management that generates terrain following versus apex-preserving hopping in man and machine. Biological Cybernetics, 2012, 106, 1–13.

[20] Saranli U, Arslan Ö, Ankarah M, Morgül Ö. Approximate analytic solutions to non-symmetric stance trajectories of the passive spring-loaded inverted pendulum with damping. Nonlinear Dynamics, 2010, 62, 729–742.

[21] Farley C T, Gonzalez O. Leg stiffness and stride frequency in human running. Journal of Biomechanics, 1996, 29, 181–186.

[22] Ferris D P, Louie M, Farley C T. Running in the real world: adjusting the leg stiffness for different surfaces. Proceedings of the Royal Society B: Biological Sciences, 1998, 265, 989–994.

[23] Nikooyan A A, Zadpoor A A, Mass-spring-damper modelling of the human body to study running and hopping an overview. Journal of Engineering in Medicine, 2011, 225, 1121–1135.

[24] Roberts T J, Azizi E. Flexible mechanisms: the diverse roles of biological springs in vertebrate movement. Journal of Experimental Biology, 2011, 214, 353–361.

[25] Weyand P G, Bundle M W. Point : artificial limbs do make artificially fast running speeds possible. Journal of Applied Physiology, 2010, 103, 1011–1023.

[26] Blickhan R, Full R J. Similarity in multi-legged locomotion: bouncing like a monopode. Journal of Comparative Physiology A, 1993, 173, 509–517.

Quick Search Adv. Search