Approximate analytic solutions to non-symmetric stance trajectories of the passive Spring-Loaded Inverted Pendulum with damping

Nonlinear Dynamics

Volumn 62, Issue 4, 2010, Pages 729-742

  Saranli, Uluç ^c   Arslan, Ömür ^a   Ankarali, M Mert ^b   Morgül, Ömer ^a  

^a BILKENT UNIVERSITY   (Turkey)

^b MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

^c NONE

Author keywords

Analytic approximations; Damping; Gait control; Hybrid dynamical systems; Legged locomotion; Spring Loaded Inverted Pendulum

Indexed keywords

ANALYTIC APPROXIMATION; GAIT CONTROL; HYBRID DYNAMICAL SYSTEMS; LEGGED LOCOMOTION; SPRING LOADED INVERTED PENDULUMS;

CONTROLLERS; DYNAMICAL SYSTEMS; PENDULUMS; POSITION CONTROL; TRAJECTORIES;

DAMPING;

EID: 78049461582     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-010-9757-8     Document Type: Article

References (37)

1. M. Ahmadi M. Buehler 2006 Controlled passive dynamic running experiments with the ARL-monopod II IEEE Trans. Robot. 22 5 974 986 10.1109/TRO.2006.878935 (Pubitemid 44604863)
2. R.M. Alexander 1990 Three uses for springs in legged locomotion Int. J. Robot. Res. 9 2 53 61 10.1177/027836499000900205
3. R.M. Alexander A.S. Jayes 1978 Vertical movement in walking and running J. Zoology, Lond. 185 27 40 10.1111/j.1469-7998.1978.tb03311.x
4. R. Altendorfer D.E. Koditschek P. Holmes 2004 Stability analysis of legged locomotion models by symmetry-factored return maps Int. J. Robot. Res. 23 10-11 979 999 10.1177/0278364904047389
5. A. Arampatzis G.-P. Briggemann V. Metzler 1999 The effect of speed on leg stiffness and joint kinematics in human running J. Biomech. 32 1349 1353 10.1016/S0021-9290(99)00133-5 (Pubitemid 29490880)
6. Arslan, O.: Model based methods for the control and planning of running robots. M.Sc., Bilkent Univ., Ankara, Turkey, July (2009)
7. Arslan, O., Saranli, U., Morgul, O.: Reactive footstep planning for a planar spring-mass hopper. In: Proceedings of the International Conference on Intelligent Robots and Systems, St. Louis, MO, October (2009)
8. R. Blickhan R.J. Full 1993 Similarity in multilegged locomotion: bouncing like a monopode J. Comp. Physiol. A Neuroethol. Sens. Neural Behav. Physiol. 173 5 509 517
9. Carver, S.: Control of a spring-mass hopper. Ph.D., Cornell University, January (2003)
10. J.G. Cham J.K. Karpick M.R. Cutkosky 2004 Stride period adaptation of a biomimetic running hexapod Int. J. Robot. Res. 23 2 141 153 10.1177/ 0278364904041323
11. J. Diamond 1983 Why animals run on legs, not on wheels Discover 4 9 64 67 728399
12. C.T. Farley D.P. Ferris 1998 Biomechanics of walking and running: center of mass movements to muscle action Exerc. Sport Sci. Rev. 26 253 283 10.1249/00003677-199800260-00012
13. R.J. Full D.E. Koditschek 1999 Templates and anchors: neuromechanical hypotheses of legged locomotion J. Exp. Biol. 202 3325 3332
14. H. Geyer A. Seyfarth R. Blickhan 2005 Spring-mass running: simple approximate solution and application to gait stability J. Theor. Biol. 232 3 315 328 2120902
15. P. Gregorio M. Ahmadi M. Buehler 1997 Design, control, and energetics of an electrically actuated legged robot IEEE Trans. Syst. Man Cybern. 27 4 626 634 10.1109/3477.604106
16. S. Grimmer M. Ernst M. Gunther R. Blickhan 2008 Running on uneven ground: leg adjustment to vertical steps and self-stability J. Exp. Biol. 211 18 2989 3000 10.1242/jeb.014357
17. P. Holmes 1990 Poincaré, celestial mechanics, dynamical-systems theory and "chaos" Phys. Rep. 193 137 163 10.1016/0370-1573(90)90012-Q 1076345 (Review Section of Physics Letters)
18. P. Holmes R. Full D. Koditschek J. Guckenheimer 2006 The dynamics of legged locomotion: models, analyses, and challenges SIAM Rev. 48 2 207 304 10.1137/S0036144504445133 2240592 (Pubitemid 43842340)
19. Hurst, J.W., Chestnutt, J.E., Rizzi, A.A.: Design and philosophy of the BiMASC, a highly dynamic biped. In: Proceedings of the International Conference on Robotics and Automation, pp. 1863-1868, April 10-14, Roma (2007)
20. D.L. Jindrich M. Qiao 2009 Maneuvers during legged locomotion Chaos 19 2 026105 10.1063/1.3143031 2548760
21. D.E. Koditschek M. Buehler 1991 Analysis of a simplified hopping robot Int. J. Robot. Res. 10 6 587 605 10.1177/027836499101000601
22. M. LaBarbera 1983 Why the wheels won't go Am. Nat. 121 3 395 408 10.1086/284068 (Pubitemid 14272794)
23. G.M. Nelson R.D. Quinn 1999 Posture control of a cockroach-like robot IEEE Control Syst. Mag. 19 2 9 14 10.1109/37.753930
24. Playter, R., Buehler, M., Raibert, M.: BigDog. Proc. SPIE 6230 (2006). doi: 10.1117/12.084087
25. Poulakakis, I., Grizzle, J.W.: Formal embedding of the spring loaded inverted pendulum in an asymmetric hopper. In: Proceedings of the European Control Conference, Kos (2007)
26. I. Poulakakis E. Papadopoulos M. Buehler 2006 On the stability of the passive dynamics of quadrupedal running with a bounding gait Int. J. Robot. Res. 25 7 669 687 10.1177/0278364906066768 (Pubitemid 43936807)
27. Pratt, J., Pratt, G.: Intuitive control of a planar bipedal walking robot. In: Proceedings of the International Conference on Robotics and Automation, pp. 2014-2021, Leuven, Belgium (1998)
28. Raibert, M.: Legged Robots that Balance. MIT Press Series in Artificial Intelligence. MIT Press, Boston (1986)
29. Saranli, U.: Dynamic locomotion with a hexapod robot. Ph.D., The University of Michigan, Ann Arbor, MI, September (2002)
30. Saranli, U., Koditschek, D.E.: Template based control of hexapedal running. In: Proceedings of the IEEE International Conference on Robotics and Automation, vol. 1, pp. 1374-1379, Taipei, Taiwan, September (2003)
31. Saranli, U., Schwind, W.J., Koditschek, D.E.: Toward the control of a multi-jointed, monoped runner. In: Proceedings of the IEEE International Conference on Robotics and Automation, vol. 3, pp. 2676-2682, New York (1998)
32. U. Saranli M. Buehler D.E. Koditschek 2001 RHex: a simple and highly mobile robot Int. J. Robot. Res. 20 7 616 631 10.1177/02783640122067570 (Pubitemid 34566119)
33. Sato, A., Buehler, M.: A planar hopping robot with one actuator: design, simulation, and experimental results. In: Proceedings of the International Conference on Intelligent Robots and Systems, vol. 4, pp. 3540-3545, Sept.-2 Oct., Sendai (2004)
34. J. Schmitt 2006 A simple stabilizing control for sagittal plane locomotion J. Comput. Nonlinear Dyn. 1 4 348 357 10.1115/1.2338650 (Pubitemid 44762419)
35. Schwind, W.J.: Spring loaded inverted pendulum running: a plant model. Ph.D., University of Michigan, Ann Arbor (1998)
36. W.J. Schwind D.E. Koditschek 2000 Approximating the stance map of a 2 DOF monoped runner J. Nonlinear Sci. 10 5 533 568 10.1007/s003320010001 1786317
37. Zeglin, G.: The Bow Leg hopping robot. Ph.D., Carnegie Mellon University, Pittsburgh, CMU-RI-TR-99-33, October (1999)