A simply stabilized running model

SIAM Review

Volumn 47, Issue 3, 2005, Pages 519-549

  Ghigliazza, R M ^a   Altendorfer, R ^b   Holmes, P ^a   Koditschek, D ^c  

^a Princeton University   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Bifurcation; Legged locomotion; Periodic gaits; Spring loaded inverted pendulum; Stability

Indexed keywords

BIFURCATION (MATHEMATICS); BIOMECHANICS; CONTROL THEORY; GAIT ANALYSIS; GRAVITATIONAL EFFECTS; SYSTEM STABILITY;

LEGGED LOCOMOTION; PERIODIC GAITS; SPRING LOADED INVERTED PENDULUM;

MATHEMATICAL MODELS;

EID: 24644499424     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/050626594     Document Type: Article

References (59)

1. R. M. Alexander, Principles of Animal Locomotion, Princeton University Press, Princeton, NJ, 2003.
2. J. Nishii, Legged insects select the optimal pattern based on the energetic cost, Biol. Cybernet., 83 (2000), pp. 435-442.
3. R. Full, D. R. Stokes, A. Ahn, and R. K. Josephson, Energy absorption during running by leg muscles in a cockroach, J. Experimental Biol., 201 (1998), pp. 997-1012.
4. K. G. Pearson, Central programming and reflex control of walking in the cockroach, J. Experimental Biol., 56 (1972), pp. 173-193.
5. M. Ahmadi and M. Buehler, Stable control of a simulated one-legged running robot with hip and leg compliance, IEEE Trans. Robotics Automation, 13 (1997), pp. 96-104.
6. J. K. Hodgkins and M. H. Raibert, Adjusting step length for rough terrain locomotion, IEEE Trans. Robotics Automation, 7 (1991), pp. 289-298.
7. G. M. Nelson and R. D. Quinn, Posture control, IEEE Control Systems Magazine, 19 (1999), pp. 9-14.
8. R. Full and D. E. Koditschek, Templates and anchors: Neuromechanical hypothesis of legged locomotion on land, J. Experimental Biol., 83 (1999), pp. 3325-3332.
9. R. Blickhan and R. Full, Similarity in multilegged locomotion: Bouncing like a monopode, J. Comp. Physiol. A, 173 (1993), pp. 509-517.
10. M. H. Dickinson, C. T. Farley, R. J. Full, M. A. R. Koehl, R. Kram, and S. Lehman, How animals move: An integrative view, Science, 288 (2000), pp. 100-106.
11. R. Altendorfer, N. Moore, H. Komsuoglu, M. Buehler, H. B. Brown, Jr., D. McMordie, U. Saranli, R. Full, and D. E. Koditschek, RHex: A biologically inspired hexapod runner, Autonomous Robots, 11 (2001), pp. 207-213.
12. T. McGeer, Passive dynamic walking, Int. J. Robotics Res., 9 (1990), pp. 62-82.
13. M. Garcia, A. Chatterjee, A. Ruina, and M. J. Coleman, The simplest walking model: Stability, complexity and scaling, ASME J. Biomech. Engrg., 120 (1998), pp. 281-288.
14. M. J. Coleman and A. Ruina, An uncontrolled walking toy that cannot stand still, Phys. Rev. Lett., 80 (1998), pp. 3658-3661.
15. M. J. Coleman, M. Garcia, K. Mombaur, and A. Ruina, Prediction of stable walking for a toy that cannot stand, Phys. Rev. E, 64 (2001), article 022901-1-3.
16. S. H. Collins, A. Ruina, R. Tedrake, and M. Wisse, Efficient bipedal robots based on passive-dynamic walkers, Science, 305 (2005), pp. 1082-1085.
17. K. D. Mombaur, R. W. Longman, H. G. Bock, and J. P. Schlöder, Stable one-legged hopping without feedback and with a point foot, in Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Vol. 4, Washington, DC, 2002, pp. 3978-3983.
18. E. Celaya and J. M. Porta, A control structure for the locomotion of a legged robot on difficult terrain, IEEE Robotics and Automation Magazine, 5 (1998), pp. 43-51.
19. T. Kubow and R. Full, The role of the mechanical System in control: A hypothesis of self-stabilization in hexapedal runners, Phil. Trans. Roy. Soc. London Ser. B Biol. Sci., 354 (1999), pp. 849-861.
20. J. Schmitt and P. Holmes, Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane I. Theory, Biol. Cybernet., 83 (2000), pp. 501-515.
21. J. Schmitt and P. Holmes, Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane II. Application, Biol. Cybernet., 83 (2000), pp. 517-527.
22. J. Schmitt and P. Holmes, Mechanical models for insect locomotion: Stability and parameter studies, Phys. D, 156 (2001), pp. 139-168.
23. J. Schmitt, M. Garcia, R. Razo, P. Holmes, and R. J. Full, Dynamics and stability of legged locomotion in the horizontal plane: A test case using insects, Biol. Cybernet., 86 (2002), pp. 343-353.
24. D. L. Jindrich and R. J. Full, Dynamic stabilization of rapid hexapedal locomotion, J. Exp. Biol., 205 (2002), pp. 2803-2823.
25. A. Seyfarth, H. Geyer, M. Günther, and R. Blickhan, A movement criterion for running, J. Biomech., 35 (2002), pp. 649-655.
26. H. Geyer, A. Seyfarth, and R. Blickhan, Spring mass running: Simple approximate solution and application to gait stability, J. Theor. Biol., 232 (2005), pp. 315-328.
27. A. Ruina, Non-holonomic stability aspects of piecewise holonomic systems, Rep. Math. Phys., 42 (1998), pp. 91-100.
28. P. Holmes, R. J. Full, D. E. Kotitschek, and J. Guckenheimer, The dynamics of legged locomotion: Models, analyses, and challenges, SIAM Rev., to appear.
29. U. Saranli, M. Buehler, and D. E. Koditschek, RHex: A simple and highly mobile hexapod robot, Internat. J. Robotics Res., 20 (2001), pp. 616-631.
30. M. Vukobratovic and B. Borovac, Zero-moment point: Thirty five years of its life, Int. J. Humanoid Robotics, 1 (2004), pp. 157-173.
31. L. Geppert, Qrio, the robot that could, IEEE Spectrum, 41 (2004), pp. 34-37.
32. E. R. Westervelt, J. W. Grizzle, and D. E. Koditschek, Hybrid zero dynamics of planar biped walkers, IEEE Trans. Automat. Control, 48 (2003), pp. 42-56.
33. C. Chevallereau, E. R. Westervelt, and J. W. Grizzle, A symptotic stabilization of a five-link, four-actuator, planar bipedal runner, in Proceedings of the 43rd IEEE Conference on Decision and Control, IEEE Press, Bahamas, 2004, pp. 303-310.
34. D. E. Koditschek, R. J. Full, and M. Buehler, Mechanical aspects of legged locomotion control, Arthropod Structure and Development, 33 (2004), pp. 251-272.
35. U. Saranli and D. E. Koditschek, Template based control of hexapedal running., in Proceedings of the IEEE Conference on Robotics and Automation, IEEE Press, Taipei, Taiwan, 2003, pp. 1374-1379.
36. R. Altendorfer, R. M. Ghigliazza, P. Holmes, and D. E. Koditschek, Exploiting passive stability for hierarchical control, in Proceedings of the Fifth International Conference on Climbing and Walking Robots (CLAWAR 2002), Professional Engineering Publishing Limited, London, 2002, pp. 177 184.
37. A. Seyfarth and H. Geyer, Natural control of spring-like running-optimized self-stabilization, in Proceedings of the Fifth International Conference on Climbing and Walking Robots (CLAWAR 2002), Professional Engineering Publishing Limited, London, 2002, pp. 81-85.
38. A. Seyfarth, H. Geyer, and H. Herr, Swing leg retraction: A simple control model for stable running, J. Exp. Biol., 206 (2003), pp. 2547-2555.
39. R. Altendorfer, D. E. Koditschek, and P. Holmes, Stability analysis of legged locomotion models by symmetry-factored return maps, Int. J. Robotics Res., 23 (2004), pp. 979-999.
40. R. Altendorfer, D. E. Koditschek, and P. Holmes, Stability analysis of a clock-driven rigid-body SLIP model for RHex, Int. J. Robotics Res., 23 (2004), pp. 1001-1012.
41. F. Gubina, H. Hemami, and R. B. McGhee, On the dynamic stability of biped locomotion, IEEE Trans. Biomedical Engrg., 21 (1974), pp. 102-108.
42. A. Back, J. Guckenheimer, and M. Myers, A dynamical simulation facility for hybrid systems, in Hybrid Systems, Lecture Notes in Comput. Sci. 736, Springer-Verlag, Berlin, 1993, pp. 649-655.
43. J. Guckenheimer and S. Johnson, Planar hybrid systems, in Hybrid Systems II, Lecture Notes in Comput. Sci. 999, Springer-Verlag, Berlin, 1995, pp. 202-225.
44. M. H. Raibert, Legged Robots that Balance, MIT Press, Cambridge, MA, 1986.
45. H. Goldstein, Classical Mechanics, 2nd ed., Addison-Wesley, Reading, MA, 1980.
46. W. J. Schwind and D. E. Koditschek, Approximating the stance map of a 2 DOF monoped runner, J. Nonlinear Sci., 10 (2000), pp. 533-568.
47. R. Blickhan, The spring-mass model for running and hopping, J. Biomech., 11/12 (1989), pp. 1217-1227.
48. V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, 1978.
49. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1990.
50. C. T. Farley and O. González, Leg stiffness and stride frequency in human running, J. Biomech., 29 (1995), pp. 181-186.
51. W. J. Schwind, Spring Loaded Inverted Pendulum Running: A Plant Model, Ph.D. thesis, University of Michigan, Ann Arbor, MI, 1998.
52. U. Saranli, W. J. Schwind, and D. E. Koditschek, Toward the control of a multi-jointed, monoped runner, in Proceedings of the IEEE International Conference on Robotics and Automation, Leuven, Belgium, 1998, pp. 2676-2682.
53. W. J. Schwind and D. E. Koditschek, Characterization of monoped equilibrium gaits, in Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque, NM, 1997, pp. 1986-1992.
54. M. J. Coleman and P. Holmes, Motions and stability of a piecewise holonomic system: The discrete Chaplygin sleigh, Regul. Chaotic Dyn., 4 (1999), pp. 55-77.
55. J. I. Neimark and N. A. Fufaev, Dynamics of Nonholonomic Systems, Transl. Math. Monogr. 33, AMS, Providence, RI, 1972.
56. P. G. Drazin and W. H. Reid, Hydrodynamic Stability, Cambridge University Press, Cambridge, UK, 1981.
57. J. Seipel and P. Holmes, Three-dimensional running is unstable but easily stabilized, in Proceedings of the Seventh International Conference on Climbing and Walking Robots (CLAWAR 2004), Springer-Verlag, New York, 2005, in press.
58. J. Seipel And P. Holmes, Running in three dimensions: Analysis of a point-mass springy-leg model, Int. J. Robotics Res., to appear.
59. S. Carver, Control of a Spring-Mass Hopper, Ph.D. thesis, Cornell University, Ithaca, NY, 2003.