Hybrid zero dynamics of planar biped walkers

IEEE Transactions on Automatic Control

Volumn 48, Issue 1, 2003, Pages 42-56

  Westervelt, E R ^a   Grizzle, J W ^a   Koditschek, D E ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Bipeds; Hybrid systems; Poincar sections; Under actuated system; Zero dynamics

Indexed keywords

ACTUATORS; CONTROL EQUIPMENT; DEGREES OF FREEDOM (MECHANICS); DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL; OPTIMIZATION; ROBOTS; WALKING AIDS;

HYBRID SYSTEMS; ZERO DYNAMICS;

BIPED LOCOMOTION;

EID: 0037246813     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2002.806653     Document Type: Article

References (64)

1. ROBEA, C. Chevallereau. [Online]. Available: http://www-lag.ensieg.inpg.fr/prc-bipedes/english/
2. Robotics publication, J.W. Grizzle. [Online]. Available: http://www.eecs.umich.edu/grizzle/papers/robotics.html
3. V. I. Babitsky, Theory of Vibro-Impact Systems and Applications, ser. Foundations of Engineering Mechanics. Berling, Germany: Springer-Verlag, 1998.
4. S. P. Banks, Control Systems Engineering. Upper Saddle River, NJ: Prentice-Hall, 1986.
5. M. D. Berkemeier and R. S. Fearing, "Tracking fast inverted trajectories of the underactuated acrobot," IEEE Trans. Robot. Automat., vol. 15, pp. 740-750, Aug. 1999.
6. P. Bézier, Numerical Control: Mathematics and Applications. New York: Wiley, 1972.
7. S. P. Bhat and D. S. Bernstein, "Continuous finite-time stabilization of the translational and rotational double integrators," IEEE Trans. Automat. Contr., vol. 43, pp. 678-682, May 1998.
8. _, "Finite-time stability of continuous autonomous systems," SIAM J. Control Optim., vol. 38, pp. 751-766, 2000.
9. W. M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry. New York: Academic, 1975.
10. B. Brogliato, Nonsmooth Impact Dynamics: Models, Dynamics and Control. London, U.K.: Springer-Verlag, 1996, vol. 220, Lecture Notes in Control and Information Sciences.
11. M. Bühler, D. E. Koditschek, and P. J. Kindlmann, "A family of robot control strategies for intermittent dynamical environments," IEEE Control Syst. Mag., vol. 10, pp. 16-22, Feb. 1990.
12. G. Cabodevilla and G. Abba, "Quasi optimal gait for a biped robot using genetic algorithm," in Proc. IEEE Int. Conf. Systems, Man, Cybernetics, Computational Cybernetics Simulations, Orlando, FL, Oct. 1997, pp. 3960-3965.
13. C. Chevallereau, "Parameterized control for an underactuated biped robot," presented at the IFAC 2002, Barcelona, Spain, July 2002.
14. C. Chevallereau and Y. Aoustin, "Optimal reference trajectories for walking and running of biped robot," Robotica, vol. 19, no. 5, pp. 557-569, Sept. 2001.
15. C. Chevallereau, A. Formal'sky, and B. Perrin, "Control of a walking robot with feet following a reference trajectory derived from ballistic motion," in Proc. IEEE Int. Conf. Robotics Automation, Albuquerque, NM, Apr. 1997, pp. 1094-1099.
16. C. Chevallereau and P. Sardain, "Design and actuation optimization of a 4 axes biped robot for walking and running," in Proc. IEEE Int. Conf. Robotics Automation, San Francisco, CA, Apr. 2000, pp. 3365-3370.
17. C. K. Chow and D. H. Jacobson, "Studies of human locomotion via optimal programming," Math. Biosci., vol. 10, pp. 239-306, 1971.
18. M. Conditt and F. Mussa-Ivaldi, "Central representation of time during motor learning," in Proc. National Academy Sciences USA, vol. 96, Sept. 1999, pp. 11625-11630.
19. J. J. Craig, Introduction to Robotics: Mechanics and Control. Reading, MA: Addison-Wesley, 1989.
20. B. Espiau and A. Goswani, "Compass gait revisited," in Proc. IFAC Symp. Robot Control, Capri, Italy, Sept. 1994, pp. 839-846.
21. R. Full and D. Koditschek, "Templates and anchors: Neuromechanical hypotheses of legged locomotion on land," J. Experiment. Biol., vol. 202, pp. 3325-3332, Dec. 1999.
22. A. Goswani, B. Espiau, and A. Keramane, "Limit cycles and their stability in a passive bipedal gait," in Proc. IEEE Int. Conference on Robotics and Automation, Minneapolis, MN, Apr. 1996, pp. 246-251.
23. J. W. Grizzle, G. Abba, and F. Plestan, "Proving asymptotic stability of a walking cycle for a five dof biped robot model," in Proc. 2nd Int. Conf. Climbing and Walking Robots, CLAWAR-99, Portsmouth, UK, Sept. 1999, pp. 69-81.
24. _, "Asymptotically stable walking for biped robots: Analysis via systems with impulse effects," IEEE Trans. Automat. Contr., vol. 46, pp. 51-64, Jan. 2001.
25. V. T. Haimo, "Finite time controllers," SIAM J. Control Optim., vol. 24, no. 4, pp. 760-770, 1986.
26. M. W. Hardt, "Multibody dynamical algorithms, numerical optimal control, with detailed studies in the control of jet engine compressors and biped walking," Ph.D. dissertation, Univ. California, San Diego, CA, 1999.
27. Y. Hasegawa, T. Arakawa, and T. Fukuda, "Trajectory generation for biped locomotion," Mechatronics, vol. 10, no. 1-2, pp. 67-89, Mar. 2000.
28. H. Hatze, "The complete optimization of a human motion," Math. Biosci., vol. 28, pp. 99-135, 1976.
29. K. Hirai, M. Hirose, Y. Haikawa, and T. Takenake, "The development of honda humanoid robot," in Proc. IEEE Int. Conf. Robotics Automation, Leuven, Belgium, May 1998, pp. 1321-1326.
30. Y. Hurmuzlu and D. B. Marghitu, "Rigid body collisions of planar kinematic chains with multiple contact points," Int. J. Robot. Res., vol. 13, no. 1, pp. 82-92, 1994.
31. A. Isidori, Nonlinear Control Systems: An Introduction, 3rd ed. Berlin, Germany: Springer-Verlag, 1995.
32. A. Isidori and C. Moog, "On the nonlinear equivalent of the notion of transmission zeros," in Proc. IIASA Conf.: Modeling Adaptive Control, C. Byrnes and A. Kurzhanski, Eds., Berlin, Germany, 1988, pp. 146-157.
33. K. Ito, F. Matsuno, and R. Takahashi, "Underactuated crawling robot," in Proc. IEEE Int. Conf. Intelligent Robotos Systems, Takamatsu, Japan, Oct.-Nov. 2000, pp. 1684-1689.
34. S. Kajita and K. Tani, "Experimental study of biped dynamic walking," IEEE Control Syst. Mag., vol. 16, pp. 13-19, Feb. 1996.
35. R. Katoh and M. Mori, "Control method of biped locomotion giving asymptotic stability of trajectory," Automatica, vol. 20, no. 4, pp. 405-414, 1984.
36. M. Kawato, "Internal models for motor control and trajectory planning," Current Opinion Neurobiol., vol. 9, pp. 718-727, 1999.
37. D. D. Koditschek and M. Buhler, "Analysis of a simplified hopping robot," Int. J. Robot. Res., vol. 10, no. 6, pp. 587-605, 1991.
38. D. W. Marhefka and D. Orin, "Simulation of contact using a nonlinear damping model," in Proc. IEEE Int. Conf. Robotics Automation, Minneapolis, MN, Apr. 1996, pp. 1662-1668.
39. T. G. McGee and M. W. Spong, "Trajectory planning and control of a novel walking biped," in Proc. IEEE Int. Conf. Control Applications, Mexico City, Mexico, Sept. 2001, pp. 1099-1104.
40. R. M. Murray, Z. Li, and S. Sastry, A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC, 1993.
41. J. Nakanishi, T. Fukuda, and D. Koditschek, "A brachiating robot controller," IEEE Trans. Robot. Automat., vol. 16, pp. 109-123, Apr. 2000.
42. H. Nijmeijer and A. J. van der Schaft, Nonlinear Dynamical Control Systems. Berlin, Germany: Springer-Verlag, 1989.
43. K. Oho, R. Takahashi, A. Imadu, and T. Shimada, "Self-excitation control for biped walking mechanism," in Proc. IEEE Int. Conf. Intelligent Robots Systems, Takamatsu, Japan, Oct.-Nov. 2000, pp. 1143-1148.
44. K. Oho, K. Yamamoto, and A. Imadu, "Control of giant swing motion of a two-link horizontal bar gymnastic robot," Adv. Robot., vol. 15, no. 4, pp. 449-465, 2001.
45. F. Plestan, J. W. Grizzle, E. R. Westervelt, and G. Abba, "Stable walking of a 7-dof biped robot," IEEE Trans. Robot. Automation., to be published.
46. J. Pratt, M. C. Chee, A. Torres, P. Dilworth, and G. Pratt, "Virtual model control: An intuitive approach for bipedal locomotion," Int. J. Robot. Res., vol. 20, no. 2, pp. 129-143, Feb. 2001.
47. J. Pratt and G. Pratt, "Intuitive control of a planar bipedal walking robot," in Proc. IEEE Int. Conf. Robot. Automat., Leuven, Belgium, May 1998, pp. 2014-2021.
48. M. H. Raibert, S. Tzafestas, and C. Tzafestas, "Comparative simulation study of three control techniques applied to a biped robot," in Proc. IEEE Int. Conf. Systems, Man, Cybernetics Systems Engineering Service Humans, Le Touquet, France, Oct. 1993, pp. 494-502.
49. A. Rizzi and D. Koditschek, "An active visual estimator for dexterous manipulation," IEEE Trans. Robot. Automat., vol. 12, pp. 697-713, Oct. 1996.
50. D. F. Rogers and J. A. Adams, Mathematical Elements for Computer Graphics, 2nd ed. New York: McGraw-Hill, 1990.
51. J. A. Rosas-Flores, J. Alvarez-Gallegos, and R. Castro-Linares, "Stabilization of a class of underactuated systems," in Proc. IEEE Int. Conf. Decision Control, Sydney, Australia, Dec. 2000, pp. 2168-2173.
52. M. Rostami and G. Bessonnet, "Sagittal gait of a biped robot during the single support phase," Robotica, vol. 19, pp. 163-176, Mar.-Apr. 2001.
53. _, "Sagittal gait of a biped robot during the single support phase, part 2: Optimal motion," Robotica, vol. 19, pp. 241-253, May-June 2001.
54. L. Roussel, "Génération de Trajectoires de Marche Optimales Pour un Robot Bipède," Ph.D., Institut National Polytechinque, Grenoble, France, 1998.
55. L. Roussel, C. Canudas-de Wit, and A. Goswami, "Generation of energy optimal complete gait cycles for biped robots," in Proc. IEEE Int. Conf. Robotics Automation, Leuven, Belgium, May 1998, pp. 2036-2041.
56. A. Sano and J. Furusho, "Realization of natural dynamic walking using the angular momentum information," in Proc. IEEE Int. Conf. Robotics Automation, Cincinnati, OH, May 1990, pp. 1476-1481.
57. U. Saranli, W. Schwind, and D. Koditschek, "Toward the control of a multi-jointed, monoped runner. In," in Proc. IEEE Int. Conf. Robotics Automation, Leuven, Belgium, May 1998, pp. 2676-2682.
58. C. L. Shih and W. A. Graver, "Control of a biped robot in the double-support phase," IEEE Trans. Syst., Man, Cybern., vol. 22, pp. 729-735, Aug. 1992.
59. M. W. Spong, "The swing up control problem for the acrobot," IEEE Control Syst. Mag., vol. 15, pp. 49-55, Feb. 1995.
60. _, "Passivity based control of the compass gait biped," presented at the IFAC World Congr., Beijing, China, July 1999.
61. M. W. Spong and M. Vidyasagar, Robot Dynamics and Control. New York: Wiley, 1989.
62. O. von Stryk, DIRCOL User's Guide, 2.1 ed. Müchen, Germany: Technische Universität Müchen, Zentrum Mathematik (SCB), Lehrstuhl M2 Höhere Mathematik und Numerische Mathematik, 1999.
63. E. R. Westervelt, J. W. Grizzle, and C. C. de Wit, "Switching and PI control of walking motions of planar biped walkers," IEEE Trans. Automat. Contr., to be published.
64. H. Ye, A. N. Michel, and L. Hou, "Stability theory for hybrid dynamical systems," IEEE Trans. Automat. Contr., vol 43, pp. 461-474, Apr. 1998.