The geometric mechanics of undulatory robotic locomotion

International Journal of Robotics Research

Volumn 17, Issue 7, 1998, Pages 683-701

  Ostrowski, Jim ^a   Burdick, Joel ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b California Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY; MECHANICS; MOTION CONTROL; ROBOTS;

HIROSE'S ACTIVE CORD MECHANISM;

ROBOTICS;

EID: 0032120192     PISSN: 02783649     EISSN: None     Source Type: Journal    
DOI: 10.1177/027836499801700701     Document Type: Article

References (42)

1. Abraham, R., and Marsden, J. E. 1978. Foundations of Mechanics, 2nd ed. Reading, MA: Addison-Wesley.
2. Bloch, A. M., Krishnaprasad, P. S., Marsden, J. E., and Murray, R. M. 1996. Nonholonomic mechanical systems with symmetry. Archive for Rational Mechanics and Analysis 136:21-99.
3. Bloch, A. M., Reyhanoglu, M., and McClamroch, N. H. 1992. Control and stabilization of nonholonomic dynamic systems. IEEE Trans. Automat. Control 37(11):1746-1757.
4. Burdick, J., Radford, J., and Chirikjian, G. 1995. A "side-winding" locomotion gait for hyper-redundant robots. Adv. Robot. 9(3): 195-216.
5. Byrnes, C. I., and Isidori, A. 1991. On the attitude stabilization of rigid spacecraft. Automatica 27:87-95.
6. Canudas de Wit, C., and Sørdalen, O. J. 1992. Exponential stabilization of mobile robots with nonholonomic constraints. IEEE Trans. Automat. Control 37(11):1791-1797.
7. Chirikjian, G., and Burdick, J. 1995. The kinematics of hyper-redundant locomotion. IEEE Trans. Robot. Automat. 11(6):781-793.
8. Furusho, J., and Sano, A. 1990. Sensor-based control of a nine-link biped. Int. J. Robot. Res. 9(2):83-98.
9. Goodwine, B., and Burdick, J. 1995. Control systems on manifolds with boundary. Technical Report RMS 95-01, California Institute of Technology.
10. Hirose, S. 1993. Biologically Inspired Robots: Snake-Like Locomotors and Manipulators (transl.). Peter Cave and Charles Goulden. Oxford: Oxford University Press.
11. Hirose, S., Masui, T., Kikuchi, H., Fukuda, Y., and Umetani, Y. 1985 (Tokyo, Japan). Titan III: A quadruped walking vehicle. 2nd Int. Symp. on Robot. Res. Cambridge, MA: MIT Press.
12. Hirose, S., and Morishima, A. 1990. Design and control of a mobile robot with an articulated body. Int. J. Robot. Res. 9(2):99-114.
13. Hirose, S., and Umetani, Y. 1976. Kinematic control of active cord mechanism with tactile sensors. Proc. 2nd Int. CISM-IFT Symp. on Theory and Practice of Robots and Manipulators, pp. 241-252.
14. Isidori, A. 1989. Nonlinear Control Systems: An Introduction. Berlin: Springer-Verlag.
15. Kajita, S., and Tani, K. 1991 (Sacramento, CA). Study of dynamic biped locomotion on nigged terrain. Proc. IEEE Int. Conf. Robot. and Automat. Los Alamitos, CA: IEEE, pp. 1405-1411.
16. Kelly, S. D., and Murray, R. M. 1995. Geometric phases and locomotion. J. Robot. Sys. 12(6):417-431.
17. Koditschek, D., and Bühler, M. 1991. Analysis of a simplified hopping robot. Int. J. Robot. Res. 10(6):587-605.
18. Krishnaprasad, P. S., and Tsakiris, D. P. 1994 (Lake Buena Vista, FL). G-snakes: Nonholonomic kinematic chains on Lie groups. Proc. 33rd IEEE Conf. on Decision and Control, IEEE, pp. 2955-2960.
19. Laumond, J.-P., Jacobs, P., Taix, M., and Murray, R. M. 1994. A motion planner for nonholonomic mobile robots. IEEE Trans, on Robot. Automat. 10(5):577-593.
20. Marsden, J. E. 1992. Lectures on Mechanics. New York: Cambridge University Press.
21. Marsden, J. E., and Ratiu, T. S. 1994. Introduction to Mechanics and Symmetry. New York: Springer-Verlag.
22. McGeer, T. 1990. Passive dynamic walking. Int. J. Robot. Res. 9(2):62-82.
23. M'Closkey, R., and Burdick, J. 1993. On the periodic motions of a hopping robot with vertical and forward motion. Int. J. Robot. Res. 12(3):197-218.
24. M'Closkey, R. T., and Murray, R. M. 1995. Exponential stabilization of driftless nonlinear control systems using homogeneous feedback. Technical Report CIT/CDS 95-012, California Institute of Technology.
25. Miura, H., and Shimoyama, I. 1984. Dynamic walk of a biped. Int. J. Robot. Res. 3(2):60-74.
26. Montgomery, R. 1990. Isoholonomic problems and some applications. Comm. Math. Physics 128(3):565-592.
27. Murray, R. M., Li, Z., and Sastry, S. S. 1994. A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC Press.
28. Murray, R. M., and Sastry, S. S. 1993. Nonholonomic motion planning: Steering using sinusoids. IEEE Trans. Automat. Control 38(5):700-716.
29. Nakamura, Y., and Mukherjee, R. 1993. Exploiting nonholonomic redundancy of free-flying space robots. IEEE Trans. Robot. Automat. 9(4):499-506.
30. Ostrowski, J., and Burdick, J. 1997. Controllability tests for mechanical systems with symmetries and constraints. J. Appl. Math. Comp. Sci. 7(2):101-127.
31. Ostrowski, J. P. 1995. The mechanics and control of undulatory robotic locomotion. Ph.D. Thesis, California Institute of Technology, Pasadena, CA. Available electronically at http://www.cis.upenn.edu/̃jpo/papers.html.
32. Ostrowski, J. P., and Burdick, J. W. forthcoming. Computing reduced equations for mechanical systems with constraints and symmetries.
33. Ostrowski, J. P., Burdick, J. W., Lewis, A. D., and Murray, R. M. 1995 (Nagoya). The mechanics of undulatory locomotion: The mixed kinematic and dynamic case. P roc. IEEE Int. Robot. and Automat. IEEE, pp. 1945-1951.
34. Ostrowski, J. P., Lewis, A. D., Murray, R. M., and Burdick, J. W. 1994 (San Diego, CA). Nonholonomic mechanics and locomotion: The snakeboard example. Proc. IEEE Int. Conf. Robot. and Automat. IEEE, pp. 2391-2397.
35. Raibert, M. 1986. Legged Robots that Balance. Cambridge, MA: MIT Press.
36. Rouchon, P., Fliess, M., Levine, J., and Martin, P. 1992. Flatness and motion planning: The car with n trailers. Proc. European Control Conf., pp. 1518-1522.
37. Shapere, A., and Wilczek, F. 1989. Geometry of self-propulsion at low Reynolds number. J. Fluid Mech. 198:557-585.
38. Song, S., and Waldron, K. 1989. Machines that Walk: The Adaptive Suspension Vehicle. Cambridge, MA: MIT Press.
39. Teel, A., Murray, R. M., and Walsh, G. 1995. Nonholonomic control systems: From steering to stabilization with sinusoids. Int. J. Control 62(4):849-870.
40. Tsakiris, D. P. 1995. Motion control and planning for nonholonomic kinematic chains. Ph.D. Thesis, University of Maryland.
41. Vakakis, A., Burdick, J. W., and Caughey, T. 1991. An interesting attractor in the dynamics of a hopping robot. Int. J. of Robot. Res. 10(6):606-618.
42. Walsh, G. C., and Sastry, S. S. 1995. On reorienting linked rigid bodies using internal motions. IEEE Trans. Robot. Automat. 11(1):139-146.