Attitude control of a space platform/manipulator system, using internal motion, is an example of a nonholonomic motion plan ning (NMP) problem arising from symmetry and conservation laws. Common to NMP problems are that an admissible con figuration space path is constrained to a given nonholonomic distribution. We formulate the dynamic equations of a system consisting of a 3-DOF PUMA-like manipulator attached to a space platform (e.g., a space station or a satellite) as an NMP problem and discuss the controllability of the system. Then we describe the application of a simple algorithm for obtaining approximate optimal solutions. We conclude with a descrip tion of simulation software implementing the algorithm and simulation results for two experiments.
References
1.
Abraham, R., and Marsden, J.1978. Foundations of Mechanics. 2nd ed. Reading, MA: Benjamin/Cummings Publishing Company.
2.
Bloch, A., McClamroch, N., and Reyhanoglu, M.1990. Controllability and stabilizability properties of a nonholonomic control system. Conf. on Decision and Control , pp. 1312-1314.
3.
Brenan, K., Campbell, S., and Petzold, L.1989. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. New York: North-Holland .
4.
Brockett, R.1981. Control theory and singular Riemannian geometry . In Hilton, P., and Young, G. (eds.): New Directions in Applied Mathematics. New York: Springer-Verlag, pp. 11-27.
5.
Brockett, R.W.1988. On the rectification of vibratory motion. Proceedings of Microactuators and Micromechanism , Salt Lake City, UT.
6.
Canny, J., and Lin, M.1990. An opportunistic global path planner. Proceedings of IEEE International Conference on Robotics and Automation , pp. 1554-1559.
7.
Coron, J.M.1991. Global asymptotical stabilization for controllable system without drift. Mathematics of Control, Signals and Systems5(3 )
8.
. Dubowsky, S., and Torres, M.1991. Path planning for space manipulators to minimize spacecraft attitude disturbance. Proceedings of IEEE International Conference on Robotics and Automation, pp. 2522-2528.
9.
Fernandes, C., Gurvits, L., and Li, Z.1991a. An efficient algorithm for optimal nonholonomic motion planningProceedings of IEEE International Conference on Robotics and Automation.
10.
Fernandes, C., Gurvits, L., and Li, Z.1991b. Foundations of nonholonomic motion planning. Technical report. Robotics Research Laboratory, Courant Institute of Mathematical Sciences.
11.
Fernandes, C., Gurvits, L., and Li, Z.1994. Near-optimal nonholonomic motion planning for a coupled rigid-body system. IEEE Trans. Auto. Control March: 39(3).
Gurvits, L., and Li, Z.1992. Smooth time-periodic feedback solutions for nonholonomic motion planning. In Li,Z.,and Canny,J.(eds.): Nonholonomic Motion Planning . Boston: Kluwer Academic Publishers.
14.
Haynes, G., and Hermes, H.1970. Nonlinear controllability via Lie theory. SIAM J. Control8(4):450-460.
15.
Koditschek, D.1987. Exact robot navigation by means of potential functions: Some topological considerations. Proceedings of IEEE International Conference on Robotics and Automation, pp. 1-6.
16.
Lafferriere, G., and Sussmann, H.1990. Motion planning for controllable systems without drift: A preliminary report. Technical report. Rutgers University Systems and Control Center Report SYCON-90-04.
17.
Li, Z., and Montgomery, R.1990. Dynamics and optimal control of a legged robot in flight phase. Proceedings of IEEE International Conference on Robotics and Automation.
18.
Montgomery, R.1992. Nonholonomic control and gauge theory. In Li, Z., and Canny, J. (eds.): Nonholonomic Motion Planning . Boston: Kluwer Academic Publishers .
19.
Murray, R., and Sastry, S.1990. Grasping and manipulation using multifingered robot hands . In Brockett, R. (ed.): Robotics: Proceedings of Symposia in Applied Mathematics. Vol. 41. Providence, RI: American Mathematical Society, pp. 91-128.
20.
Nakamura, Y., and Mukherjee, R.1990. Nonholonomic path planning of space robotics via bidirectional approach. Proceedings of IEEE International Conference on Robotics and Automation.
21.
Papadopoulos, E., and Dubowsky, S.1990. On the nature of control algorithms for space manipulators . Proceedings of IEEE International Conference on Robotics and Automation.
22.
Reyhanoglu, M., McClamroch, N., and Bloch, A.1992. Motion planning for nonholonomic dynamic systems . In Li, Z., and Canny, J. (eds.): Nonholonomic Motion Planning . Boston: Kluwer Academic Publishers.
23.
Sussmann, H., and Liu, W.1991. Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories. Technical report. Rutgers University Center for System and Control Report, SYCON-91-02.
24.
Sussmann, H., and Liu, W.1992. Lie bracket extensions and averaging: The single-bracket case. In Li, Z., and Canny, J. (eds.): Nonholonomic Motion Planning. Boston: Kluwer Academic Publishers.
25.
Vafa, Z., and Dubowsky, S.1987. On the dynamics of manipulators in space using the virtual manipulator approach. Proceedings of IEEE International Conference on Robotics and Automation.
26.
Vafa, Z., and Dubowsky, S.1990. On the dynamics of space manipulators using virtual manipulator, with applications to path planning. J. Astronaut. Sci.38(4).
