Radial basis function network architecture for nonholonomic motion planning and control of free-flying manipulators

This paper considers a problem of nonholonomic motion planning. A practical paradigm for planning and stabilization of motion in a class of multivariate nonlinear (nonholonomic) systems is presented and applied to a planar free-floating manipulator system. The controller architecture designed in the paper is based on the radial basis function approximation of an optimal control program for any desired motion. This architecture also incorporates a sampled-data feedback stabilization algorithm. The proposed control technique overcomes certain problems associated with other control approaches available for nonholonomic systems. The presented simulation results reveal a promising potential of the proposed control paradigm. This paradigm can be extended to a broader class of nonlinear control problems.

[1]  Jean-Michel Coron,et al.  Global asymptotic stabilization for controllable systems without drift , 1992, Math. Control. Signals Syst..

[2]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[3]  Dimitry M. Gorinevsky.  Direct learning of feedforward control for manipulator path tracking , 1992, Proceedings of the 1992 IEEE International Symposium on Intelligent Control.

[4]  A. Goldenberg,et al.  Design of smooth dynamic feedback for stabilization of nonholonomic systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[5]  S. Shankar Sastry,et al.  Dynamic Control of Redundant Manipulators , 1988, 1988 American Control Conference.

[6]  C. Micchelli.  Interpolation of scattered data: Distance matrices and conditionally positive definite functions , 1986 .

[7]  Thomas H. Connolly,et al.  Comparison of Some Neural Network and Scattered Data Approximations: The Inverse Manipulator Kinematics Example , 1994, Neural Computation.

[8]  Yoshihiko Nakamura,et al.  Nonholonomic path planning of space robots via bi-directional approach , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[9]  Robert M. Sanner,et al.  Gaussian Networks for Direct Adaptive Control , 1991, 1991 American Control Conference.

[10]  S. Shankar Sastry,et al.  Dynamic control of redundant manipulators , 1989, J. Field Robotics.

[11]  Stephen A. Billings,et al.  International Journal of Control , 2004 .

[12]  Mahmut Reyhanoglu,et al.  Planar Reorientation Maneuvers of Space Multibody Systems Using Internal Controls , 1992 .

[13]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[14]  D.M. Gorinevsky.  Learning and approximation in database for feedforward control of flexible manipulator , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[15]  F. Girosi,et al.  Networks for approximation and learning , 1990, Proc. IEEE.

[16]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[17]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[18]  Zexiang Li,et al.  Smooth Time-Periodic Feedback Solutions for Nonholonomic Motion Planning , 1993 .

[19]  Andrew A. Goldenberg,et al.  Dynamic control and motion planning technique for a class of nonlinear systems with drift , 1993 .

[20]  Nira Dyn,et al.  Interpolation of scattered Data by radial Functions , 1987, Topics in Multivariate Approximation.

[21]  Steven Dubowsky,et al.  On the nature of control algorithms for free-floating space manipulators , 1991, IEEE Trans. Robotics Autom..

[22]  R. Brockett.  Control Theory and Singular Riemannian Geometry , 1982 .

[23]  R. V. Dooren,et al.  A Chebyshev technique for solving nonlinear optimal control problems , 1988 .

[24]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[25]  H. Hermes,et al.  Nonlinear Controllability via Lie Theory , 1970 .

[26]  A. Bloch,et al.  Control and stabilization of nonholonomic dynamic systems , 1992 .

[27]  Dimitry M. Gorinevsky.  Learning Open-Loop Terminal Control , 1992, 1992 American Control Conference.