Nonlinear model predictive control for constrained mechanical systems with state jump

In this paper, a nonlinear model predictive control (MPC) scheme for constrained mechanical systems with state discontinuity, or state jump, is examined. The proposed control method extends a fast numerical algorithm based on continuation and GMRES methods, allowing online implementation for mechanical systems possible. The validity of the strategy is demonstrated through numerical simulations, applying the method to landing control of a simplified humanoid model. The system is constrained to restrict the position of the zero moment point (ZMP) of the robot and state discontinuity exists at the landing instant.

[1]  Toshiyuki Ohtsuka,et al.  Nonlinear receding horizon control of an RC hovercraft , 2002, Proceedings of the International Conference on Control Applications.

[2]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[3]  Mark Cannon,et al.  Efficient nonlinear model predictive control algorithms , 2004, Annu. Rev. Control..

[4]  Masaki Yamakita,et al.  An extension of nonlinear receding horizon control for switched system with state jump , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[5]  M. Vukobratovic,et al.  On the stability of anthropomorphic systems , 1972 .

[6]  C. V. Rao,et al.  Steady states and constraints in model predictive control , 1999 .

[7]  C. Kelley.  Iterative Methods for Linear and Nonlinear Equations , 1987 .

[8]  D. Mayne,et al.  Robust receding horizon control of constrained nonlinear systems , 1993, IEEE Trans. Autom. Control..

[9]  Raymond A. DeCarlo,et al.  Continuation methods: Theory and applications , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  H. Michalska,et al.  Receding horizon control of nonlinear systems , 1988, Proceedings of the 28th IEEE Conference on Decision and Control,.

[11]  James B. Rawlings,et al.  Tutorial overview of model predictive control , 2000 .

[12]  Toshiyuki Ohtsuka,et al.  Continuation/GMRES method for fast algorithm of nonlinear receding horizon control , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[13]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[14]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .