Nonlinear control of a nonholonomic free joint manipulator with the averaging method

In our previous work, we analyzed nonlinear behaviours of a 2DOF free-joint manipulator with a periodic input and developed a positioning of the both joints by modulating the amplitude of the input. The strategy was effective but very heuristic and cannot be applied to other systems. In this paper, we apply the averaging method to the system and derive its behaviour from the averaged system. We also discuss its feedback control and design a feedback stabilization to a desired manifold. Even though its concept is the same as in Suzuki et al. (1996), the control strategy is analytically constructed. The feedback control is designed by a Lyapunov function for the averaged system and it is also effective for the real system.

[1]  Giuseppe Oriolo,et al.  Free-joint manipulators: motion control under second-order nonholonomic constraints , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[2]  S. Wiggins.  Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[3]  Yoshihiko Nakamura,et al.  Chaos and nonlinear control of a nonholonomic free-joint manipulator , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[4]  F. Verhulst,et al.  Averaging Methods in Nonlinear Dynamical Systems , 1985 .

[5]  Susumu Tachi,et al.  Position control of manipulator with passive joints using dynamic coupling , 1991, IEEE Trans. Robotics Autom..

[6]  Yoshihiko Nakamura,et al.  Control of Nonholonomic Mechanisms with Drift , 1995 .