An open-loop control for underactuated manipulators using oscillatory inputs: steering capability of an unactuated joint

An open-loop control for underactuated mechanical systems using oscillatory inputs with amplitude and frequency modulations is investigated. Once all actuated joints are moved to their desired positions, oscillatory inputs are applied to an actuated joint to move the remaining unactuated joints. The steering force of the unactuated joints is achieved by utilizing the dynamic coupling between actuated and unactuated joints. Such a dynamic coupling occurs due to the oscillatory motions of an actuated joint. Once the frequency of the oscillatory input is decided, the amplitude is determined by analyzing a time-invariant system, which is derived from the unactuated joint dynamics by the method of averaging. A systematic way, via a generating equation and a coordinate transformation derived from the generating equation, for converting the unactuated joint dynamics into the standard form of averaging is proposed. In the event of an actuator failure in outer space, the failed joint can be steered by adopting the method proposed. Illustrating examples are given. Experimental results are provided.

[1]  Warren P. Seering,et al.  Time-Optimal Negative Input Shapers , 1997 .

[2]  Yoshihiko Nakamura,et al.  Nonlinear control of a nonholonomic free joint manipulator with the averaging method , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[3]  Y. Nakamura,et al.  Control of 2R underactuated manipulator with friction , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[4]  Semyon M. Meerkov,et al.  Vibrational control of nonlinear systems: Vibrational stabilizability , 1986 .

[5]  Yoshihiko Nakamura,et al.  Control of manipulators with free-joints via the averaging method , 1997, Proceedings of International Conference on Robotics and Automation.

[6]  N. Bogolyubov,et al.  Asymptotic Methods in the Theory of Nonlinear Oscillations , 1961 .

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

[8]  Giuseppe Oriolo,et al.  Stabilization of underactuated robots: theory and experiments for a planar 2R manipulator , 1997, Proceedings of International Conference on Robotics and Automation.

[9]  Yoshihiko Nakamura,et al.  Nonlinear behavior and control of a nonholonomic free-joint manipulator , 1997, IEEE Trans. Robotics Autom..

[10]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[11]  Keum-Shik Hong,et al.  Vibrational stabilization of nonlinear parabolic systems with Neumann boundary conditions , 1991 .

[12]  J. Bentsman,et al.  Transient behavior analysis of vibrationally controlled nonlinear parabolic systems with Neumann boundary conditions , 1993, IEEE Trans. Autom. Control..

[13]  Keum-Shik Hong,et al.  Vibrational control of underactuated mechanical systems: control design through the averaging analysis , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[14]  S. Peresada,et al.  Feedback linearizing control of switched reluctance motors , 1987 .

[15]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[16]  Keum-Shik Hong,et al.  Stability Criterion For Linear Oscillatory Parabolic Systems , 1992 .

[17]  Erik I. Verriest,et al.  Vibrational control of nonlinear time lag systems with bounded delay: averaging theory, stabilizability, and transient behavior , 1994, IEEE Trans. Autom. Control..

[18]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[19]  Keum Shik Hong,et al.  Vibrational control of nonlinear time lag systems: Vibrational stabilization and transient behavior , 1991, Autom..

[20]  Scott A. Bortoff.  Approximate state-feedback linearization using spline functions , 1997, Autom..

[21]  Giuseppe Oriolo,et al.  Steering a class of redundant mechanisms through end-effector generalized forces , 1998, IEEE Trans. Robotics Autom..

[22]  Yangsheng Xu,et al.  Optimal control sequence for underactuated manipulators , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[23]  Fumihito Arai,et al.  Swing and locomotion control for a two-link brachiation robot , 1993, IEEE Control Systems.

[24]  Keum Shik Hong,et al.  Application of averaging method for integro-differential equations to model reference adaptive control of parabolic systems , 1994, Autom..

[25]  Semyon Meerkov,et al.  Principle of vibrational control: Theory and applications , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

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

[27]  Susumu Tachi,et al.  Dynamic control of a manipulator with passive joints in operational space , 1993, IEEE Trans. Robotics Autom..

[28]  Keum-Shik Hong,et al.  Vibrational control of underactuated mechanical systems control design through averaging analysis , 1999 .

[29]  C. Samson.  Control of chained systems application to path following and time-varying point-stabilization of mobile robots , 1995, IEEE Trans. Autom. Control..

[30]  Mark W. Spong,et al.  The swing up control problem for the Acrobot , 1995 .

[31]  Semyon M. Meerkov,et al.  Vibrational control of nonlinear systems: Vibrational controllability and transient behavior , 1986 .