Attitude control of the space robot with two arms of single degree of freedom

This paper deals with an attitude control of the space robot having two arms. These arms are located at both ends of the base, and they are perpendicular to each other, As there are no external torques, the inputs only act as internal torques generated by joint motors. By exploiting the non-integrability of the conservation law of angular momentum, the system can be expressed as a 5-state 2-input nonholonomic system that is controllable with second order of two generators. Based on time-state control form, the system can be transformed into two time-state control form subsystems. We propose a control strategy to switching each subsystem, The transformed subsystems are time-varying, the convergence in the neighborhood of the origin is assured based on quadratic stability by LMI.

[1]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[2]  O. J. Sørdalen,et al.  Exponential stabilization of nonholonomic chained systems , 1995, IEEE Trans. Autom. Control..

[3]  Mitsuji Sampei,et al.  A control strategy for a class of nonholonomic systems - time-state control form and its application , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[4]  François Delebecque,et al.  LMITOOL: a Package for LMI Optimization in Scilab User's Guide , 1995 .

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

[6]  Mitsuji Sampei,et al.  Simultaneous control of position and orientation for ball-plate manipulation problem based on time-State control form , 2004, IEEE Transactions on Robotics and Automation.

[7]  Ilya Kolmanovsky,et al.  Developments in nonholonomic control problems , 1995 .

[8]  Jean-Baptiste Pomet.  Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift , 1992 .

[9]  Takateru Urakubo,et al.  Discontinuous feedback stabilization of a class of nonholonomic systems based on Lyapunov control , 2005, Proceedings of the Fifth International Workshop on Robot Motion and Control, 2005. RoMoCo '05..

[10]  Mitsuji Sampei,et al.  Necessary and sufficient conditions for transformation of nonholonomic system into time-state control form , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[11]  P. Hughes.  Spacecraft Attitude Dynamics , 1986 .

[12]  A. Astolfi.  Discontinuous control of nonholonomic systems , 1996 .

[13]  M. Ishikawa.  SWITCHING FEEDBACK CONTROL OF NON-HOLONOMIC SYSTEMS WITH MULTI-GENERATORS , 2002 .

[14]  Richard M. Murray,et al.  Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems , 1994, Math. Control. Signals Syst..

[15]  Masato Ishikawa.  Symmetric Affine Systems with Two-Generators: Topology and Discontinuous Feedback Control , 2001 .

[16]  Mitsuji Sampei,et al.  Time-State Control Form and its Application to a Non-Holonomic Space Robot , 1995 .

[17]  Mitsuji Sampei,et al.  An adaptive control of a nonholonomic space robot , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[18]  Mitsuji Sampei,et al.  Manipulation problem of a ball between two parallel plates based on time-state control form , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[19]  C. C. Wit,et al.  On the Construction of Stabilizing Discontinuous Controllers for Nonholonomic Systems , 1995 .