Decentralized adaptive sliding mode control of a space robot actuated by control moment gyroscopes

An adaptive sliding mode control (ASMC) law is proposed in decentralized scheme for trajectory tracking control of a new concept space robot. Each joint of the system is a free ball joint capable of rotating with three degrees of freedom (DOF). A cluster of control moment gyroscopes (CMGs) is mounted on each link and the base to actuate the system. The modified Rodrigues parameters (MRPs) are employed to describe the angular displacements, and the equations of motion are derived using Kane's equations. The controller for each link or the base is designed separately in decentralized scheme. The unknown disturbances, inertia parameter uncertainties and nonlinear uncertainties are classified as a "lumped" matched uncertainty with unknown upper bound, and a continuous sliding mode control (SMC) law is proposed, in which the control gain is tuned by the improved adaptation laws for the upper bound on norm of the uncertainty. A general amplification function is designed and incorporated in the adaptation laws to reduce the control error without conspicuously increasing the magnitude of the control input. Uniformly ultimate boundedness of the closed loop system is proved by Lyapunov's method. Simulation results based on a three-link system verify the effectiveness of the proposed controller.