Adaptive Invariant Manifold Based Switching Control for Planer Two-Link Space Robot

Abstract

Controlling of a space robot without actuators on the main body is an underactuated control problem. As stabilization methods, time-varying feedback controllers, discontinuous feedback controllers, center manifold based methods, zero-dynamics methods, and sliding mode controllers have been proposed. However, these methods sometime suffer from slow rate of convergence. In addition, modeling errors and delay time have not been sufficiently considered in the past studies. In order to obtain faster convergence time and compensate modeling errors and delay time, the adaptive invariant manifold based switching control method is proposed. Firstly the link angles are controlled to reach the invariant manifold by constant periodic motion and the modeling error is estimated by a discrete adaptive method. In the first stage, the delay time is also detected by measuring the difference between the predicted response and the actual one. Secondly the angular velocity rate of the two links is controlled to constant so that the state slides on the invariant manifold and reaches the goal state. In order to evaluate performance of the proposed control method, numerical simulations are conducted for not only the case with modeling error, but also with delay time.