Control of a 3D Ball-in-Socket Joint Space Robot Model with Initial Angular Momentum based on the Near-Optimal Control Algorithm

Abstract

Control of space robots in 3D space is known as a difficult problem in nonlinear control theory, and if there exists initial angular momentum for space robots, the control problem becomes an increasing challenge. However, it is quite important to take into account the existence of initial angular momentum from the aspect of realistic situations. This paper deals with a control problem for a 3D space robot of two rigid bodies with initial angular momentum. First, we derive give a model of a space robot with initial angular momentum, called the ball-in-socket joint model. We next propose a near-optimal control method for nonlinear affine control systems based on the finite dimensional Fourier basis and give some theoretical analysis on the method. Moreover, a near-optimal control algorithm is also shown. Then, we apply the near-optimal control algorithm to a 3D attitude control problem for the ball-in-socket joint model with initial angular momentum, and illustrate a numerical simulation to show the effectiveness of our method.