A near-optimal control approach to 3D ball-in-socket joint space robot models with initial angular momenta

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