Laguerre Model Predictive Control for Accompanying Satellite Trajectory Generation

This paper proposes a Laguerre Model Predictive Control (LMPC) method for trajectory generation of the accompanying satellite in space station to execute detection tasks. The design of ensuring the accompanying satellite reach the target position and avoid obstacles simultaneously are difficult due to the critical non-convex and nonlinear constraints, and solving the large number of decision variables as a result of model predictive control is too computationally intensive to be implemented. To counter this problem, the trajectory generation problem is reformulated as a mixed integer quadratic programming (MIQP) problem according to the quadratic objective function and obstacles constraints, and the LMPC with smaller variables method is employed in this paper. The obstacles avoidance constraints are solved by mixed integer quadratic programming with LMPC framework, with particularly advantages of the method could obtain a feasible and satisfied solution when the constraints are rigorous. Besides, this paper introduces a LMPC approach to reduce the computational burden by a set of Laguerre functions, guaranteed the long control horizon condition is solved by the small number of control variables. Application for trajectory generation of satellite in highly constrained space station is conducted to demonstrate the effectiveness of the newly proposed method.