An impulse control approach to spacecraft autonomous rendezvous based on genetic algorithms

This paper proposes a novel approach to spacecraft impulse autonomous rendezvous by using genetic algorithms. Based on the Clohessy–Wiltshire (C–W) equations, the whole rendezvous process is described as a switching system composed of closed-loop system and open-loop system, which correspond to the impulse action phase and free motion phase during the rendezvous process. Based on Lyapunov theory, the autonomous rendezvous problem is regarded as an asymptotic stabilization problem. By introducing two virtual energy functions, the stability of the switching system is analyzed, and the duration of the impulse action and the thrust limitation are considered synthetically. Then, a state-feedback controller design method is proposed, and an approach based on linear matrix inequality and genetic algorithm (GA) is proposed to solve the controller design problem and the calculation steps are presented. With the designed controller, the impulse thrust which satisfies the given thrust constraint is determined according to the real-time relative state between two spacecraft at the impulse instant, and the impulse duration is kept as short as possible. The effectiveness of the proposed approach is illustrated by simulation examples.