Energy optimal guidance for proximity approach with obstacle avoidance

This paper presents an energy optimal guidance algorithm for the approach of a damaged spacecraft with the consideration of the arbitrary number of moving obstacles. The proposed optimal guidance laws are derived by projecting the control function in L₂ Space to obtain the minimum norm controller. Unlike conventional trajectory optimization, this algorithm constructs an L₂ space based on the state transfer matrix and describes the path constraints as inner products in L₂ space. Following this, the proximity approach and obstacle avoidance/rendezvous are combined into a single but global optimal step by the Projection Theorem while obtaining the analytical energy consumption. Examples for multiple static and moving obstacles are presented to demonstrate the advantages of the proposed guidance over traditional trajectory optimization methods. The optimization result of the proposed method is slightly better than GPOPS and the computation time is about five-thousandths of GPOPS.