Optimal spacecraft docking maneuver using direct and indirect collocation method and particle swarm optimization

In this paper, an indirect method combined with a heuristic approach is investigated to solve an optimal spacecraft docking maneuver problem. The relative dynamic frames used are the fully nonlinear Clohessy-Wiltshire equations for relative translation dynamics and the Euler equations of rotation for rotation of the two spacecrafts. Both direct and indirect collocation methods are implemented and results from these two optimization methods are compared and discussed. Theoretically, the indirect method presents the difficulty that the problem size is large due to discretization of the costates in addition to requiring good enough initial guesses for the costates variables. This paper presents a new approach where a heuristic optimization (HO) algorithm is used beforehand to generate a sufficiently accurate initial guess for the costates variables used for the collocation method applied later on. The heuristic algorithm is able to perform a global search in the space of the unknown costates in order to efficiently initialize the collocation algorithm. In this work, the method will focus on a minimum time maneuver problem and a combined minimum time and minimum energy problem. Results show that the indirect collocation method with a good guess performs better than a purely direct approach. However, the direct method is useful to compare and gain insights for different kinds of problems as well as to give initial estimations of the total time and energy cost.