Time optimal trajectory planning for reconfiguration of satellite formation with collision avoidance

This paper aims to design a general formulation for time optimal trajectory planning of satellites formation reconfiguration using pseudospetral method. The basic problem is all the satellites take a specified rest-to-rest maneuver synchronously without colliding with each other in a shortest time. First we discretize the state and input vectors at Legendre-Gauss-Lobatto (LGL) points and accordingly transform the model of satellite, the objective function and the non-convex constraints of collision avoidance to a parameter optimization nonlinear programming (NLP) problem using Legendre pseudospectral method. Then this NLP problem is solved by searching the state and control vectors to minimize the objective function. At the end of this paper, an example is worked out to show that the Legendre pseudospectral method is well suited for formation reconfiguration problem. The results demonstrate that our method could solve the problem in a short time with high accuracy so that it can be used as the on-line algorithm of time optimal trajectory generation for formation reconfiguration.