Deep space formation reconfiguration using pseudospectral method

In this paper we employ pseudospectral method to solve the problem of trajectory optimization for satellites formation reconfiguration in deep space. The basic problem is all the satellites take a specified rest-to-rest maneuver synchronously without colliding with each other. First, the state and input vectors are discretized at Legendre-Gauss-Lobatto (LGL) points, and the objective function is selected as minimizing the total fuel consumption during maneuver. Then the optimization problem is converted into a parameter nonlinear programming problem with the non-convex constraints of collision avoidance as inequality equations using Legendre pseudospectral method. At the end of this paper, an example is worked out and the simulation results demonstrate that the proposed approach can produce high approximation accuracy and a small computational amount, which makes the algorithm of trajectory generation for formation reconfiguration used on-line possible.