Pseudospectral method for optimal motion planning of a rigid underactuated spacecraft

This paper discusses the problem of optimal motion planning for a rigid underactuated spacecraft. Firstly, we derive the dynamic and kinematic equations of the spacecraft, and for given initial and terminal states, the performance index to be optimized is selected as minimizing the total fuel consumption. Moreover, the control input saturation restriction is transformed into an inequality constraint. Then, the optimal motion planning problem can be converted into a nonlinear programming problem using Legendre pseudospectral method at a set of discretization points. Simulation results demonstrate that the obtained optimal trajectories satisfy the constraint conditions well and the proposed approach can also be used on-line in application practice with its small computational amount and low computational complexity.