Time-Optimal Trajectory Planning for Underactuated Rigid Spacecraft using Differential Flatness

A novel time-optimal trajectory planning approach for underactuated spacecraft is presented by using differential flatness in this paper.For given initial and final states,a performance index is used to minimize the maneuvering time subject to control input saturation constraints.An asymmetric underactuated spacecraft is non-flat unless a fictitious control variable is employed along the uncontrolled axis.Then,the attitudes and inputs can be parameterized in terms of a set of flat outputs and their derivatives.However,in order to ensure the equivalence,an additional constraint to maintain the fictitious input zero must exist.Further,discretizing the flat outputs by pseudospectral method,the optimization problem is ultimately converted into a lower-dimensional nonlinear programming problem,which contains only algebraic constraints and can be solved numerically without integrating differential dynamics equations.Simulation results demonstrate that this proposed approach is effective in decreasing required solution time and provides comparable computational accuracy.