Optimal trajectory generation of an asymmetric underactuated spacecraft based on orbital flatness

In this paper, an asymmetric underactuated spacecraft is proven to be orbitally flat by employing a suitable time-scaling function and based on this property, a method for time-optimal trajectory generation is proposed. Firstly, for given initial and terminal states, the performance index to be optimized is selected as minimizing maneuvers time, and control input saturation constraints and singularity constraints can also be regarded as inequality constraints of this dynamic optimization problem. Then, using orbital flatness property, the dynamic optimization problem is converted into a semi-infinite optimization problem in form of nonlinear algebra equations, which can be solved by a nonlinear programming method or a matrix analysis method without integrating differential dynamic equations. Simulation results demonstrate that the obtained trajectories satisfy the constraint conditions well and the proposed approach can also be used on-line in application practice with its computational efficiency.