Real-time trajectory optimization of an underactuated rigid spacecraft using differential flatness

A real-time trajectory optimization approach is developed for an underactuated rigid spacecraft using differential flatness property. By employing a fictitious input variable along the uncontrolled axis, a general underactuated spacecraft is proven to be flat. Then, the original optimization problem is reformulated in flat output space, and the dynamical restrictions of system are entirely eliminated. Further, unlike conventional discretization schemes, in this approach, we discretize this continuous flat system by a fixed count of control steps, and the corresponding sampling period is treated as a variable to be determined in optimization process. Thus, the optimization problem is ultimately converted into a constrained nonlinear programming problem, which contains only algebraic constraints and can be solved by at most two iterations. Simulation results show that the proposed approach is effective in reducing the required computational time and feasible trajectories can be generated real-time.