Path planning for satellite slew manoeuvres: a combined flatness and collocation-based approach

Path planning for satellite slew manoeuvres is considered as an optimal control problem. The goal is to design rapid manoeuvres with the resting time vibrational modes as short as possible in order to provide more time for space imagery. This problem of optimal time and control effort is addressed using differential flatness and B-spline collocation. The flatness allows for reformulating the original optimal control problem as a tractable geometric programming problem with no numerical integration, and with a minimal number of decision variables. A direct consequence of flatness is that the transformed constraints describe generally a non-convex subspace. In the proposed approach, a flat suboptimal convex problem is derived by means of offline convex approximations of the feasible space and a measure of its conservatism is given. Numerical results are discussed and compared with the results generated from an in-service industrial path planner available at the French Space Agency, CNES.