Time-Suboptimal satellite formation maneuvers using inverse dynamics and differential evolution

This paper presents an open-loop planner for near-time-optimal maneuvers performed by satellite formations during proximity operations and reconfiguration maneuvers. Using a differential flatness parameterization, which is an inverse-dynamics method with a minimal set of independent functions, a new optimization technique based on the differential evolution is presented. The linearized dynamical model including the J2 perturbation is taken into account. The differential flatness formulation is implemented to obtain the control policy and the full state as a function of the relative displacements in the local reference frame. The differential evolution algorithm with a local neighborhood, in which the risk of stopping at local minima is reduced, is employed. The technique is computationally efficient and evaluates near-optimal solutions characterized by approximated bang–bang control policies. Results are reported to evaluate the performances of the proposed technique, and aMonte Carlo simulation has been run to prove the efficiency of the planner over a variety of different scenarios. Moreover, the Chebyshev and the B-spline approximations are compared to establish that the latter approach guarantees better results than the former, in terms of maneuver time and computational effort.