Waypoint-based ZEM/ZEV feedback guidance: Applications to low-thrust interplanetary transfer and orbit raising

Low-thrust guided trajectories for space missions are extremely important for fuel-efficient autonomous space travel. The goal of this paper is to design an optimized, waypoint-based, closed-loop solution for low-thrust, long duration orbit transfers. The Zero-Effort-Miss/Zero-Effort-Velocity (ZEM/ZEV) feedback guidance algorithm which has been demonstrated to exhibit great potential for autonomous onboard implementation is applied in a waypoint fashion. Generally, ZEM/ZEV is derived by solving an optimal guidance problem under well-defined assumptions, where the gravitational acceleration is either constant or time-dependent and the thrust/acceleration command is unlimited. If gravity is not constant, the target state is generally achieved in a suboptimal fashion. A way to improve the performances is to divide total trajectory into many segments, and determining with a rigorous optimization method near-optimal waypoints to connect the different segments. Here we consider two possible scenarios, i.e. 1) a low-thrust transfer Earth-Mars and 2) a low-thrust orbit raising from LEO to GEO. For both cases, open-loop energy and fuel-optimal trajectories generated by L. Ferrella and F. Topputo are considered as reference trajectories where a set of arbitrary points are targeted by the ZEM/ZEV guidance in a sequential fashion. An initial parametric study is conducted to evaluate guidance performances as function of the number of the selected waypoints. Subsequently, a global optimization problem, parametrized with the position of the points on the trajectory is solved using a genetic algorithm to determine the minimum set of waypoints necessary for close-to-fuel-optimal waypoint space guidance. The optimization results are compared with the parametric analysis for both scenarios to show that the proposed approach is feasible in achieving quasi-optimal performances even for challenging cases where 500 revolutions are required for low-thrust orbit raising in the Earth gravitational field. Finally, the proposed waypoint-based guidance algorithm is simulated in a more realistic scenarios including perturbing acceleration to verify the robustness of the system via a Monte Carlo analysis.