Optimization for the Aeroassisted Orbital Plane Change with the Synergetic Maneuver Using the $hp$-Adaptive Pseudospectral Method

The thrust synergetic maneuver, i.e., during the atmospheric flight, the flight trajectory of the vehicle is modulated by both the aerodynamic force and thrust, can potentially lower fuel consumption in comparison with the all-propulsive maneuver to implement orbital plane changes. This paper fully studies the optimal synergetic maneuver for the orbital plane change problem with heating-rate constraints. By using the $hp$-adaptive pseudospectral method, the global solution of a synergetic maneuver has been found, and the corresponding optimal trajectories have been shown. The trend of the control variables indicates that the global optimal solution is more like a combination of aerocruise and aerobang. In consideration of different maximum allowable heating rates and orbital altitudes, the maximum abilities of orbital plane change and significant features of the trajectories during atmospheric flight are demonstrated. The comparisons between the global solution and aerobang about maximum orbital inclination changes under different constraints have been made to confirm the optimality of the results in this paper and show the gap of the aerobang. The optimal results of this work exactly give the ultimate ability of orbital plane change, and demonstrate that the synergetic maneuver is obviously efficient for orbital plane changes, especially for low orbit and relaxed heating rate constraint.