Trajectory Optimization for Lunar Hover Hop with Multi Constraints

The multi-constrained trajectory of minimal fuel consumption was achieved in this paper for the lunar hover hop without lateral thrusters. The hover hop was divided to 3 phases: the vertical rise, the horizontal traverse and the vertical descent. The optimal control of the vertical rise and the vertical descent was bang-bang function. For the first time the control variable of the horizontal traverse was converted from thrust to angle rate, with position, velocity and angle rate considered. The preliminary form of the optimal angle rate for the horizontal traverse was developed by application of the Pontryagin’s minimum principle. With further study on the continuity of the singular point and the number of switching times of the control variable, it was confirmed that the optimal angle rate program consisted of either the maximum or the minimum and there were 2 switchings. A numerical approach to searching the switching points was presented. Simulation results show that the approach with high accuracy and low complexity can potentially be implemented onboard for trajectory optimization.