Large-Scale Lunar Transportation Trajectory Optimal Programming Method Based on the Bilevel Convexification Model

Abstract

In order to solve the trajectory planning problem of the launch vehicle during the large-scale lunar transportation, which involves vertical takeoff and landing, multiple maneuvers, and high landing accuracy requirements. Firstly, the equations of motion of the vehicle's center of mass are established, and a large-scale trajectory optimization model is constructed considering initial position, terminal position, velocity constraints, and thrust constraints. The nonlinear optimization problem is linearized and discretized using convex optimization methods; Secondly, the large-scale optimal trajectory planning problem is converted into a bilevel convex optimization problem. The optimization problems in the dynamic ascent phase, the large-scale dynamic flight phase, and the vertical descent phase are treated as the inner layer convex optimization problems, and solved using the interior point method. At the same time, combined with the fuel optimization purpose, the objective function is designed as the outer layer convex optimization problem, and iterative calculations are performed using the gradient descent method, obtain the optimal fuel trajectory for a wide range of vertical takeoff and landing. Simulation experiments show that the algorithm proposed in this paper ensure the vertical landing of the vehicle which meets the requirements of high-precision landing. Monte Carlo simulation is conducted considering position errors, and the results show that the algorithm has good robustness.

Keywords

lunar vehicle / large-scale transportation / bilevel convexification / trajectory programming / optimal control