Fuel-optimal trajectory optimization for lunar soft landing via enhanced simultaneous dynamic optimization approach

Abstract

In this study, the fuel-optimal trajectory optimization problem of lunar soft landing using variable-thrust propulsion is considered. First, we formulate the trajectory optimization problem of lunar soft landing with three-dimensional kinematics and dynamics, boundary constraints, and path constraints strictly described. The formulated trajectory optimization problem is then solved by the simultaneous dynamic optimization approach. With bounds imposed on the magnitude of the engine thrust, the optimal thrust profile typically has a “bang-bang” profile. The general simultaneous dynamic optimization approach has difficulty handling breakpoints of control profiles. A novel adaptive mesh refinement strategy based on a constant Hamiltonian profile is proposed to address the difficulty of locating breakpoints of the thrust profile. Simulation results show that the enhanced simultaneous dynamic optimization approach with the adaptive mesh refinement strategy can effectively capture breakpoints of the optimal thrust profile and obtain more refined optimal solutions, compared with the general simultaneous dynamic optimization approach.