Trajectory optimization for lunar soft landing with a Hamiltonian-based adaptive mesh refinement strategy

Abstract

In this study, the problem of fuel-optimal lunar soft landing trajectory optimization using variable-thrust propulsion is considered. First, the lunar soft landing trajectory optimization problem with three-dimensional kinematics and dynamics model, boundary conditions, and path constraints strictly described is formulated. Then, the formulated trajectory optimization problem is solved by the simultaneous dynamic optimization approach. With bounds imposed on the magnitude of engine thrust, the optimal control solutions typically have a “bang-bang” thrust profile. The general simultaneous dynamic optimization approach has difficulty handling breakpoints in the control profiles. A novel adaptive mesh refinement strategy based on a constant Hamiltonian profile is proposed to address the difficulty of locating breakpoints in the thrust profile. Two cases are simulated. The engine of the first case is throttleable between zero and full thrust. The engine of the second case is throttleable between 10% and 60% of full thrust, and at full thrust. Union property of R-function method is utilized to express the thrust profile of the second case in the trajectory optimization problem. Simulation results show that the enhanced simultaneous dynamic optimization approach with adaptive mesh refinement strategy can effectively capture the breakpoints in the optimal thrust profile and obtain more refined lunar soft landing optimal solutions, compared with the results obtained by the general simultaneous dynamic optimization approach.