Fuel-Optimal Guidance for End-to-End Human-Mars Entry, Powered-Descent, and Landing Mission

This article investigates the fuel-optimal guidance problem of the end-to-end human-Mars entry, powered-descent, and landing (EDL) mission. It applies a unified modeling scheme and develops a computationally efficient new optimization algorithm to solve the multiphase optimal guidance problem. The end-to-end EDL guidance problem is first modeled as a multiphase optimal control problem with different dynamics and constraints at each phase. Via polynomial approximation and discretization techniques, this multiphase optimal control problem is then reformulated as a polynomial programming problem. By introducing intermediate variables and quadratic equality constraints, a polynomial program is equivalently converted into a nonconvex quadratically constrained quadratic program (QCQP). Then, a novel customized alternating direction method of multipliers (ADMM) is proposed to efficiently solve the large-scale QCQP with convergence proof to a local optimum under certain conditions on the algorithmic parameters. The fuel savings under the end-to-end human-Mars EDL guidance are verified by comparing to the fuel consumption using the separate phase guidance approach. Furthermore, the computational efficiency of the customized ADMM algorithm is validated by comparing to the state-of-the-art nonlinear programming method. The robustness of the customized ADMM algorithm is verified via extensive simulation cases with random initial conditions.