Abstract:

We present an optimization-based method for the fuel-optimal powered descent of a six- degree-of-freedom (6-DoF) lander while ensuring passive safety for a specified duration with respect to an avoid set near the landing site. In other words, the ballistic trajectory of the vehicle, in the event of unplanned engine failure, does not enter an avoid set (e.g., containing critical infrastructure) for a specified time horizon. The proposed solution method leverages the recently introduced CT-SCVX framework, wherein the set-based passive-safety constraint is subjected to an isoperimetric reformulation. The resulting free- final-time optimal control problem is solved through: 1) time-dilation, 2) multiple-shooting discretization, 3) l1-exact penalization of nonconvexities, and 4) the prox-linear method, which is a convergence-guaranteed sequential convex programming (SCP) algorithm for convex-composite minimization. The proposed approach eliminates the commonly encountered inter-sample constraint violation without the need for computationally expensive mesh-refinement heuristics; i.e., we can generate a high-fidelity feasible solution on coarse discretization grids. We provide a numerical demonstration of the proposed approach on a realistic lunar-landing example.