Indirect optimization of multi-phase Mars entry, descent, and landing trajectory involving arbitrary discrete logic

Abstract

Vehicles employed in entry, descent, and landing (EDL) missions fly multi-phase trajectories consisting of multiple flight segments whose transitions may be triggered by boolean logic. When the boolean logic is represented using only continuous states and/or time, the EDL system is termed an autonomously switched hybrid system. The relaxed autonomously switched hybrid system approach (RASHS) was previously introduced to simplify the trajectory optimization process of such systems in the indirect framework when the boolean logic only involves AND and NOT operations. This investigation solves a multi-phase EDL trajectory optimization problem when the boolean logic involves a combination of AND, OR and NOT operations. Specifically, the parachute descent segment is in progress when the velocity is below the parachute deployment velocity OR the altitude is below the parachute deployment altitude, AND the altitude is above the powered descent initiation altitude. Because this set of conditions additionally involves OR logic, the previously introduced RASHS approach cannot be employed. To address this limitation, this investigation introduces a new method termed the Generalized Relaxed Autonomously Switched Hybrid System (GRASHS) approach. Similar to the RASHS approach, the outcome of the GRASHS approach is the transformation of the necessary conditions of optimality from a multi-point boundary value problem (MPBVP) to a two-point boundary value problem (TPBVP), which is simpler to handle. Because any boolean logic can be solely represented using AND, OR and NOT operations, the GRASHS approach can be applied to any autonomously switched hybrid system involving arbitrary discrete logic.