  Application of traditional indirect optimization methods to optimal control
problems (OCPs) with control and state path constraints is not a
straightforward task. However, recent advances in regularization techniques and
numerical continuation methods have enabled application of indirect methods to
very complex OCPs. This study demonstrates the utility and application of an
advanced indirect method, the Unified Trigonometrization Method (UTM), to a
Mars Science Laboratory type entry problem. The objective is to maximize the
parachute deployment altitude for a free-time, fixed-final-velocity entry
trajectory. For entry vehicles, in addition to the bank angle that is
characterized by bang-bang control profiles, there are typically three state
path constraints that have to be considered, namely, the dynamic pressure, heat
rate and g-load. This study shows that the UTM enables simultaneous
regularization of the bang-bang control and satisfaction of the state path
constraints. Two scenarios with and without state path constraints are
considered. The results obtained using the UTM for both of these cases are
found to be in excellent agreement with a direct optimization method.
Furthermore, an interesting feature emerges in the optimal control profile of
the UTM during the initial high-altitude part of the resulting optimal
trajectory for the scenario with state path constraints, which has an appealing
practical implication.
