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Application of traditional indirect optimization methods to optimal controlproblems (OCPs) with control and state path constraints is not astraightforward task. However, recent advances in regularization techniques andnumerical continuation methods have enabled application of indirect methods tovery complex OCPs. This study demonstrates the utility and application of anadvanced indirect method, the Unified Trigonometrization Method (UTM), to aMars Science Laboratory type entry problem. The objective is to maximize theparachute deployment altitude for a free-time, fixed-final-velocity entrytrajectory. For entry vehicles, in addition to the bank angle that ischaracterized by bang-bang control profiles, there are typically three statepath constraints that have to be considered, namely, the dynamic pressure, heatrate and g-load. This study shows that the UTM enables simultaneousregularization of the bang-bang control and satisfaction of the state pathconstraints. Two scenarios with and without state path constraints areconsidered. The results obtained using the UTM for both of these cases arefound to be in excellent agreement with a direct optimization method.Furthermore, an interesting feature emerges in the optimal control profile ofthe UTM during the initial high-altitude part of the resulting optimaltrajectory for the scenario with state path constraints, which has an appealingpractical implication.

Entry Trajectory Optimization for Mars Science Laboratory Class Missions Using Indirect Unified Trigonometrization Method