Fast Trajectory Optimization with Chance Constraints

This chapter investigates the optimal flight of aero-assisted reentry vehicles during the atmospheric entry flight phase while taking into account both deterministic and control chance constraints. We construct a chance-constrained optimal control model in order to depict the mission profile. However, standard numerical trajectory planning methods cannot be directly used to solve the problem due to the existence of probabilistic constraints (chance constraints). Therefore, to make the optimal control model solvable for standard trajectory optimization algorithms, we introduce an approximation-based strategy such that the probabilistic constraint is replaced by deterministic version. To achieve improved computational performance, we provide an alternative optimal control formulation that incorporates the convex-relaxed technique. This involves convexifying the vehicle nonlinear dynamics and constraints, as well as incorporating a convex probabilistic constraint handling approach. The effectiveness of the two chance-constrained optimization strategies and their corresponding probabilistic constraint handling methods is validated through numerical simulations.