Stochastic Trajectory Optimization Problems with Chance Constraints

This chapter investigates a computational framework based on optimal control for addressing the problem of stochastic trajectory optimization with the consideration of chance constraints. This design employs a discretization technique to parametrize uncertain variables and create the trajectory ensemble. Subsequently, the resulting discretized version of the problem is solved by applying standard optimal control solvers. In order to provide reliable gradient information to the optimization algorithm, a smooth and differentiable chance-constraint approximation method is proposed to replace the original probability constraints. The established methodology is implemented to explore the optimal trajectories for a spacecraft entry flight planning scenario with noise-perturbed dynamics and probabilistic constraints. Simulation results and comparative studies demonstrate that the present chance-constraint-handling strategy can outperform other existing approaches analyzed in this study, and the developed computational framework can produce reliable and less conservative solutions for the chance-constrained stochastic spacecraft trajectory planning problem. We hope that by reading this section, readers can gain a better understanding in terms of the definitions, solution approaches, and current challenges of the stochastic spacecraft trajectory design problems.