Stochastic Optimal Control under Non-Gaussian Uncertainties via Entropy Minimization and Dynamical Indicators

Robust and optimal trajectory planning in the face of nonlinear dynamics and non-gaussian uncertainties poses a fundamental challenge in the field of astronautics. This research paper delves into the exploration of entropy and dynamical indicators associated with Lagrangian Coherent Structures (LCS), specifically the Finite-Time Lyapunov Exponent (FTLE) and PseudoDiffusion Exponent, for addressing optimal control problems amidst uncertainties characterized by non-Gaussian probabilities. To accomplish this, sampling-based approaches and the Perron-Frobenius transfer operator are employed to generate open-loop stochastic optimal controls. Sparse grids are utilized to generate trajectory samples and reformulate stochastic optimal control as a deterministic optimization problem across the domain of uncertainty. Subsequently, SC-EPOCS is employed to tackle the resulting optimization problem and a comparative analysis of maximum terminal altitude and covariances is conducted to assess robustness exhibited by each metric in the context of trajectory planning for a Mars entry problem, considering uncertainties in both the initial state and model parameters.