Uncertain trajectory planning integrating polynomial chaos and convex programming

The present work explores the robust trajectory optimization scheme considering both the initial state disturbance and multiple constraints. An uncertain multi-constraint optimization model has been first established. Due to the existence of the stochastic disturbance, standard numerical trajectory planning algorithms cannot be directly applied to address the considered issue. Hence, based on the intrusive polynomial chaos expansion, we present a deterministic quantification for the stochastic state and constraints, so that the transformed optimization model becomes solvable for standard numerical optimization methods. To obtain the enhanced computational performance, an hp pseudo-spectral sequential convex programming procedure combined with a penalty function and backtracking search is proposed. This is achieved by discretizing and convexifying the nonlinear dynamics/constraints using hp quadrature collocation and successive linearization, respectively, and by adjusting the confidence region manually in the iteration. The simulation of a three-dimensional interception with the specific impact angle is conducted to verify the effectiveness. The simulation results show that the initial solutions are insensitive to the convex optimization, and the control commands generated by the proposed algorithm are effective against the initial state disturbance.