Stochastic Trajectory Planning Considering Parameter and Initial State Uncertainties

The present work explores the stochastic trajectory planning problem considering the parametric and initial condition uncertainties. To address this issue, a novel stochastic trajectory planning (STP) procedure integrating the non-intrusive polynomial chaos expansion and the convex optimization technique is proposed in this paper. This is achieved by transforming the nonconvex and infinite dimensional optimization problem into convex and discrete optimization problem with high efficiency in solving optimal control. Subsequently, the stochastic parametric convex dynamics and path constraints are surrogated by deterministic versions by taking advantage of the high accuracy of the non-intrusive polynomial chaos expansion (NTPCE) without tedious modification of governing equations. The proposed STP procedure is applied to generate the optimal control profile of a three-dimensional interception with the specific impact angle. For comparative studies, the optimal control profile of original optimization problem without disturbance is also derived by the convex optimization technique based on the same scenario. The simulation results show that the optimal control profile obtained by the proposed STP approach is more robust to the parametric and initial condition uncertainties under the open-loop control policy and don't need significant increase of computational cost. These results demonstrate the effectiveness of the proposed procedure.