We propose a framework based on stochastic collocation to solve autonomous vehicle optimal trajectory planning problems with probabilistic uncertainty. We model uncertainty from the location and size of obstacles. We develop stochastic pseudospectral methods to solve the minimum expectation cost of differential equation, which meets path, control, and boundary constraints. Results are shown on two examples of autonomous vehicle trajectory planning under uncertainty, which illustrated the feasibility and applicability of our method.
The problem of planning flight trajectories is studied for multiple unmanned combat aerial vehicles (UCAVs) performing a cooperated air-to-ground target attack (CA/GTA) mission. Several constraints including individual and cooperative constraints are modeled, and an objective function is constructed. Then, the cooperative trajectory planning problem is formulated as a cooperative trajectory optimal control problem (CTP-OCP). Moreover, in order to handle the temporal constraints, a notion of the virtual time based strategy is introduced. Afterwards, a planning algorithm based on the differential flatness theory and B-spline curves is developed to solve the CTP-OCP. Finally, the proposed approach is demonstrated using a typical CA/GTA mission scenario, and the simulation results show that the proposed approach is feasible and effective.
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