Receding Horizon Trajectory Planning with an Environment-Based Cost-to-go Function

This paper presents a general framework for trajectory planning in three dimensions for vehicles with broad maneuvering capabilities operating in continuously evolving environments. The approach combines an online receding horizon trajectory optimization and a cost-to-go function computed offline that approximates the performance of the vehicle in the global environment and provides the terminal cost for the receding horizon optimization. This breakdown permits a computationally tractable implementation. To enable an efficient computation of the cost-to-go function, a finite dimensional decomposition of the global environment is used. The paper describes how this decomposition is set up to compute the cost-to-go function, as well as its integration with the online receding horizon trajectory optimization. An example is used to demonstrate the system´s basic capabilities. This approach combines key results from robotics motion planning and vehicle trajectory optimization.