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.