Stable Receding Horizon Trajectory Control for Complex Environments

Abstract

This paper presents a stable receding horizon controller for the minimum time trajectory optimization problem with a vehicle flying in a complex environment with obstacles and no-fly zones. The trajectory optimization is done using mixed-integer linear programming (MILP), which can directly incorporate logical constraints such as obstacle avoidance and waypoint selection and provides an optimization framework that can account for basic dynamic constraints such as turn limitations. Previous work introduced a receding horizon control that significantly reduces the computational effort for solving MILP problems. A straight line approximation used beyond the planning horizon gives a good estimate of the cost-to-go, but is shown to fail when no kinodynamically feasible trajectory could be constructed. A new formulation in this paper solves this problem by using a modified form of Dijkstra’s algorithm to construct a path approximation that is kinodynamically feasible from the start to the goal. With this revised path approximation and the new terminal constraints in the MILP formulation, the receding horizon MILP optimization problem is proven to have a feasible solution, which guarantees that the vehicle can reach the goal in bounded time. The simulation results show this new formulation is computationally tractable.