Trajectory planning for unmanned vehicles using robust receding horizon control

Abstract

This thesis presents several trajectory optimization algorithms for a team of cooperating unmanned vehicles operating in an uncertain and dynamic environment. The first, designed for a single vehicle, is the Robust Safe But Knowledgeable (RSBK) algorithm, which combines several previously published approaches to recover the main advantages of each. This includes a sophisticated cost-to-go function that provides a good estimate of the path beyond the planning horizon, which is extended in this thesis to account for three dimensional motion; constraint tightening to ensure robustness to disturbances, which is extended to a more general class of disturbance rejection controllers compared to the previous work, with a new off-line design procedure; and a robust invariant set which ensures the safety of the vehicle in the event of environmental changes beyond the planning horizon. The system controlled by RSBK is proven to robustly satisfy all vehicle and environmental constraint under the action of bounded external disturbances. Multi-vehicle teams could also be controlled using centralized RSBK, but to reduce computational effort, several distributed algorithms are presented in this thesis. The main challenge in distributing the planning is to capture the complex couplings between vehicles.

(cont.) A decentralized form of RSBK algorithm is developed by having each vehicle optimize over its own decision variables and then locally communicate the solutions to its neighbors. By integrating a grouping algorithm, this approach enables simultaneous computation by vehicles in the team while guaranteeing the robust feasibility of the entire fleet. The use of a short planning horizon within RSBK enables the use of a very simple initialization algorithm when compared to previous work, which is essential if the technique is to be used in dynamic and uncertain environments. Improving the level of cooperation between the vehicles is another challenge for decentralized planning, but this thesis presents a unique strategy by enabling each vehicle to optimize its own decision as well as a feasible perturbation of its neighboring vehicles' plans. The resulting cooperative form of the distributed RSBK is shown to result in solutions that sacrifice local performance if it benefits the overall team performance. This desirable performance improvement is achieved with only a small increase in the computation and communication requirements. These algorithms are tested and demonstrated in simulation and on two multi-vehicle testbeds using rovers and quadrotors.

(cont.) The experimental results demonstrate that the proposed algorithms successfully overcome the implementation challenges, such as limited onboard computation and communication resources, as well as the various sources of real-world uncertainties arising from modeling error of the vehicle dynamics, tracking error of the low-level controller, external disturbance, and sensing noise.