Convex relaxation for optimal rendezvous of unmanned aerial and ground vehicles

Abstract

In this paper, we present an optimal rendezvous approach that facilitates the coordination of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs). Of particular interest is the problem of UAV-UGV rendezvous for autonomous aerial refueling, which is an important capability for the future use of UAVs. The main contribution of this work is the development of a promising method for the generation of optimal rendezvous trajectories in real time using convex optimization. First, the UAV-UGV rendezvous problem is formulated as a nonconvex optimal control problem using an error dynamic model, where the state and control variables are highly coupled. Then, great effort is devoted to reducing the nonconvexity and coupling of the dynamics through change of variables. Based on a lossless convexification technique, a sequential convex programming algorithm is designed and the solution is obtained by solving a sequence of convex optimization problems. Theoretical proof is provided to demonstrate the exactness of convexification. Furthermore, a simple line search technique is introduced to handle the model error resulting from the linear approximations and to improve the convergence of the designed successive process. Simulation results of two refueling rendezvous situations validate that the proposed method is capable of converging to the solutions within a second, which shows great potential for real-time applications.