Optimal Rendezvous Trajectory for Unmanned Aerial-Ground Vehicles

Fixed-wing unmanned aerial vehicles (UAVs) can be an essential tool for low-cost aerial surveillance and mapping applications in remote regions. There is, however, a key limitation, which is the fact that low-cost UAVs have limited fuel capacity and, hence, require periodic refueling to accomplish a mission. Moreover, the usual mechanism of commanding the UAV to return to a stationary base station for refueling can result in the fuel wastage and inefficient mission operation time. Alternatively, one strategy could be the use of an unmanned ground vehicle (UGV) as a mobile refueling unit, where the UAV will rendezvous with the UGV for refueling. In order to accurately perform this task in the presence of wind disturbances, we need to determine an optimal trajectory in three-dimensional taking UAV and UGV dynamics and kinematics into account. In this paper, we propose an optimal control formulation to generate a tunable UAV trajectory for rendezvous on a moving UGV that also addresses the possibility of the presence of wind disturbances. By a suitable choice of the value of an aggressiveness index that we introduce in our problem setting, we are able to control the UAV rendezvous behavior. Several numerical results are presented to illustrate the reliability and effectiveness of our approach.