A general framework for multiple vehicle time-coordinated path following control

This paper describes a general framework for the study of multiple vehicle, time-coordinated path following (TC-PF) control problems. An example is the situation where a group of vehicles is tasked to maneuver and arrive at pre-assigned final positions at the same time in a collision-free manner, while reducing some optimality criterion. The time of arrival is not fixed a priori, and the vehicles must negotiate their speeds along the spatial paths that they follow in order to arrive simultaneously and avoid collision. The general framework adopted leads to integrated solutions to TC-PF problems that unfold in three steps: 1) generation of deconflicted trajectories for a group of vehicles, 2) path following for each vehicle along its assigned path, and 3) coordination of the relative motion of the vehicles along their paths, so as to guarantee deconfliction and meet desired temporal constraints such as equal times of arrival. The last step is accomplished by varying the speed of each vehicle about the nominal speed profile computed in step 1, based on the exchange of information with its neighbors. The paper formulates the problem mathematically, offers a general framework for its solution, and illustrates the efficacy of the proposed methodology in simulation with dynamic models of autonomous underwater vehicles (AUVs).