A Preset-Time Method for Multi-Robot Coordination With Application to Package Delivery

In this paper, we study the package delivery problem where the transportation tasks, including arriving at the delivery locations and returning to the depots, are required to be completed within a time window. To this end, a time-homogeneous preset-time algorithm is presented to coordinate multiple vehicles within an identical time window, where arrival time delays are used to characterize the arrival time of the vehicles. Consequently, the considered package delivery problem is formulated by two phases: “Active phase” and “Sleeping phase”, over which vehicles use the neighboring information to achieve coordination. For the proposed algorithm, we use Lyapunov based method to derive condition guaranteeing the coordination of vehicles, under a very mild communication topology condition. As an extension, a time-heterogeneous preset-time algorithm is designed. We demonstrate that coordination among vehicles is determined by the maximal preset-time. Built upon this observation, we further show that there is an equivalence between the proposed formulation and the dynamical equation of the interacting vehicles. Finally, a numerical example for a package delivery problem, comprised of two coordination phases, is carried out to illustrate the proposed preset-time coordination formulation, and the time-heterogeneous case is further discussed as well.