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Coordinated Path-Following in the Presence of Communication Losses and Time Delays

This paper addresses the problem of steering a group of vehicles along given spatial paths while holding a desired time-varying geometrical formation pattern. The solution to this problem, henceforth referred to as the coordinated path-following (CPF) problem, unfolds in two basic steps. First, a path-following (PF) control law is designed to drive each vehicle to its assigned path, with a nominal speed profile that may be path dependent. This is done by making each vehicle approach a virtual target that moves along the path according to a conveniently defined dynamic law. In the second step, the speeds of the virtual targets (also called coordination states) are adjusted about their nominal values so as to synchronize their positions and achieve, indirectly, vehicle coordination. In the problem formulation, it is explicitly considered that each vehicle transmits its coordination state to a subset of the other vehicles only, as determined by the communications topology adopted. It is shown that the system that is obtained by putting together the PF and coordination subsystems can be naturally viewed as either the feedback or the cascade connection of the latter two. Using this fact and recent results from nonlinear systems and graph theory, conditions are derived under which the PF and the coordination errors are driven to a neighborhood of zero in the presence of communication losses and time delays. Two different situations are considered. The first captures the case where the communication graph is alternately connected and disconnected (brief connectivity losses). The second reflects an operational scenario where the union of the communication graphs over uniform intervals of time remains connected (uniformly connected in mean). To better root the paper in a nontrivial design example, a CPF algorithm is derived for multiple underactuated autonomous underwater vehicles (AUVs). Simulation results are presented and discussed.