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This paper addresses a novel approach to the n-vehicle collision avoidance problem. The vehicle model used is a planar constant-speed unicycle, chosen for its wide applicability to ground, sea, and air vehicles. An algorithm is developed which guarantees all vehicles remain free of collisions while attempting to attain their trajectory goals (given certain restrictions on their initial conditions). This controller is reactive and decentralized, making it well suited for real time applications, and explicitly accounts for actuation limits. Results are demonstrated in simulation.