In this paper we address the obstacle avoidance motion planning problem for leader-follower vehicles configurations operating in static environments. By resorting to set-theoretic ideas, a receding horizon control algorithm is proposed for robots modelled by linear time-invariant (LTI) systems subject to input and state constraints. Terminal robust positively invariant regions and sequences of precomputed inner approximations of the one-step controllable sets are on-line exploited to compute the commands to be applied in a receding horizon fashion. Moreover, we prove that the design of both terminal sets and one-step ahead controllable regions is achieved in a distributed sense. An illustrative example is used to show the effectiveness of the proposed control strategy.
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