Abstract
This paper addresses decentralized motion planning among a homogeneous set of feedback-controlled, decision-making agents. It introduces the continuous control obstacle ( C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -CO), which describes the set of C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -continuous control sequences (and thus trajectories) that lead to a collision between interacting agents. By selecting a feasible trajectory from C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -CO's complement, a collision-free motion is obtained. The approach represents an extension to the reciprocal velocity obstacle (RVO, ORCA) collision-avoidance methods so that trajectory segments verify C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> continuity rather than piecewise linearity. This allows the large class of robots capable of tracking C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -continuous trajectories to employ it for partial motion planning directly-rather than as a mere tool for collision checking. This paper further establishes that both the original velocity obstacle method and several of its recently developed reciprocal extensions (which treat specific robot physiologies only) correspond to particular instances of C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -CO. In addition to the described extension in trajectory continuity, C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -CO thus represents a unification of existing RVO theory. Finally, the presented method is validated in simulation-and a parameter study reveals under which environmental and control conditions C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -CO with admits significantly improved navigation performance compared with inflated approaches based on ORCA.
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