A notion of robustness for a mobile robot trajectory is introduced. It captures the sense that there are nearby trajectories which are also collision-free and satisfy the kinematic constraints. An algorithm is presented which is guaranteed to plan robust paths with a running time of O(n/sup 4/ log n+n/sup 2// delta /sup 2/), where n is the number of obstacle vertices and delta is a measure of the robustness of the path. Also discussed are the modifications required for the algorithm to allow for uncertainty in position.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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