This paper presents work on sensor-based motion planning in initially unknown dynamic environments. Motion detection and probabilistic motion modeling are combined with a smooth navigation function to perform on-line path planning and replanning in cluttered dynamic environments such as public exhibitions. The SLIP algorithm, an extension of Iterative Closest Point, combines motion detection from a mobile platform with position estimation. This information is then processed using probabilistic motion prediction to yield a co-occurrence risk that unifies dynamic and static elements. The risk is translated into traversal costs for an E^* path planner. It produces smooth paths that trade off collision risk versus detours. © Springer.