An algorithm is described for planning the motions of several mobile robots which share the same workspace. Each robot is capable of independent translational motion in two dimensions, and the workspace contains polygonal obstacles. The algorithm computes a path for each robot which avoids all obstacles in the workspace as well as the other robots. It is guaranteed to find a solution if one exists. The algorithm takes a cell decomposition approach, where the decomposition used is based on the idea of a product operation defined on the cells in a decomposition of a two-dimensional free space. This algorithm is being implemented for the case of two robots as part of ongoing research into useful algorithms for task-level programming of the RobotWorld system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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