An algorithm is presented for generating near-time-optimal trajectories for an open-kinematic-chain manipulator moving in a cluttered workspace. This is the first algorithm to guarantee bounds on the closeness of an approximation to a time-optimal trajectory. The running time and space required are polynomial in the desired accuracy of the approximation. The user may also specify tolerances by which the trajectories must clear obstacles in the workspace to allow modeling of control errors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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