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A methodology for computing a collision-free trajectory for mobile robots amidst moving objects is presented. This planner is based on a technique for computing the minimum translational distance between two mobile objects. This distance is then used for predicting and avoiding a collision. The computation of this distance is based on the application of the GJK algorithm to a particular subset of the Minkowski difference set of the involved objects. This subset states the separation or penetration distance between two objects along their given motions. When a collision is predicted, a collision-free intermediate temporal-position is generated avoiding such a collision.