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This paper addresses the problem of using three disc-shaped robots to manipulate a polygonal object in the plane in the presence of obstacles. The proposed approach is based on the computation of maximal discs (dubbed maximum independent capture discs, or MICaDs) where the robots can move independently while preventing the object from escaping their grasp. It is shown that, in the absence of obstacles, it is always possible to bring a polygonal object from any configuration to any other one with robot motions constrained to lie in a set of overlapping MICaDs. This approach is generalized to the case where obstacles are present by decomposing the corresponding motion planning task into the construction of a collision-free path for a modified form of the object, and the execution of this path by a sequence of simultaneous and independent robot motions within overlapping MICaDs. The proposed algorithm is guaranteed to generate a valid plan, provided a collision-free path exists for the modified form of the object. It has been implemented and experiments with Nomadic Scout mobile robots are presented.