An implemented planner for manipulating a polygonal object in the plane with three disc-shaped mobile robots

This paper presents an implementation of a planner that uses three disc-shaped robots to manipulate a polygonal object in the plane in the presence of obstacles. The approach is based on the computation of the maximal discs (dubbed maximal independent capture discs or MICaDs) where the robots can move independently while preventing the object from escaping their grasp. It has been 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 motion planning task into (1) the construction of a collision-free path for a modified form of the object, and (2) the execution of this path by a sequence of simultaneous and independent robot motions within overlapping MICaDs. The approach is guaranteed to work provided a collision free path exists for the modified form of the object. Experiments with Nomadic Scouts and a visual localization system are presented.