A geometrical approach to planning manipulation tasks. The case of discrete placements and grasps
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This paper presents a new geometrical formulation of the manipulation task planning problem in robotics. The problem is shown to be a constrained instance of the coordinated motion planning problem for multiple moving bodies. The constraints are related to the placement and the motion of objects, and can be expressed geometrically.
We give a general paradigm for building Manipulation Task Planners based on the proposed formulation. A manipulation task appears as a path in the configuration space of the robot and all movable objects. A {\em manipulation path} is a sequence of constrained paths: {\em transit-paths}, where the robot moves "alone'', and {\em transfer-paths}, where the robot holds an object. The approach consists in building a {\em Manipulation Graph} that models
the connectivity between certain regions in the global configuration space by transit-paths and transfer-paths.
This approach is then applied to the case of a finite number of object placements and grasps. The nodes in the Manipulation Graph correspond to well identified configurations and the edges correspond to paths built from a series of configuration space slices. An implemented system is presented and discussed.