On Fitted Stratified and Semi-Stratified Geometric Manipulation Planning with Fingertip Relocations

This paper presents two object manipulation planning methods based on fitted stratified and semi-stratified approaches using finger relocations. The problem is discussed in the framework of a motion planning problem. The goal of the methods is to steer an object from an initial configuration to a final configuration while it is possible to reposition the fingertips on the surface in a predefined way. We assume there is no rolling and sliding but finger relocations are allowed. The first technique follows a pure stratified approach, however unlike the previously published method, the exact kinematic model of the manipulation system is matched with a virtual model masking the behavior of the original system. This provides a simpler model than the earlier stratified method by reducing the generally hard symbolic computation problem to a simple (almost pure numerical) one. The paper also introduces a semi-stratified manipulation planning based on the newly defined fitted system. This second method enhances the stratified motion planning with a definition of systematic finger relocation sequence. The proposed decomposition is based on the selection of suitable reference contact points. As the main benefit, the method enables a greater freedom in defining the desired fingertip trajectories. The methods are illustrated through an example of object reorientation. KEY WORDS—stratified motion planning, dexterous manipulation, fingertip relocations, differential geometry The International Journal of Robotics Research Vol. 21, No. 5-6, May-June 2002, pp. 489-510, ©2002 Sage Publications