Minimum-deflection grasps and fixtures

This paper presents an approach to planning compliant grasps and fixtures in which the object exhibits minimal deflection under external disturbances. The approach, which applies to general two- and three-dimensional grasps and fixtures represented by any quasi-rigid compliance model, employs a quality measure that characterises the grasped or fixtured object's worst-case deflection caused by disturbing wrenches lying in the unit wrench ball. To ensure well-defined notions of deflection and wrench balls, frame-invariant rigid body velocity and wrench norms are used. As illustrated by its application to fixtures of polygonal objects, our minimum-deflection approach can be effectively applied to planning grasps and fixtures where deflection significantly influences performance.