An Object Shape Dependent Kinematic Manipulability Measure for Path and Trajectory Synthesis and Shape Optimization

Abstract

The manipulability of robot manipulators has been studied with respect to the ability to position the end-effector in its workspace. However, since manipulators have to manipulate objects with finite dimensions, the ability of a manipulator to position and orient an object is quite different from its end-effector manipulability. Object shape dependent kinematic manipulability measures are essential for the formulation of optimal path planning and trajectory synthesis algorithms used for moving objects in operations such as mating parts and for formulating related object shape optimization problems. The optimality criterion may be related to part positioning accuracy, mating accuracy, kinematics performance of the manipulator for applying force (torque) to the object at some stage of the assembly, or a number of other accuracy, force or control measures. In the present study, a class of shape dependent kinematics measures is developed for the object manipulability. The measures can be used to evaluate the manipulability of objects with various shapes, for path and trajectory synthesis, and for designing object shapes. No rigid body constraint is imposed and the object considered may be deforming, stretching or shrinking during its manipulation. A number of examples are presented.