An Angle–Axis Space-Based Orientability Index Characterizing Complete Orientations

The development of new materials/actuators in robotics leads to the rapid growth of new types of robots, including soft/continuum robots, reconfigurable robots, exoskeleton robots, haptic master devices, and so on. When designing a new robot, orientability is an important performance index to evaluate its dexterity. However, a theoretical investigation of the orientability is still lacking. The existing orientability index can only characterize the reachability of a line, rather than a complete orientation. To evaluate the reachability of complete orientations, in this article, we propose a novel orientability index based on the angle–axis space, which is bijective to the rotation group SO(3). Furthermore, a relative orientability index is proposed to characterize the matching degree of the workspace of a given robot to its target workspace. The proposed orientability and relative orientability indices are then used to evaluate and compare the dexterity of three 6-DOF continuum robots and a haptic master device. The results validate the effectiveness of the proposed orientability in evaluating the dexterity.