Optimization of workspace through perturbation analysis of rehabilitation cable robot

It is well known that planar robots may have singular configurations that can result in a loss of full control the mechanisms. In fact, the uncontrollable area is existed as close to singularity, although the robot is operated inside the analyzed workspace. According to the distance to singularity, this comes from the difference of the sensitivity of singular values to be changed easily through the disturbance. However, the conventional workspace analysis estimated by cable tensions has a difficulty giving you the information of singular value sensitivity. In this paper, we focus on the optimization of workspace through perturbation analysis, which estimates the quantity of linear independence for singular value sensitivity. Accordingly, we show the method of perturbation analysis for a 3-DOF cable-driven parallel robot, and then simulation results of optimized workspace to be made change by the acceptable quantity of perturbation.

I. Introduction

Fig. 1 shows the cable robot for upper limb rehabilitation [1]. The patient rehabilitates the upper limb and shoulder by keeping up with the trace of handle while watching the monitor. According to the state of necessary rehabilitation, the level of training is able to be regulated automatically by the computer. When the patient draws the necessary trace with the handle, it seems that there is no problem in the middle area of workspace. However, as close to the edge or corner of workspace, the cable robot doesn't get to work properly. Some cables get to have larger tensions or the slack state. Although the robot is operated inside the available workspace, the uncontrollable area is still existed. We may think that this situation comes from the wrong direction of force caused by the patient, but we're sure that there is no problem if the cable robot has the enough robust for the perturbation. Accordingly, we get to know the necessity to reflect the influence of perturbation when the workspace analysis is performed.