The singularity problem is an inherent problem in controlling robot manipulators with articulated configuration. In this paper, we propose to determine the joint motion for the requested motion of the endeffector by evaluating the feasibility of the joint motion. The determined joint motion is called an inverse kinematic solution with singularity robustness, because it denotes feasible solution even at or in the neighborhood of singular points. The singularity robust inverse (SR-inverse) is introduced as an alternative to the pseudoinverse of the Jacobian matrix. The SR-inverse of the Jacobian matrix provides us with an approximating motion close to the desired Cartesian trajectory of the endeffector, even when the inverse kinematic solution by the inverse or the pseudoinverse of the Jacobian matrix is not feasible at or in the neighborhood of singular points. The properties of the SR-inverse are clarified by comparing it with the inverse and the pseudoinverse. The computational complexity of the SR-inverse is considered to discuss its implementability. Several simulation results are also shown to illustrate the singularity problem and the effectiveness of the inverse kinematic solution with singularity robustness.

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