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.

In this paper, we describe a new scheme for redundancy control of robot manipulators. We introduce the concept of task priority in relation to the inverse kinematic problem of redundant robot manipulators. A required task is divided into subtasks according to the order of priority. We propose to determine the joint motions of robot manipulators so that subtasks with lower priority can be performed utilizing re dundancy on subtasks with higher priority. This procedure is formulated using the pseudoinverses of Jacobian matrices. Most problems of redundancy utilization can be formulated in the framework of tasks with the order of priority. The results of numerical simulations and experiments show the effectiveness of the proposed redundancy control scheme.

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This paper discusses the optimal redundancy control problem of robot manipulators. The redundancy control problem has mostly been discussed in the framework of instantaneously optimal control. In this paper, the globally optimal redun dancy control problem is solved strictly by using Pontryagin's maximum principle. According to the proposed method, the optimal trajectory is necessarily obtained if it evists. If only kinematics is considered, the optimal problem is reduced to minimal value searching in a space of as many dimensions as the degrees of redundancy. If dynamics is also taken into consideration, the optimal problem is reduced to minimum value searching in a space of twice as many dimensions as the degrees of redundancy.

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