Redundant manipulators have more degrees of freedom (DOF) than the DOF of the task space. This implies that the number of joint position variables is greater than the number of variables specifying the task. The problem of solving the kinematic equations for the joint variables is underspecified unless additional equations/constraints are introduced to obtain a well-posed problem. A dynamic level redundancy resolution is proposed. The joint space model is transformed to a reduced-order model in the pseudovelocity space. The elements of the foregoing transformation matrix indirectly determine the contribution of each joint to the total motion. These elements are selected using two fuzzy logic-based methods so as to minimize the instantaneous manipulator power: (1) in the velocity method, a nullspace vector in the velocity relationship between the two spaces is determined by imposing a constraint on the continuity of the joint velocities at the time instant when the elements of the transformation matrix experience a discontinuity and (2) in the torque method, an alternative approach introduced to reduce the computational complexity, the changes in the transformation matrix are made continuous with respect to time by the appropriate choice of a nullspace vector in the joint torque expression. Simulations are given.

Redundant manipulators have more degrees of freedom (DOF) than the DOF of the task space. The redundancy resolution can be based on the kinematic or the dynamic equations of the manipulator. In the article, a dynamic level redundancy resolution is proposed. The manipulator dynamical model in the joint space is first transformed to a reduced-order model in the pseudovelocity space. The elements of the foregoing transformation matrix indirectly determine the contribution of each joint to the total motion. These elements are selected using a fuzzy logic based method so as to minimize the instantaneous manipulator power. A nullspace vector in the velocity relationship between the two spaces is determined by imposing a constraint on the continuity of the joint velocities at the time instant when the elements of the transformation matrix experience a discontinuity. The application of the proposed method to resolve the redundancy is illustrated by simulations.

The transformations between the (Cartesian) p-space, the (joint) q-space of a manipulator and a (reduced dimensional) /spl mu/-space are first presented. On the basis of the reduced order model in the /spl mu/-space, a low-dimensional torque control is determined. For implementation, it is transformed into the q-space while constraints are taken into account. It is then demonstrated that the foregoing transformation can be determined so that a well-defined performance criterion is optimized. The proposed approaches are illustrated by simulations.