Fuzzy logic-based optimization for redundant manipulators

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, i.e., the redundancy is resolved. The redundancy resolution can be based on the kinematic or the dynamic equations of the manipulator. In this paper, 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 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. The applications of these two methods to resolve the redundancy are illustrated by simulations. The methods are discussed with regard to their computational efficiency and are compared with other redundancy resolution approaches.