Optimal dynamical control of redundant manipulators
Abstract
The primary task of a manipulator is specified by requirement that the end-effector tracks a desired trajectory in the Cartesian space. This task consists of moving the end-effector of the manipulator from an initial location to a final location in the Cartesian space by following a desired path. Redundant manipulators have more degrees of freedom (DOF) than the DOF of the task space. It 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., unless the redundancy is resolved. The redundancy resolution can be based on the kinematic or the dynamic equations of the manipulator. In this thesis, a dynamic level redundancy resolution is proposed. The manipulator dynamical model in the joint space is first converted to a reduced-order model in the pseudovelocity space by means of a mapping specified by a transformation matrix. The primary objective is the tracking of the desired end-effector Secondary objectives such as the minimization of the total energy of motion or the minimization of instantaneous power are discussed. The minimization is performed with respect to the elements of the transformation matrix. The transformation matrix determines the contributions of each joint to the total motion velocity. The elements of the transformation matrix can be selected as binary numbers, rational numbers and based on fuzzy logic. The elements of the foregoing transformation matrix are determined by two fuzzy logic based methods in this thesis: (i) the Velocity method and (ii) the Torque method. In the Velocity method, the 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. These elements are determined using fuzzy logic in an attempt to minimize the manipulator power. The Torque method is an alternative approach introduced to reduce the computational complexity. In this case, the nullspace vector in the joint torque expression is determined so that the changes in the transformation matrix are continuous with respect to time. The two methods to resolve the redundancy are illustrated by simulations. The methods are discussed in regard to their computational efficiency and compared with other redundancy resolution approaches.
Degree
Ph.D.
Advisors
Koivo, Purdue University.
Subject Area
Electrical engineering
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