Isotropic and Uniform Inertial and Acceleration Characteristics: Issues in the Design of Redundant Manipulators

Abstract

The paper investigates the dynamic characterization of redundant manipulators and formalizes the problem of dynamic optimization in manipulator design. The dynamic performance of a manipulator is described by both inertial and acceleration characteristics as perceived at the end-effector operational point. The inertial characteristics at this point are given by the operational space kinetic energy matrix (pseudo-kinetic energy matrix for a redundant manipulator) which is dependent on the kinematic and inertial parameters of the manipulator and varies with its configuration. The acceleration characteristics of the end-effector are described by a joint torque/acceleration transmission matrix. In addition to their dependency on the kinematic and inertial parameters, the acceleration characteristics depend on the velocities and actuator torque bounds. The dynamic optimization is formalized in terms of finding the design parameters under the various constraints to achieve the smallest most isotropic and most uniform end-effector inertial properties, while providing the largest, most isotropic, and most uniform bounds on the magnitude of end-effector acceleration. This approach is used in the design of ARTISAN, a ten-degree-of-freedom manipulator currently under development at Stanford University.