In this dissertation, a systematic approach using the linear mapping theory for studying the dynamic performance of the redundant manipulator is developed. The dynamic performance of the manipulator represents the motion characteristics of the manipulator's end-effector having consideration of the manipulator's dynamics and is closely related with the acceleration analysis for the end-effector. Generally, the representative requirement needed in robot applications is to perform a given task rapidly and exactly. Thus, in this study, the dynamic performance of the manipulator is analyzed on the basis of two viewpoints of the accelerating capability and the tracking capability for the end-effector.
The accelerating capability indicates how rapidly the manipulator can move its end-effector. Thus, the accelerating capability represents the maneuverability to cope with the arbitrary situations such as the emergence of the moving obstacle, the abrupt change of the movement direction. Also, since the task time is affected greatly by the amount of time elapsed in the initial acceleration and the final deceleration stage, the large accelerating capability is necessary in reduction of the task time. In order to measure quantitatively such accelerating capability of the manipulator, the acceleration polyhedron(AP) is proposed, which is defined as the set of all end-effector accelerations that are realizable under the torque limit of the actuator. In the previous studies, to represent the accelerating capability, the dynamic manipulability ellipsoid(DME) proposed by Yoshikawa has been widely used. It is shown that the AP is physically proper than the DME in view of the definition of the set of available torques.
The tracking capability indicates how accurately the manipulator can move its end-effector, and is influenced by the various factors in the position control. In those factors, one important thing is the dynamic load due to a payload at the end-effector. In this study, only the tracking capability for the uncertainty of the payload is treated. In order to measure quantitatively such tracking capability, the trackability polyhedron(TP) is proposed, which is defined as the set of all end-effector accelerations that are realizable under the error limit of the controller. Also, in the definition of the TP, the computed torque control method is considered as the basic position control law.
The AP and the TP are all applicable to both of the redundant and the non-redundant manipulators. For application of the joint trajectory planning of the redundant manipulator, the isotropic acceleration and the trackability acceleration are suggested as the performance indices for the AP and TP, respectively. For these performance indices, the optimal joint trajectory is obtained through the null-space projection method being one of the kinematic redundancy resolution methods. Also, as an example of the dynamic redundancy resolution of the redundant manipulator, the local torque optimization is considered. By using the geometrical properties of the AP, a new algorithm of the stabilized minimum infinity-norm torque solution is developed, and then the effectiveness of the proposed algorithm is shown in comparison with the previous methods through some numerical simulations.
