A unified motion planning approach for redundant and nonredundant manipulators with actuator constraints

The term trajectory-planning has been used to refer to the process of determining the time-history or "joint trajectory" of each joint variable corresponding to a specified trajectory of the end-effector. The trajectory-planning problem, in its original form, was solved as a purely kinematic problem. The drawback of this approach is that there is no guarantee that the actuators can deliver the effort necessary to track the planned trajectory. Furthermore, feedback-controller synthesis was addressed as a separate problem and without consideration of the actuator constraints. Later studies, which were concerned with the development of high-speed and high-precision manipulators did take actuator constraints into account but the control strategy used was primarily based on the classical open-loop optimal control approach. The performance of the robot manipulator resulting from the implementation of such an open-loop approach is extremely sensitive to uncertainty in the dynamic model and disturbances. The addition of a feedback controller may not resolve this problem because the feedback control law is usually synthesized without taking the actuator constraints into account. To overcome these limitations, we have developed a motion planning approach which addresses the kinematics, dynamics and feedback-control of a manipulator in a unified-framework. Actuator constraints are taken into account explicitly and a-priori in the synthesis of the feedback control law. Therefore the result of applying the motion planning approach described in this thesis is not only the determination of the entire set of joint trajectories but also a complete specification of the feedback-control strategy which would yield these joint trajectories without violating actuator constraints.;The effectiveness of the unified motion planning approach is demonstrated on two problems which are of practical interest in manipulator robotics. In the first problem feedback-controlled motions which minimize task time are planned for non-redundant manipulators. The second problem, which has useful applications in Space Robotics, addresses the use of kinematic redundancy in planning motions which minimize the magnitude of the reactions transmitted to the base of a manipulator.