A Unified Motion Planning Approach for Redunant and Non-Redundant Manipulators with Actuator Constraints

Abstract

To overcome the limitations of traditional trajectory-planning approaches, 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 report 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 motion planning framework is developed in an optimization setting, which allows the analyst to (i) exploit any available freedom in the task specification of the manipulator, and (ii) exploit (kinematic) redundancy in the case of kinematically redundant manipulators. 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.