Dynamic modeling and cooperative control of a redundant manipulator based on decomposition

This paper demonstrates the use of a redundant manipulator to execute multiple tasks specified at different points on the manipulator. This is accomplished by decomposing a redundant arm at an intermediate arm location, called “elbow”, into two non-redundant local arms, referred to as the “bascarm” and the forearm. This decomposition transforms a redundant arm into a “serially linked dual-arm system,” where the cooperation between the basearm and the forearm is carried out through the task distribution and the elbow control. To distribute a given task to individual local arms according to their dynamic capabilities, the Cartesian space model of a serially linked dual-arm system is derived using Lagrangian mechanics. The Cartesian space dynamic model enables us to quantify the dynamic capbilities of individual arms based on two hyper ellipsoids: the Cartesian Force Ellipsoid (C. F. E.) representing the range of Cartesian forces due to the unit norm of joint torques, and Cartesian Acceleration Ellipsoid (C. A. E.) representing the range of Cartesian accelerations due to the unit norm of Cartesian forces. In addition to the local dynamic characteristics, the global task requirements such as singularity avoidance, joint torque limit avoidance, motion generation efficiency, and accurate motion control, are improved by elbow control. Elbow control can also be used to execute a subtask at the elbow, for example, obstacle avoidance.