Tham khảo tài liệu 'control of redundant robot manipulators - . patel and f. shadpey part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 20 2 Redundant Manipulators Kinematic Analysis and Redundancy Resolution Analytic Expression for Additional Tasks The general strategies for defining additional tasks - inequality and optimization tasks - were explained in Section In this section the additional tasks most commonly encountered are formulated analytically under configuration control. Figure Kinematic control loop for a redundant manipulator Joint Limit Avoidance JLA Joint variables of actual mechanisms are obviously limited by mechanical constraints. In actual implementations if some joint variables computed by the inverse kinematic module exceed their limits these joints would be fixed at their extreme values which would restrict movement in certain directions in task space. In this section we first introduce some relevant terminology based on which a feasibility analysis of using kinematic redundancy resolution for joint limit avoidance will be presented. Then we shall use two different approaches for defining algorithms which solve the problem of JLA. The performance of these algorithms will be analyzed by using computer simulations. Analytic Expression for Additional Tasks 21 Definition of Terms and Feasibility Analysis The reachable workspace of a robot manipulator is defined by the geometrical locus of the position and orientation pose of the end-effector y e W when the joint variables q E w n m range between two extreme values. qimin - qi - qimax i 1 2 . n The volume of the reachable workspace is finite connected and therefore is entirely defined by its boundary surface. Obviously on this boundary some loss of mobility occurs. Therefore the Jacobian matrix becomes rank deficient. The boundary of the reachable workspace can be found numerically by constrained optimization routines or by applying an inverse kinematics algorithm 62 . As an example in Figure we show the reachable workspace of a two-link manipulator using an optimization based approach .
