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Control of Redundant Robot Manipulators - R.V. Patel and F. Shadpey Part 5

Tham khảo tài liệu 'control of redundant robot manipulators - r.v. patel and f. shadpey part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 3.3 Kinematic Simulation for a 7-DOF Redundant Manipulator 51 Figure 3.10 Cylinder-Sphere Collision Detection 3.3 Kinematic Simulation for a 7-DOF Redundant Manipulator In this section the redundancy-resolution scheme described in Chapter 2 is extended for the general case of a 7-DOF redundant manipulator working in a 3-D workspace and applied to REDIESTRO. The feasibility of the algorithms is illustrated using a kinematic simulation 52 3 Collision Avoidance for a 7-DOF Redundant Manipulator Figure 3.11 Sphere-Sphere Collision Detection 3.3.1 Kinematics of REDIESTRO The kinematic description of REDIESTRO a photograph of REDI-ESTRO is shown in Figure 3.1 is obtained by assigning a coordinate frame to each link with its z axis along the axis of rotation. Frame 1 is the workspace fixed frame and frame 8 is the end-effector frame. Two consecutive frames i and i 1 are related by the 4 X 4 homogenous transformation matrix cos Qi - cos a sin Qi sin a sin Qi Uị cos Qị t i 1T sin Qi cos Qị cos a - sin a cos Qi dị sin Q 0 sin i cos i bi _ 0 0 0 1 _ 3.3 Kinematic Simulation for a 7-DOF Redundant Manipulator 53 i 1Rh X 3 Pi 1 3 X 1 0 1 3.3.1 i 1 7 where i 1 7 i 0i bi and a are the twist angle joint angle offset and link length respectively. The Denavit-Hartenberg parameters of REDI-ESTRO are given in Table A-1 . The homogenous transformation relating Frame 8 end-effector frame to the base frame is given by ỳ T T. t 3.3.2 3.3.2 Main Task Tracking The main task is described by the pose position and orientation of the end-effector defined by the position vector P 3 X 1 and the rotation matrix 1r 3 3 of the transformation matrix 8t . The pose is thus dimensionally non-homogenous and needs different treatment for the 3dimensional vector representing the end-effector position from the 3 X 3 rotation matrix representing orientation. Therefore the main task is divided into two independent sub-tasks. 3.3.2.1 Position Tracking The position is described in the workspace-fixed reference .