Gross Motion of a Kinematically Redundant Manipulator

. . . . . . . . . . . . . . . . . . v 1 . INTRODUCTION . . . . . . . . . . . . . . . . 1 2 . PROBLEM STATEMENT AND SYSTEM DESCRIPTION . . . . 3 2.1 SYSTEM VARIABLES AND COORDINATE FRAMES . . . . 3 2.2 KINEMATIC MANIPULATOR MODEL . . . . . . . . . 3 2.3 DYNAMIC MANIPULATOR MODEL . . . . . . . . . 5 3 . RESOLUTION OF KINEMATIC REDUNDANCY . . . . . . . 7 3.1 SELECTION OF E AND k . . . . . . . . . . . . . 8 3.2 SELECTION OF B SUCH THAT E IS A SUBSET OF 4 . . . . 9 3.3 CHOOSING B ORTHOGONAL TO THE ROWS O F J . . . . 13 3.4 SELECTING B BY APPLICATION OF THE ZERO-EIGENV.4LUE MATRIX THEOREM . . . . . . . . . . . . . . 16 3.5 THE VECTOR CROSS PRODUCT METHOD FOR PLANAR MANIPULATORS . . . . . . . . . . . . . . . 17 4 . RIGID BODY DYNAMICAL MODEL AND CONTROL ARCHITECTURE 23 5 . CONCLUSION AND FUTURE WORK . . . . . . . . . . 25 6 . ACKNOWLEDGMENT . . . . . . . . . . . . . . . 27 APPENDIX A . . . . . . . . . . . . . . . . . . 29 APPENDIXB . . . . . . . . . . . . . . . . . . 31 APPENDIX C . . . . . . . . . . . . . . . . . . 39 REFERENCES . . . . . . . . . . . . . . . . . . 41