LIST OF FIGURES Q 1 System configuration and coordinate system assignment. 4 Rotation of (X0, ]Po, Z0) coordinate frame about unit vector n by angle _ to obtain (XN, ]IN, ZN) coordinate frame .... 10 Open loop redundancy resolution to the plant ..... Closed loop redundancy resolution to the plant ...... 28 iv Abstract°T he report discusses the orientation tracking control problem for a kinematically redundant, autonomous manipulator moving in a three dimensional. workspace. The orientation error is derived using the normalized quaternion error method of Ickes [7], the Luh, Walker, and Paul error method [11], and a method suggested here utilizing the Rodrigues parameters, all of which are expressed in terms of normalized quaternions. The analytical time derivatives of the orientation errors are determined. The latter, along with the translational velocity error, form a closed loop kinematic velocity model of the manipulator using normalized quaternion and translational position feedback. An analysis of the singularities associated with expressing the models in a form suitable for solving the inverse kinematics problem is given. Two redundancy resolution algorithms originally developed using an open loop kinematic velocity model of the manipulator are extended to properly take into account the orientation tracking control problem. This report furnishes the necessary mathematical framework required prior to experimental implementation of the orientation tracking control schemes on the seven axis CESARm research manipulator [21, 36, 37, 38] or on the seven-axis Robotics Research K1207i dexterous manipulator, the latter of which is to be delivered to the Oak Ridge National Laboratory in 1993.
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