Symbolic automation and numerical synthesis for robot kinematics

This research analyzes three topics in robot arm kinematics. First, the direct kinematics which determines the Cartesian position and orientation of the end effector for the specified values of joint parameters is analyzed. Second, the differential motions concerning the differential relationships between the command variables in position and orientation of the end effector and the joint-controlled variables are studied. Finally, the inverse kinematics which determines the joint variables for a specified Cartesian position and orientation of the end effector is considered. This dissertation presents a methodology for incorporating the artificial intelligence types of knowledge into automating solutions for the direct kinematics problem and the manipulator Jacobian matrix. Furthermore, the dissertation utilizes the backward recursive techniques, the trigonometric identity rules, and a set of heuristic rules for implementing this methodology. To expedite computation efforts, a new algorithm is developed to obtain a differential relationship of a robotic manipulator via the vector kinematics method. Moreover, the speed control model for general robotic manipulators, together with the inverse Jacobian regarding cases of under-determined and over-determined of joint-controlled variables, are also discussed. Three mathematical approaches are proposed for solving the inverse kinematics problem: the inverse homogeneous transformation matrices approach, the geometric approach, and the arm-wrist partitioned synthesis approach. The first two approaches yield the symbolic closed-form solutions; the last approach, based on the iterative technique, provides a maximum of 16 distinct solutions of joint motion variables for any given position and orientation of the end effector in the workspace --Abstract, pages ii-iii