Date of Award

1988

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Frederick E. Sistler

Abstract

This dissertation treats the modeling, analysis, and trajectory control of a robotic manipulator to execute specified point-to-point tasks. The relative coordinate representation of kinematic and dynamic variables is defined using vectors and matrices based on coordinate transformations. A kinematic modeling of a manipulator is performed using Denavit-Hartenberg link parameters. For given end-effector information (location and orientation), a stable and efficient iterative numerical algorithm for a joint solution is developed. A modified general Gauss elimination and a direct minimum search are combined with other refinements to yield fast convergency and stable results. This algorithm can be used as a routine solution for various simple structured manipulators and for general structured manipulators for point-to-point and trajectory following. Two major formulations of robot dynamic modeling, the recursive Newton-Euler and the Largrange-Euler are reviewed utilizing the results of the kinematic analysis. The motion effects of dynamic terms and their relative significance on the nominal joint torque are determined in conjunction with the minimum time motion strategy. The relative significance of dynamic terms is analyzed for a given joint space trajectory. The motion effect of dynamic terms is analyzed by comparing the minimum time motion to the conventional optimum straight line trajectory in joint configuration space. A motion trend for a manipulator under minimum time execution is inferred from the simulation results. An efficient general solution algorithm for generating the minimum time trajectory for a point-to-point task subject to the actuator torque constraints is developed. A series of parametric cubic spline segments is used to represent the continuous joint trajectory. A formulation of an n segmented cubic spline satisfying second derivative continuity at knot points is derived. A Runge-Kutta 4th order, two starting point, forward and backward numerical integration and a non-derivative multi-variable minimum search are performed with a penalty function imposing the constraints on search parameters and kinematic motion parameters. Information for manipulator structure and controller design and trajectory planning for a notable increase in dynamic performance are obtained using the algorithms developed.

Pages

230

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