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UBC Theses and Dissertations

The performance of robot manipulation van den Doel, Cornelis Pieter


A theory of the performance of robot manipulation is presented. The theory deals with general robotic manipulation, which is viewed as the physical interaction between a generalized manipulator and a generalized object. The generalized manipulator can be arbitrarily complex, i.e. it can consist of any number of robotic devices. Similarly, the generalized object represents the set of all the material bodies manipulated by the robot in the environment. The study of the performance of such systems is somewhat analogous to the study of the performance of algorithms and complexity theory in computer science. A digital computer produces certain desired changes in information, it transforms input into output, and complexity theory deals with the efficiency of this process. Similarly, a robotic device transforms the state of the objects it manipulates. The manipulation we are concerned with here is only different in that material objects are affected and the measure for the resources needed to perform certain tasks is not runtime or memory usage. How performance should then be measured instead is the subject of this thesis. The theory regards the manipulation as a mapping from the space of all manipulator configurations to the space of all object configurations. By endowing these manifolds with Riemannian metrics we can quantify motion in the manifolds. Performance measures, which quantify how well the robot is executing its manipulation task, arise naturally as geometrical objects associated with the mapping and the metric structure of the manifolds. Generalizations of known measures (agreeing with those previously defined for the simplest kinds of systems) arise naturally in this formalism and we construct several new types of measures. The new types of measures presented here are the effective inertia on work space, the kinematic and dynamic anisotropy measures for redundant manipulators, non-linearity measures, and redundancy measures. An extension of the theory broadens its domain of application to situations in which the relation between the robot and the object it is manipulating can not be given in explicit form, but by a set of constraint equations (possibly non-holonomic) that define it implicitly. The main contribution of this work is the theory of manipulation, which provides a theoretical foundation for robot manipulation. Computational aspects of the theory are described briefly and the theory is applied to some simple planar manipulating devices, for which several of the measures have been constructed and optimized. These applications are given here for illustrative purpose.

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