Visual Attention

Abstract

A spatial operator algebra for modeling, control, and trajectory designof manipulators is discussed. The elements of this algebra are linearoperators whose domain and range spaces consist of forces, moments,velocities, and accelerations. The operators themselves are elementsin the algebra of linear bounded operators. The effect of these operatorswhen operating on elements in the domain is equivalent to a spatialrecursion along the span of a manipulator. Inversion of operatorscan be efficiently obtained via techniques of spatially recursivefiltering and smoothing. The operator algebra provides a high-levelframework for describing the dynamic and kinematic behavior of amanipulator and for developing corresponding control and trajectorydesign algorithms. Expressions interpreted within the operator algorithmframework led to enhanced conceptual and physical understanding ofmanipulator dynamics and kinematics. Furthermore, implementable recursivealgorithms can be immediately derived from the high-level operatorexpressions by inspection. Thus, the transition from an abstractproblem formulation and solution to the detailed mechanization ofspecific algorithms has been greatly simplified. The analytical formulationof the operator algebra and its implementation in Ada are discussed