A Spatial Operator Algebra for Manipulator Modeling and Control

Abstract

A recently developed spatial operator algebra for manipu lator modeling, control, and trajectory design is dis cussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high- level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced concep tual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus the transition from an abstract problem formulation and solution to the detailed mechanization of specific algorithms is greatly simplified.