A spatial operator algebra for manipulator modeling and control

A spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The operators themselves are elements in the algebra of linear bounded operators. The effect of these operators when operating on elements in the domain is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of spatially recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for developing corresponding control and trajectory design algorithms. Expressions interpreted within the operator algorithm framework led to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the high-level operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanization of specific algorithms has been greatly simplified. The analytical formulation of the operator algebra and its implementation in Ada are discussed