A Spatial Operator Algebra for Manipulator Modeling

A recently developed spatial operator algebra for manipulator modeling, control and tra-jectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The eeect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be eeciently obtained via techniques of recursive ltering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipu-lator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual 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 speciic algorithms is greatly simpliied.