A Spatial Operator Algebra For Manipulator Modeling And Control

G. Rodriguez; K. Kreutz; M. Milman

doi:10.1117/12.949073

27 October 1988 A Spatial Operator Algebra For Manipulator Modeling And Control

G. Rodriguez, K. Kreutz, M. Milman

Proceedings Volume 1006, Space Station Automation IV; (1988) https://doi.org/10.1117/12.949073
Event: 1988 Cambridge Symposium on Advances in Intelligent Robotics Systems, 1988, Boston, MA, United States

Abstract

A recently developed 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 the corresponding control and trajectory design algorithms. Expressions interpreted within the algebraic framework lead 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 specific algorithms is greatly simplified. This paper discusses the analytical formulation of the operator algebra, as well as its implementation in the Ada programming language.

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G. Rodriguez, K. Kreutz, and M. Milman "A Spatial Operator Algebra For Manipulator Modeling And Control", Proc. SPIE 1006, Space Station Automation IV, (27 October 1988); https://doi.org/10.1117/12.949073

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KEYWORDS

Space operations

Composites

Algorithm development

Computing systems

Digital filtering

Kinematics

Control systems

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