A computational analysis of screw transformations in robotics

A computational analysis and a comparison of line-oriented representations of general (i.e. rotational and translational) spatial displacements of rigid bodies are presented. Four mathematical formalisms for effecting a general spatial screw displacement are discussed and analyzed in terms of computational efficiency in performing common operations needed in kinematic analysis of multilinked spatial mechanisms. The corresponding algorithms are analyzed in terms of both sequential and parallel execution. It is concluded that the dual-unit quaternion representation offers the most compact and most efficient screw transformation formalism but that line-oriented methods in general are not well suited for efficient kinematic computations or real-time control applications. Owing to line-based geometry, underlying its definition, screw calculus represents a set of valuable tools in theoretical kinematics. However, the mathematical redundancy inherent in Plucker coordinate space representation makes the screw calculus computationally less attractive than the corresponding point-oriented formalisms. >

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