Walker/Orin

Walker and Orin [42] present one of the most familiar and efficient approaches for the computation of the inertia matrix in the so-called Composite-Rigid-Body Method [9]. This algorithm utilizes the concq>t of composite-rigid-body inertias to simplify the calculation of the manipulator inotia matrix. The computational complexity of this approach, 0(N% is significantly reduced compared to those described above, but the restriction to revolute and/w prismatic Joints remains. 

Parallel computation methods have also been investigated for the Joint space inertia matrix. Amin-Javaheri and Orin [1], as well as Fijany and Bejczy [10], have achieved bett performance by developing parallel and/or pipelined algorithms. In both cases, the parallel forms are based to a great extent on the serial Composite-Rigid-Body Method of Walker and Orin [42], and, of course, the improvement in performance is dependent on an increased number of processes. 

It may be shown that this procedure for ccmiputing the spatial composite-rigid-body inertia is exactly equivalent to the procedure used by Walker and Orin in [42]. That is, if the composite mass, composite center of mass, and composite moment of inertia matrix are computed for links i through iV, they may be combined to obtain the spatial matrix K,-. After studying this equivalent approach, howev, it appears that the congruence transformation method given hoe is more efficioit... 

More specifically. Methods m and IV have been shown to have improved computational efficiency over previous algorithms for typical robot configurations. Method m is the most efficient algorithm for the calculation of H and J together and the best method for H alone for N < 6. Method IV is the most efficient algorithm for H for V > 6. It should be noted that the efficiency gained by either of these methods may be used to reduce the total computation required for dynamic simulation according to the Walker and Orin approach [42]. 

N), O(N ) and OQfi) formulations and gives a unified approach for serial open-loop systems. Well-known formulations, such as those developed by Walker and Orin (1982), Featherstone (1987), Armstrong (1979), Bae and Haug (1987) and Rosenthal (1987), are among the formulations reviewed. 

Fiiany and Beczy (1990) presented an improved version of Walker and Orin s (1982) 0(N ) method and developed an algorithm well suited for parallel implementation on massively parallel computers. 

Walker, M. W. and Orin, 1982, Efficient Dynamic Computer Simulation of Robotic Mechanisms , ASME Journal of Dynamic Systems and Measurement Control, vol. 104, pp. 205-211. 

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