Symbolically efficient formulations for computational robot dynamics

In 1983, the authors implemented the computer program Algebraic Robot Modeler (ARM) to generate symbolically complete closed-form and recursive dynamic robot models.1–4 Then, in 1985, we incorporated in ARM heuristic rules for the systematic organization of dynamic robot models to reduce the computational requirements of customized forward and inverse dynamics calculations. We compare the symbolic efficiencies of six robot dynamics formulations for generating closed-form and recursive models. We find that our Lagrange-Christoffel formulation is the most symbolically efficient generator of closed-form dynamic robot models. In our companion paper,3 we resolve the issue of numerical efficiency of customized closed-form and recursive algorithms for computing the forward and inverse dynamics of kinematically and dynamically structured manipulators.

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