A numeric derivation for fast regressive modeling of manipulator dynamics

Abstract

We present Pseudo-Symbolic Dynamic Modeling (PSDM), a novel method of deriving the closed-form equations of motion of a serial kinematic chain, using base inertial parameters. PSDM is a numerical algorithm, yet allows for model simplification and pre-computation generally only possible using symbolic software. In PSDM, we characterize the form of the dynamic equations to build a set of functions guaranteed to form a linear basis for the inverse dynamics function of the manipulator. Then, a two-step numerical analysis is performed to reduce this set into a minimal dynamic model, in regressor form. PSDM offers a fast and procedural method of generating simplified dynamic models. Extensions to the algorithm allow for fast real-time code generation, forward dynamic modeling, and increased model efficiency through the elimination of minimally important model elements. The algorithm is benchmarked on common robot configurations and shown to be attractive for the dynamic modeling of up to 7-DOF manipulators, in terms of derivation time and real-time evaluation speed. Additionally, a MATLAB implementation of the algorithm has been developed and is made available for general use.