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.

中文翻译：

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机械手动力学快速回归建模的数值推导

摘要 我们提出了伪符号动力学建模 (PSDM)，这是一种使用基本惯性参数推导串联运动链的闭式运动方程的新方法。PSDM 是一种数值算法，但允许模型简化和预计算，通常只能使用符号软件。在 PSDM 中，我们表征了动力学方程的形式，以构建一组保证形成机械臂逆动力学函数的线性基础的函数。然后，执行两步数值分析，以回归量形式将这个集合简化为最小动态模型。PSDM 提供了一种生成简化动态模型的快速程序方法。该算法的扩展允许快速实时代码生成、前向动态建模、并通过消除最不重要的模型元素来提高模型效率。该算法在常见机器人配置上进行了基准测试，并且在推导时间和实时评估速度方面显示出对多达 7 自由度机械手的动态建模具有吸引力。此外，还开发了该算法的 MATLAB 实现并可供一般使用。