An Analytical Method For Sensitivity Analysis Of Rigid Multibody System Dynamics Using Projective Geometric Algebra

IF 1.9 4区工程技术 Q3 ENGINEERING, MECHANICAL

Journal of Computational and Nonlinear Dynamics Pub Date : 2023-08-24 DOI:10.1115/1.4063225

Guangzhen Sun, Ye Ding

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引用次数: 0

Abstract

The analytical sensitivity analysis, i.e., the analytical first-order partial derivatives of dynamical equations, is one key to improving descent-based optimization methods for motion planning and control of robots. This paper proposes an efficient algorithm that recursively evaluates the analytic gradient of the dynamical equations of a multibody system. The theory of projective geometric algebra (PGA) is used to generate the algorithm. It provides a systemic and geometrically intuitive interpretation for the multibody system dynamics, and the resulting algorithm is highly efficient, with concise formula. The algorithm is first applied to the open-chain system and extended for the cases when kinematic loops are contained. The runtime varying with respect to the degree of freedom (DOF) of the system is analyzed. The results are compared with that obtained from the algorithm based on spatial vector algebra (SVA) using open-source MATLAB codes. A 2-DOF serial robot, a 3-DOF robot with a kinematic loop and the PUMA560 robot are used for the validation of the minimum-effort motion planning, and it is verified that the proposed algorithm improves the efficiency.

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基于投影几何代数的刚体多体系统动力学灵敏度分析方法

解析灵敏度分析，即动力学方程的解析一阶偏导数，是改进基于下降点的机器人运动规划与控制优化方法的关键之一。本文提出了一种递归求多体系统动力学方程解析梯度的有效算法。利用射影几何代数(PGA)理论生成该算法。它为多体系统动力学提供了系统的、几何上直观的解释，所得算法效率高，公式简洁。首先将该算法应用于开链系统，并将其推广到包含运动环的情况。分析了系统运行时间随系统自由度的变化规律。利用开放源代码的MATLAB代码，将结果与基于空间向量代数(SVA)的算法进行了比较。以2-DOF串联机器人、3-DOF带运动环机器人和PUMA560机器人为例，验证了最小努力运动规划算法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Nonlinear Dynamics 工程技术-工程：机械

CiteScore

4.00

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.