R-Graph：面向机器人机构智能设计的表征与计算框架

Robot Graph Structure: A Representation and Computational Framework for Intelligent Design of a Robotic Mechanism

摘要

智能化是机器人创新设计的必然趋势,其核心在于利用人工智能技术从设计数据中学习机器人机构组成规律,并模拟人类思维开展设计．实现机器人智能设计需满足两个基本前提：一是提出有效的机器人机构数字化表征方法,全面、准确地描述机器人机构信息,以便于设计数据的计算机识别和存储；二是具备快速计算机器人机构运动、力学等性能的能力,这些性能指标也反映了机器人机构设计需求．本文提出一种新的数字化语言——机器人图结构(R-Graph),用于表征和计算机器人机构及其性质．首先,利用异构图的节点和边分别表示机器人机构组成构件及其连接关系,揭示R-Graph具有的性质,分别定义节点特征和边特征的存储结构．在此基础上,提出了一种基于图相似度匹配的机构拓扑同构判别方法,并利用图信息传递机制实现了机器人机构运动/力性质的自动求解．最后,讨论了R-Graph在机器人机构智能创新设计中的潜在应用．与传统拓扑图相比,R-Graph不仅能够捕捉运动变量及相关信息,还将轴线关系的表示从布尔值转换为实数矩阵,从而在欧几里得空间和非欧几里得空间中实现统一表征．通过利用这一全面的信息表征结构,能够实现机构运动和力的自动计算,为机器人机构的智能设计提供结构化的数据基础．R-Graph为机器人机构的智能设计提供了新的理论基础和工具,有望推动机器人设计自动化和智能化的发展．

Abstract

Intelligence represents an inevitable trend in the innovative design of robotics. Its core comprises the utilization of artificial intelligence to learn the laws governing the composition of robotic mechanisms from design data, as well as to simulate human thought in the design process. Two fundamental prerequisites are essential for realizing intelligent design in robotics: an effective digital representation of robotic mechanisms, which comprehensively and accurately describes their information, thereby facilitating computer recognition and storage, and a rapid computation of the performances of these robotic mechanisms, which is also the primary objective of mechanism design. In this study, a novel digital language—robot graph structure(R-Graph)—was introduced for the representation and computation of robotic mechanisms and their properties. In this structure, the nodes and edges of a heterogeneous graph were firstly used to represent the components of a robotic mechanism and their connecting relationships, respectively. Thereafter, the node and edge feature matrices were defined, followed by the analysis of the properties of R-Graph. On this basis, a method for discriminating the topological isomorphism of mechanisms was proposed based on graph similarity matching, yielding the automatic solution of the motion/force properties of the mechanisms based on graph information transfer mechanisms. Finally, the potential applications of R-Graph in the innovative, intelligent design of robotic mechanisms were explored. Compared with traditional topological graphs, the results reveal that the proposed R-Graph captures motion variables and related information, as well as transforms the representation of axis relationships from Boolean values to real number matrices, realizing unified representations in Euclidean and non-Euclidean spaces. Further, this comprehensive information representation structure can facilitate automatic motion/force computations, providing an institutionalized data foundation for intelligent robotic mechanism design. Overall, R-Graph offers a novel theoretical foundation, as well as tools, for intelligent robotic mechanism design, which can advance robotic design automation and intelligence.

关键词

机器人机构表征 / 运动/力计算 / 拓扑图 / 智能设计

Key words

robotic mechanism representation / motion/force computation / topological graph / intelligent design

参考文献

[1] Jing G Q, Qin X Y, Wang H Y, et al. Developments, challenges, and perspectives of railway inspection robots[J]. Automation in Construction, 2022, 138:104242.

[2] Zhao A, Xu J, Konaković—Luković M, et al. RoboGrammar: Graph grammar for terrain—optimized robot design[J]. ACM Transactions on Graphics, 2020, 39(6):1-16.

[3] Mruthyunjaya T S. Kinematic structure of mechanisms revisited[J]. Mechanism and Machine Theory, 1999, 34(7):279-320.

[4] Freudenstein F, Dobrjanskyj L. On a theory for the type synthesis of mechanisms[C]// Proceedings of 11th International Congress of Applied Mechanics. Berlin, Germany, 1966:420-428.

[5] Freudenstein F. The basic concepts of Polya’s theory of enumeration, with application to the structural classification of mechanisms[J]. Journal of Mechanisms, 1967, 2(3):275-290.

[6] Talabə D. Mechanical models and the mobility of robots and mechanisms[J]. Robotica, 2014, 33(1):181-193.

[7] Yang W, Ding H, Zi B, et al. New graph representation for planetary gear trains[J]. Journal of Mechanical Design, 2018, 140(1):012303.

[8] Ding H, Zhao J, Huang Z. Unified topological representation models of planar kinematic chains[J]. Journal of Mechanical Design, 2009, 131(11):1145031-1145036.

[9] Ding H, Yang W, Huang P, et al. Automatic structural synthesis of planar multiple joint kinematic chains[J]. Journal of Mechanical Design, 2013, 135(9):091007.

[10] Xia Z H, Tian C X, Li L Q, et al. The novel synthesis of origami—inspired mechanisms based on graph theory[J]. Mechanism and Machine Theory, 2024, 192:105547.

[11] Dai J S, Jones J R. Matrix representation of topological changes in metamorphic mechanisms[J]. Journal of Mechanical Design, 2005, 127(4):837-840.

[12] Laman G. On graphs and rigidity of plane skeletal structures[J]. Journal of Engineering Mathematics, 1970, 4(4):331-340.

[13] Müller A, Shai O. Constraint graphs for combinatorial mobility determination[J]. Mechanism and Machine Theory, 2017, 108:260-275.

[14] Müller A. Generic mobility of rigid body mechanisms[J]. Mechanism and Machine Theory, 2009, 44(6):1240-1255.

[15] Wittenburg J. Dynamics of Systems of Rigid Bodies[M]. Wiesbaden: Vieweg & Teubner Verlag, 1977.

[16] Woo L S. Type synthesis of plane linkages[J]. Journal of Manufacturing Science and Engineering, 1967, 89(1):159-170.

[17] Lu Y, Ye N J. Type synthesis of parallel mechanisms by utilizing sub—mechanisms and digital topological graphs[J]. Mechanism and Machine Theory, 2017, 109:39-50.

[18] Alberto S. Distance measure based on tree—graph—grammars: A way of recognizing hidden and deformed 3D complex objects[C]// Proceedings in International Conference on Pattern Recognition. Montreal, Canada, 1984:739-741.

[19] 卢策吾, 王鹤. 具身智能[EB/OL]. https://www.ccf.rg.cn/Media_list/gzwyh/jsjsysdwyh/2023—07—22/794317.tml, 2023—07—22.

[20] Lu Cewu, Wang He. Embodied Artificial Intelligence[EB/OL]. https://www.ccf.org.cn/Media_list/gzwyh/jsjsdwyh/2023—07—22/794317.tml, 2023—07—22(in Chinese).

[21] 张伟男, 刘挺. 具身智能的研究与应用[J]. 智能系统学报, 2025, 20(1):255-262.

[22] Zhang Weinan, Liu Ting. Research and application of embodied intelligence[J]. CAAI Transactions on Intelligent Systems, 2025, 20(1):255-262(in Chinese).

基金资助

国家自然科学基金资助项目(52275028)

天津市杰出青年科学基金资助项目(22JCJQJC00050)

天津市应用基础研究项目(22JCZDJC00350)

天津市应用基础研究项目(22JCYBJC01670)