结构仿生六杆张拉整体机器人折叠控制的形态智能方法

石家旭; 陶子辰; 桂昀; 刘珂; 刘华平; 方浩; 杨庆凯

doi:10.16383/j.aas.c250529

结构仿生六杆张拉整体机器人折叠控制的形态智能方法

doi: 10.16383/j.aas.c250529 cstr: 32138.14.j.aas.c250529

石家旭^{1, 2,},
陶子辰^{1, 2,},
桂昀^{1, 2,},
刘珂^3,,
刘华平^4,,
方浩^{1, 2,},
杨庆凯^{1, 2,}

1.
北京理工大学自动化学院北京 100081
2.
自主智能无人系统全国重点实验室北京 100081
3.
北京大学先进制造与机器人系北京 100091
4.
清华大学计算机科学与技术系北京 100084

基金项目: 国家重点研发项目(2022YFB4702000), 国家自然科学基金项目(62373048, U1913602, 62025304, 62088101)

详细信息

作者简介:
石家旭：北京理工大学硕士研究生. 2024年获得河北工业大学人工智能学院自动化学士学位. 主要研究方向为张拉整体机械结构设计与形态智能控制. E-mail: sjasiu@foxmail.com

陶子辰：北京理工大学博士研究生. 2024年获得北京交通大学自动化学院轨道交通信号与控制学士学位. 主要研究方向为张拉整体跨域机器人的仿真与运动控制. E-mail: zichentao@outlook.com

桂昀：北京理工大学博士研究生. 2024年获得北京理工大学电气工程与自动化学士学位. 主要研究方向为基于扩散模型的张拉整体构型生成与优化. E-mail: 3220245213@bit.edu.cn

刘珂：北京大学先进制造与机器人学院研究员. 2019年博士毕业于美国佐治亚理工学院. 主要研究方向为柔性结构与软体机器的设计、分析与应用. E-mail: liuke@pku.edu.cn

刘华平：清华大学计算机科学与技术系教授. 2004年获得清华大学博士学位. 主要研究方向为具身感知与学习. E-mail: hpliu@tsinghua.edu.cn

方浩：北京理工大学自动化学院教授. 2002年获得西安交通大学博士学位. 主要研究方向为全地形移动机器人、机器人控制与多智能体系统. E-mail: fangh@bit.edu.cn

杨庆凯：北京理工大学自动化学院教授. 2018年获得北京理工大学控制科学与工程博士学位, 同年获得荷兰格罗宁根大学系统控制博士学位. 主要研究方向为形态智能机器人设计与控制、多机器人智能协同运动控制. 本文通信作者. E-mail: qingkai.yang@bit.edu.cn

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出版历程
- 收稿日期: 2025-10-10
- 录用日期: 2026-01-04
- 网络出版日期: 2026-03-10

A Morphological-Intelligence Approach to Folding Control of a Structurally Bioinspired Six-Bar Tensegrity Robot

SHI Jia-Xu^{1, 2
,},
TAO Zi-Chen^{1, 2
,},
GUI Yun^{1, 2
,},
LIU Ke^3
,,
LIU Hua-Ping^4
,,
FANG Hao^{1, 2
,},
YANG Qing-Kai^{1, 2
,}

1.
School of Automation, Beijing Institute of Technology, Beijing 100081
2.
State Key Laboratory of Autonomous Intelligent Unmanned Systems, Beijing 100081
3.
Department of Ad-vanced Manufacturing and Robotics, Peking University, Beijing 100091
4.
Department of Computer Science and Technology, Tsinghua University, Beijing 100084

Funds: Supported by National Key Research and Development Program of China(2022YFB4702000) and National Natural Science Foundation of China(62373048, U1913602, 62025304, 62088101)

More Information

Author Bio:
SHI Jia-Xu　Master student at Beijing Institute of Technology. He received his bachelor degree in Automation from the School of Artificial Intelligence, Hebei University of Technology in 2024. His research interests include the design of tesegrity mechanical structures and morphological intelligent control

TAO Zi-Chen　Ph.D. candidate at Beijing Institute of Technology. He received his bachelor degree in rail transit signal and control from the School of Automation, Beijing Jiaotong University in 2024. His research interest covers motion control and simulation of tensegrity based multi-domain robot

GUI Yun　Ph.D. candidate at Beijing Institute of Technology. He received his bachelor degree in electrical engineering and automation from Beijing Institute of Technology in 2024. His research interests include tensegrity morphology generation and optimization by diffusion model

LIU Ke　Research Fellow at School of Advanced Manufacturing and Robotics, Peking University. He received his Ph.D. degree from Georgia Institute of Technology, GA, USA, in 2019. His research interests include Design, Analysis and Application of Flexible Structures and Soft Machines

LIU Hua-Ping　Professor in the Department of Computer Science and Technology, Tsinghua University. He received his Ph.D. degree from Tsinghua University in 2004. His main research interest is embodied perception and learning

Fang Hao　Professor at the School of Automation, Beijing Institute of Technology. He received his Ph.D. degree from Xi’an Jiaotong University in 2002. His research interests include all-terrain mobile robots, robotic control, and multi-agent systems

YANG Qing-Kai　Professor at the School of Automation, Beijing Institute of Technology. He received his Ph.D. degree in control science and engineering from Beijing Institute of Technology, Beijing, China, and the Ph.D. degree in system control from the University of Groningen, Groningen, The Netherlands, both in 2018. His research interests include the design and control of morphological intelligent robots and intelligent cooperative locomotion control of multiple robots. Corresponding author of this paper

摘要

摘要: 形态智能通常指机器人利用"身体"的物理特性、几何结构以及动力学特征等简化复杂的计算(如控制器设计), 具备良好环境适应性的特点, 是实现具身智能的核心机制. 本文针对六杆张拉整体完全折叠问题, 提出一种利用形态智能机理简化控制方法, 实现部分绳驱下机器人整体的等效折叠. 首先基于"端点聚拢"形态构造折叠目标, 通过结构对称性分析得到四种折叠模式及对应的绳长变化量. 再通过图论回路空间分析, 识别由几何构型产生的冗余绳长变化量, 基于此确定折叠过程中的被控绳. 然后在静力学框架下建立电机输入与绳长变化映射关系并给出可达性判据, 以此得到每种模式下简化控制策略. 最后通过MATLAB准静态仿真及实物实验, 验证了所提方法的有效性. 四种折叠模式下的简化控制策略均能实现机器人完全折叠, 驱动绳的数量可由传统方法的24降低至9. 展现了形态智能在简化机器人控制器设计方面的潜力.
- 张拉整体机器人 /
- 折叠控制 /
- 平衡流形 /
- 形态智能
Abstract: Morphological intelligence refers to leveraging a robot’s physical body—its material properties, geometric structure, and intrinsic dynamics—to offload computation (e.g., controller design) and enhance environmental adaptability; it is a core mechanism of embodied intelligence. This paper targets complete folding of a six-bar tensegrity robot and develops a morphology-driven simplified control method that achieves whole-body folding under partial cable actuation. A folding objective based on endpoint aggregation is first formulated; symmetry analysis then enumerates four folding patterns together with their associated cable-length variations. A graph-theoretic cycle-space analysis is employed to identify redundancy in length changes induced by geometric coupling, from which the actuated-cable set during folding is determined. Within a static framework, the mapping from motor inputs to cable-length variations is established and a reachability criterion is provided, yielding a simplified control strategy for each pattern. Quasi-static MATLAB simulations and hardware experiments validate the approach: across all four patterns, complete folding is achieved while the number of actively actuated cables is reduced from 24 to 9. The results highlight the potential of morphological intelligence to simplify controller design for tensegrity robots.
- Tensegrity robot /
- folding control /
- equilibrium manifold /
- morphological intelligence

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图 1 基于张拉整体结构的管道爬行机器人

Fig. 1 The tensegrity structures-based in-pipe crawing robot

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图 2 六杆张拉整体机器人三角形折叠

Fig. 2 Triangular folding of six-bar tensegrity robot

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图 3 六杆张拉整体机器人六边形折叠

Fig. 3 Hexagonal folding of six-bar tensegrity robot

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图 4 六杆张拉整体机器人一维构型折叠

Fig. 4 One-dimensional folding of six-bar tensegrity robot

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图 5 六杆张拉整体球形机器人

Fig. 5 Six-bar spherical tensegrity robot

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图 6 六杆张拉整体拓扑结构

Fig. 6 Six-bar tensegrity topology

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图 7 折叠模式O₁的弹力网络

Fig. 7 Elastic network of folding mode O₁

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图 8 六杆张拉整体折叠过程仿真

Fig. 8 Folding simulation of six-bar tensegrity

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图 9 六杆张拉整体机器人

Fig. 9 Six-bar tensegrity robot

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图 10 六杆张拉整体机器人折叠与展开过程

Fig. 10 Folding and deployment process of six-bar tensegrity robot

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表 1 绳索编号

Table 1 Cable number

绳索	编号	绳索	编号	绳索	编号
$ A_{11}B_{11} $	1	$ A_{21}B_{12} $	9	$ B_{11}C_{11} $	17
$ A_{11}B_{21} $	2	$ A_{21}B_{22} $	10	$ B_{11}C_{21} $	18
$ A_{11}C_{11} $	3	$ A_{21}C_{11} $	11	$ B_{12}C_{11} $	19
$ A_{11}C_{12} $	4	$ A_{21}C_{12} $	12	$ B_{12}C_{21} $	20
$ A_{12}B_{11} $	5	$ A_{22}B_{12} $	13	$ B_{21}C_{12} $	21
$ A_{12}B_{21} $	6	$ A_{22}B_{22} $	14	$ B_{21}C_{22} $	22
$ A_{12}C_{21} $	7	$ A_{22}C_{21} $	15	$ B_{22}C_{12} $	23
$ A_{12}C_{22} $	8	$ A_{22}C_{22} $	16	$ B_{22}C_{22} $	24

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表 2 四种折叠模式簇划分

Table 2 Cluster partitioning under four folding patterns

模式	$ C_L $	$ C_R $	$ C_M $
$ O_1 $	$A_{11},\; A_{21},\; B_{11},\; $$ B_{21},\; C_{11},\; C_{21}$	$A_{12},\;A_{22},\;B_{12},\; $$ B_{22},\;C_{12},\;C_{22}$	/
$ O_2 $	$A_{11},\; A_{21},\; B_{11},\; $$ B_{21},\; C_{11},\; C_{22}$	$A_{12},\; A_{22},\; B_{12},\; $$ B_{22},\; C_{12},\; C_{21}$	/
$ O_3 $	$A_{11},\; A_{21},\; B_{11},\; $$ B_{22},\; C_{11},\; C_{22}$	$A_{12},\; A_{22},\; B_{12},\; $$ B_{21},\; C_{12},\; C_{21}$	/
$ O_4 $	$ {A_{11},\;B_{11},\;C_{11}} $	$ {A_{22},\;B_{22},\;C_{22}} $	$A_{12},\; A_{21},\; B_{12},\; $$ B_{21},\; C_{12},\; C_{21}$

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