基于节律动态运动基元与机器人动力学的多空间融合周期性变阻抗技能学习

doi:10.3901/JME.2025.01.150

摘要/Abstract

摘要： 当前人-机器人技能传递方法主要集中于离散的点到点或运动学方面，而周期性的动力学技能学习没有被恰当考虑。本文提出了一种基于节律动态运动基元的多空间融合技能学习框架用于从人类示范中学习周期性变阻抗技能(包括运动轨迹与变刚度特征)。机器人工作空间的力感知信息被用于估计端点刚度矩阵，但由于其对称正定(Symmetric positive definite，SPD)特性与传统节律动态运动基元(Rhythmic dynamic movement primitive，rDMP)对欧氏空间数据的依赖性，研究设计了一种基于黎曼度量的节律动态运动基元(Riemannian metric-based rhythmic dynamic movement primitive，RM-rDMP)技能学习方法以适应SPD流形上的刚度矩阵信息，并采用自适应振荡器估计系统的频率与相位。通过基于机器人动力学模型的阻抗控制策略，将运动轨迹与变刚度特性同时赋予机器人以完成变阻抗技能编码。通过仿真与实验研究表明，所提方法可成功将类人的运动学与动力学技能传递给机器人，并使其具备再现与泛化能力。综上，所提方法包括一个端点刚度估计模型和一个多空间融合的周期性变阻抗技能学习框架，适用于需要同时考虑欧氏空间位置和黎曼空间刚度矩阵的人-机器人技能传递控制方法。

关键词: 机器人动力学, 周期性可变阻抗技能, 节律动态运动基元, 黎曼流形, 人-机器人技能传递

Abstract: The current methods for human-robot skill transfer in robotics mainly focus on discrete point-to-point or kinematic aspects, while the learning of periodic dynamic skills has not been adequately considered. This article proposes a multi-space fusion skill learning framework based on rhythmic dynamic movement primitive (rDMP) for learning periodic impedance skills (including motion trajectories and variable stiffness features) from human demonstrations. The force perception information of the robot’s workspace is used to estimate the endpoint stiffness matrix. However, due to its symmetric positive definite (SPD) characteristics and the dependence of traditional rDMP on Euclidean space data, this research designs a Riemannian metric-based rhythmic dynamic movement primitive (RM-rDMP) skill learning method to adapt to the stiffness matrix information on the SPD manifold and adopts an adaptive oscillator estimation system for frequency and phase. By using an impedance control strategy based on the robot’s dynamics model, both motion trajectories and variable stiffness features are assigned to the robot to achieve variable impedance skill encoding. Simulation and experimental studies demonstrate that the proposed method successfully transfers human-like kinematic and dynamic skills to the robot and enables it to have reproduction and generalization capabilities. In summary, the proposed method includes an endpoint stiffness estimation model and a multi-space fusion framework for periodic impedance skill learning, which is applicable to human-robot skill transfer control methods that need to consider both Euclidean space position and Riemannian space stiffness matrix.

Key words: robot dynamics, periodic variable impedance skill, rhythmic dynamic movement primitive, Riemannian manifold, human-robot skill transfer

中图分类号:

TH113

刘程果, 合烨, 陈小安, 王光建. 基于节律动态运动基元与机器人动力学的多空间融合周期性变阻抗技能学习[J]. 机械工程学报, 2025, 61(1): 150-161.

LIU Chengguo, HE Ye, CHEN Xiaoan, WANG Guangjian. Multi-space Fused Periodic Variable Impedance Skill Learning Based on Rhythmic Dynamic Movement Primitive and Robot Dynamics[J]. Journal of Mechanical Engineering, 2025, 61(1): 150-161.

参考文献

[1] YANG G Z，BELLINGHAM J，CHOSET H，et al. Science for robotics and robotics for science[J]. Science Robotics，2016，1(1)：2099.
[2] 刘辛军，于靖军，王国彪，等. 机器人研究进展与科学挑战[J]. 中国科学基金，2016，30(5)：425-431. LIU Xinjun，YU Jingjun，WANG Guobiao，et al. Research trend and scientific challenge of robotics[J]. Bulletin of National Natural Science Foundation of China，2016，30(5)：425-431.
[3] 赵杰，武睿，张赫，等. 面向复杂力交互任务的操作技能传递与控制研究[J]. 机械工程学报，2022，58(18)：116-132. ZHAO Jie，WU Rui，ZHANG He，et al. Research on operation skill transfer and control oriented to complex force interaction tasks[J]. Journal of Mechanical Engineering，2022，58(18)：116-132.
[4] HOGAN N. Impedance control：An approach to manipulation[C]. Proceedings of the American Control Conference，San Diego，USA，1984，304-313，IEEE.
[5] RAVICHANDAR H，POLYDOROS A S，CHERNOVA S，et al. Recent advances in robot learning from demonstration[J]. Annual review of Control，Robotics，Autonomous Systems，2020，3：297-330.
[6] YU X B，LIU P S，HE W，et al. Human-robot variable impedance skills transfer learning based on dynamic movement primitives[J]. IEEE Robotics and Automation Letters，2022，7(3)：6463-6470.
[7] ZENG C，LI S，FANG B，et al. Generalization of robot force-relevant skills through adapting compliant profiles[J]. IEEE Robotics and Automation Letters，2022，7(2)：1055-1062.
[8] 邢宏军，丁亮，高海波，等. 基于阻抗控制的机器人旋拧阀门轴向位置自适应跟踪[J]. 机械工程学报，2019，55(15)：124-134. XING Hongjun，DING Liang，GAO Haibo，et al. Adaptive tracking of axial position for valve-turning with a robot based on impedance control[J]. Journal of Mechanical Engineering，2019，55(15)：124-134.
[9] 曾晨东，艾海平，陈力. 空间机械臂在轨插、拔孔操作力/位姿阻抗控制[J]. 机械工程学报，2022，58(03)：84-94. ZENG Chendong，AI Haiping，CHEN Li. Force/pose impedance control for space manipulator orbit insertion and extraction[J]. Journal of Mechanical Engineering，2022，58(03)：84-94.
[10] LIAO Z W，JIANG G D，ZHAO F，et al. Dynamic skill learning from human demonstration based on the human arm stiffness estimation model and riemannian DMP[J]. IEEE/ASME Transactions on Mechatronics，2022：1-12.
[11] AJOUDANI A，FANG C，TSAGARAKIS N，et al. Reduced-complexity representation of the human arm active endpoint stiffness for supervisory control of remote manipulation[J]. The International Journal of Robotics Research，2017，37(1)：155-167.
[12] PERREAULT E J，KIRSCH R F，ACOSTA A M. Multiple-input，multiple-output system identification for characterization of limb stiffness dynamics[J]. Biological Cybernetics，1999，80(5)：327-337.
[13] WU Y Q，ZHAO F，KIM W，et al. An intuitive formulation of the human arm active endpoint stiffness[J]. Sensors，2020，20(18)：5357.
[14] ABU-DAKKA F J，ROZO L，CALDWELL D G. Force-based variable impedance learning for robotic manipulation[J]. Robotics and Autonomous Systems，2018，109：156-167.
[15] CALINON S，BRUNO D，CALDWELL D G. A task-parameterized probabilistic model with minimal intervention control[C]. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA)，Hong Kong，China，2014，3339-3344，IEEE.
[16] CALINON S，D’HALLUIN F，SAUSER E L，et al. Learning and reproduction of gestures by imitation an approach based on hidden markov model and gaussian mixture regression[J]. IEEE Robotics and Automation Magazine，2010，17(2)：44-54.
[17] LEONEL R，JOÃO S，SYLVAIN C，et al. Learning controllers for reactive and proactive behaviors in human-robot collaboration[J]. Frontiers in Robotics and AI，2016，3(30)：1-11.
[18] IJSPEERT A J，NAKANISHI J，HOFFMANN H，et al. Dynamical movement primitives： learning attractor models for motor behaviors[J]. Neural Computation，2013，25(2)：328-373.
[19] PARASCHOS A，DANIEL C，PETERS J，et al. Probabilistic movement primitives[J]. Autonomous Robots，2014，42(3)：529-551.
[20] HUANG Y L，ROZO L，SILVÉRIO J，et al. Kernelized movement primitives[J]. International Journal of Robotics Research，2019，38(7)：833-852.
[21] GAO X，SILVÉRIO J，PIGNAT E，et al. Motion mappings for continuous bilateral teleoperation[J]. IEEE Robotics and Automation Letters，2020，6(3)：5048-5055.
[22] KHANSARI-ZADEH S M，BILLARD A. Learning stable nonlinear dynamical systems with gaussian mixture models[J]. IEEE Transactions on Robotics，2011，27(5)：943-957.
[23] ABU-DAKKA F J，KYRKI V. Geometry-aware dynamic movement primitives[C]. proceedings of the IEEE International Conference on Robotics and Automation (ICRA)，Paris，France，2020，4421-4426，IEEE.
[24] ABU-DAKKA F J，HUANG Yunlong，SILVÉRIO J，et al. A probabilistic framework for learning geometry-based robot manipulation skills[J]. Robotics and Autonomous Systems，2021，141：103761.
[25] IJSPEERT A J，NAKANISHI J，SCHAAL S. Learning rhythmic movements by demonstration using nonlinear oscillators[C]. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)，Lausanne，Switzerland，2002，958-963，IEEE.
[26] GAMS A，IJSPEERT A J，SCHAAL S，et al. On-line learning and modulation of periodic movements with nonlinear dynamical systems[J]. Autonomous Robots，2009，27(1)：3-23.
[27] PETRIC T，GAMS A，IJSPEERT A J，et al. On-line frequency adaptation and movement imitation for rhythmic robotic tasks[J]. The International Journal of Robotics Research，2011，30(14)：1775-1788.
[28] PENNEC X，FILLARD P，AYACHE N. A riemannian framework for tensor computing[J]. International Journal of Computer Vision，2006，66(1)：41-66.
[29] SRA S，HOSSEINI R. Conic geometric optimization on the manifold of positive definite matrices[J]. Siam Journal on Optimization，2015，25(1)：713-739.
[30] LEE. Introduction to smooth manifolds (Graduate Texts in Mathematics) [M]. New York：Springer，2012.
[31] JAQUIER N，ROZO L，CALDWELL D G，et al. Geometry-aware manipulability learning，tracking，and transfer[J]. International Journal of Robotics Research，2021，40(2-3)：624-650.
[32] ROZO L，CALINON S，CALDWELL D G，et al. Learning collaborative impedance-based robot behaviors[C]. Proceedings of the AAAI Conference on Artificial Intelligence，2013.
[33] HIGHAM N J. Computing a nearest symmetric positive semidefinite matrix[J]. Linear Algebra and Its Applications，1988，103：103-118.
[34] 李海源，刘畅，严鲁涛，等. 上肢外骨骼机器人的阻抗控制与关节试验研究[J]. 机械工程学报，2020，56(19)：200-209. LI Haiyuan，LIU Chang，YAN Lutao，et al. Research on impendence control of an upper limb exoskeleton robot and joint experiments[J]. Journal of Mechanical Engineering，2020，56(19)：200-209.
[35] 琦歆，俞滨，王春雨，等. 液压驱动单元基于力的阻抗控制系统前馈抗扰控制研究[J]. 机械工程学报，2023，59(04)：295-307. ZHU Qixin，YU Bin，WANG Chunyu，et al. Research on feedforward disturbance rejection control for force-based impedance control system of hydraulic drive unit[J]. Journal of Mechanical Engineering，2023，59(03)：295-307.
[36] 李洋，朱立爽，刘今越，等. 基于动力学模型辨识的全臂柔顺控制[J]. 机械工程学报，2022，58(03)： 45-54. LI Yang，ZHU Lishuang，LIU Jinyue，et al. Dynamic model identification for whole-arm compliance control[J]. Journal of Mechanical Engineering，2022，58(03)：45-54.
[37] MARKUS L. Asymptotically autonomous differential systems[J]. Contributions to the Theory of Nonlinear Oscillations，2016，3(17).
[38] FIORI S. Manifold calculus in system theory and control—Fundamentals and first-order systems[J]. Symmetry，2021，13(11)：2092.
[39] SLOTINE J-J E，LI W. Applied nonlinear control [M]. Prentice hall Englewood Cliffs，NJ，1991.