基于改进高阶无迹卡尔曼滤波的膝踝康复矫形器预测控制与实验研究

doi:10.3901/JME.2025.11.057

摘要/Abstract

摘要： 针对康复机器人人机协同运动时的运动行为估计和轨迹跟踪控制问题，提出了一种膝踝康复矫形器力矩估计和模型预测控制算法。首先，建立基于拉格朗日函数和负载方程的机器人关节动力学模型，提出了一种高阶无迹卡尔曼滤波(Unscented Kalman filter, UKF)算法，实现不依靠力矩传感器的关节力矩估计。其次，设计H_∞滤波器降低UKF算法中因不确定性噪声带来的估计误差，提高了估计算法的鲁棒性。然后，改进模型预测控制器，将非线性滤波的后验估计值作为系统的输出反馈，提高了机器人力矩跟踪精度并收敛了误差范围。最后，搭建物理样机进行相关的空载实验和人机协同运动实验，验证了力矩估计方法的准确性和控制算法的有效性。

关键词: 康复机器人, 状态估计, 非线性滤波, 模型预测控制

Abstract: To solve the problems of motion behavior estimation and trajectory tracking control for human-manchine collaborative motion of rehabilitation robots, a torque estimation and model predictive control algorithm for knee ankle rehabilitation orthotics is proposed. Firstly, a robot joint dynamics model based on Lagrange function and load equation is established, and a high-order unscented Kalman filter (UKF) algorithm is proposed to achieve joint torque estimation without relying on torque sensors. Secondly, the H_∞ filter is designed to reduce estimation errors caused by uncertain noise in the UKF algorithm and improves the robustness of the estimation algorithm. Then, the model predictive controller is improved by using the posterior estimation value of nonlinear filtering as the output feedback of the system, which improve the accuracy of robot torque tracking and converged the error range. Finally, a physical prototype is constructed for no-load experiments and human-machine collaborative motion experiments, verifying the accuracy of the torque estimation method and the effectiveness of the control algorithm.

Key words: rehabilitation robot, state estimation, nonlinear filtering, model predictive control

中图分类号:

TP242

李元, 孙智, 訾斌, 陈兵. 基于改进高阶无迹卡尔曼滤波的膝踝康复矫形器预测控制与实验研究[J]. 机械工程学报, 2025, 61(11): 57-71.

LI Yuan, SUN Zhi, ZI Bin, CHEN Bing. Predictive Control and Experimental Study of Knee Ankle Rehabilitation Orthosis Based on Improved High-order Unscented Kalman Filters[J]. Journal of Mechanical Engineering, 2025, 61(11): 57-71.

参考文献

[1] 杜鹏，李龙. 新时代中国人口老龄化长期趋势预测[J]. 中国人民大学学报，2021，35(1)：96-109. DU Peng，LI Long. Long-term trends projection of China's population aging in the new era[J]. Journal of Renmin University of China，2021，35(1)：96-109.
[2] United Nations Department of Economic and Social Affairs，Population Division. World population prospects 2022：Summary of results[R]. New York：United Nations，2022.
[3] KIM H J，LIM D H，KIM W S，et al. Development of a passive modular knee mechanism for a lower limb exoskeleton robot and its effectiveness in the workplace[J]. International Journal of Precision Engineering and Manufacturing，2020，21：227-236.
[4] ZHANG M，WANG C，ZHANG C，et al. A unified switching control framework for continuous robot-assisted training[J]. IEEE/ASME Transactions on Mechatronics，2024，29(4)：2743-2755.
[5] 丁逸苇，涂利娟，刘怡希，等. 可穿戴式下肢外骨骼康复机器人研究进展[J]. 机器人，2022，44(5)：522-532. DING Yiwei，TU Lijuan，LIU Yixi，et al. Progress of wearable lower-limb exoskeleton rehabilitation robots[J]. Robot，2022，44(5)：522-532.
[6] LI Y，ZI B，SUN Z，et al. Smooth trajectory planning for a cable driven parallel waist rehabilitation robot based on rehabilitation evaluation factors[J]. Chinese Journal of Mechanical Engineering，2023，36：73.
[7] PAIS-VIEIRA C，ALLAHDAD M，NEVES-AMADO J，et al. Method for positioning and rehabilitation training with the ExoAtlet® powered exoskeleton[J]. MethodsX，2020，7：100849.
[8] SHI D，ZHANG W，ZHANG W，et al. A review on lower limb rehabilitation exoskeleton robots[J]. Chinese Journal of Mechanical Engineering，2019，32：74.
[9] SOMMERHALDER M，ZIMMERMANN Y，SONG J，et al. Polymorphic control framework for automated and individualized robot-assisted rehabilitation[J]. IEEE Transactions on Robotics，2024，40：298-315.
[10] 李元，訾斌，孙智. 基于伪刚体模型的腰部训练装置的运动学分析[J]. 机械工程学报，2019，55(23)：67-74. LI Yuan，ZI Bin，SUN Zhi. Kinematic analysis of the waist rehabilitation robot based on pseudo-rigid-body model[J]. Journal of Mechanical Engineering，2019，55(23)：67-74.
[11] CHEN Q，ZI B，SUN Z，et al. Design and development of a new cable-driven parallel robot for waist rehabilitation[J]. IEEE/ASME Transactions on Mechatronics，2019，24(4)：1497-1507.
[12] LI Y，ZI B，SUN Z，et al. Implementation of cable-driven waist rehabilitation robotic system using fractional-order controller[J]. Mechanism and Machine Theory，2023，190：105460.
[13] PÉREZ-SAN LÁZARO R，SALGADO I，CHAIREZ I. Adaptive sliding-mode controller of a lower limb mobile exoskeleton for active rehabilitation[J]. ISA Transactions，2021，109：218-228.
[14] SONG J，ZHU A，TU Y，et al. Novel design and control of a crank-slider series elastic actuated knee exoskeleton for compliant human-robot interaction[J]. IEEE/ASME Transactions on Mechatronics，2022，28(1)：531-542.
[15] SHI D，ZHANG W，WANG L，et al. Joint-angle adaptive coordination control of a serial-parallel lower limb rehabilitation exoskeleton[J]. IEEE Transactions on Medical Robotics and Bionics，2022，4(3)：775-784.
[16] 徐铃辉，杨巍，杨灿军，等. 基于运动预测的髋关节外骨骼实时助力控制[J]. 机器人，2021，43(4)：473-483. XU Linghui，YANG Wei，YANG Canjun，et al. Real-time assistance control of hip exoskeleton based on motion prediction[J]. Robot，2021，43(4)：473-483.
[17] SIVIY C，BAKER L M，QUINLIVAN B T，et al. Opportunities and challenges in the development of exoskeletons for locomotor assistance[J]. Nature Biomedical Engineering，2023，7(4)：456-472.
[18] EDELMAN B J，MENG J，SUMA D，et al. Noninvasive neuroimaging enhances continuous neural tracking for robotic device control[J]. Science Robotics，2019，4(31)：eaaw6844.
[19] ZHANG L，YU Z，SU P，et al. Design of a parallel wrist rehabilitation robot and analysis of physiological effect on training[J]. IEEE/ASME Transactions on Mechatronics，2024，29(5)：3401-3414.
[20] ZHANG L，ZHU X，GUTIERREZ-FAREWIK E M，et al. Ankle joint torque prediction using an NMS solver informed-ANN model and transfer learning[J]. IEEE Journal of Biomedical and Health Informatics，2022，26(12)：5895-5906.
[21] MCCAIN E M，DICK T J M，GIEST T N，et al. Mechanics and energetics of post-stroke walking aided by a powered ankle exoskeleton with speed-adaptive myoelectric control[J]. Journal of Neuroengineering and Rehabilitation，2019，16：57.
[22] 胡少康，张道辉，赵新刚，等. 基于特征工程与级联森林的中风患者手部运动肌电识别方法[J]. 机器人，2021，43(5)：526-538. HU Shaokang，ZHANG Daohui，ZHAO Xingang，et al. An semg-based hand motion recognition method for stroke patients with feature engineering and cascade forest[J]. Robot，2021，43(5)：526-538.
[23] 陈望隆，杨述焱，胡权，等. 面向运动力学测量的无线六维力传感器[J]. 仪器仪表学报，2019，40(4)：129-136. CHEN Wanglong，YANG Shuyan，HU Quan，et al. Wireless six-dimensional force sensor for motion mechanics measurement[J]. Chinese Journal of Scientific Instrument，2019，40(4)：129-136.
[24] 左盟，陈伟球，杨明，等. Y形横梁六维力/力矩传感器的应变分析[J]. 机械工程学报，2020，56(12)：1-8. ZUO Meng，CHEN Weiqiu，YANG Ming，et al. Strain analysis of six-axis force/torque sensors with y-shaped crossbeam[J]. Journal of Mechanical Engineering，2020，56(12)：1-8.
[25] WANG W，LIANG X，LIU S，et al. Drivable space of rehabilitation robot for physical human-robot interaction：Definition and an expanding method[J]. IEEE Transactions on Robotics，2022，39(1)：343-356.
[26] 张铁，梁骁翃. 平面关节型机器人关节力矩的卡尔曼估计[J]. 浙江大学学报(工学版)，2018，52(5)：951-959. ZHANG Tie，LIANG Xiaohong. Kalman filter-based SCARA robot joint torque estimation[J]. Journal of Zhejiang University(Engineering Science)，2018，52(5)：951-959.
[27] VEZZANI G，PATTACINI U，BATTISTELLI G，et al. Memory unscented particle filter for 6-DOF tactile localization[J]. IEEE Transactions on Robotics，2017，33(5)：1139-1155.
[28] RAWLINGS J B，MAYNE D Q，DIEHL M. Model predictive control：Theory，computation，and design[M]. Madison：Nob Hill Publishing，2017.
[29] 陈万鑫，张弼，张庆超，等. 面向康复外骨骼的串联弹性关节设计与控制[J]. 机器人，2023，45(5)：554-567. CHEN Wanxin，ZHANG Bi，ZHANG Qingchao. et al. Design and control of a series elastic joint for rehabilitation exoskeleton[J]. Robot，2023，45(5)：554-567.
[30] RAMADAN A，CHOI J，RADCLIFFE C J，et al. Inferring control intent during seated balance using inverse model predictive control[J]. IEEE robotics and automation letters，2018，4(2)：224-230.
[31] SUN Z，LI Y，ZI B，et al. Development and dynamic state estimation for robotic knee-ankle orthosis with shape memory alloy actuators[J]. Journal of Mechanical Design，2024，146(1)：013302.
[32] SUN Z，LI Y，ZI B，et al. Design，modeling，and evaluation of a hybrid driven knee-ankle orthosis with shape memory alloy actuators[J]. Journal of Mechanical Design，2023，145(6)：063301.
[33] ZHAO J，MILI L. A decentralized H-infinity unscented Kalman filter for dynamic state estimation against uncertainties[J]. IEEE Transactions on Smart Grid，2018，10(5)：4870-4880.
[34] HUANG Y，ZHANG Y. Design of high-degree student’s t-based cubature filters[J]. Circuits，Systems，and Signal Processing，2018，37：2206-2225.