Lower Limb Exoskeleton Gait Trajectory Tracking Control Based on Udwadia-Kalaba Control Theory

XIAO Zhiyi; SHA Liansen; ZOU Xuekun; HUANG Kun; LI Yongbin; LIU Bin

doi:10.7652/xjtuxb202501014

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Lower Limb Exoskeleton Gait Trajectory Tracking Control Based on Udwadia-Kalaba Control Theory

更新时间：2026-01-06

- Lower Limb Exoskeleton Gait Trajectory Tracking Control Based on Udwadia-Kalaba Control Theory
- Journal of Xi’an Jiaotong University Vol. 59, Issue 1, Pages: 148-158(2025)
- 作者机构：
  
  1.中国科学技术大学生物医学工程学院（苏州）， 215000，江苏苏州
  2.中国科学院苏州生物医学工程技术研究所， 215000，江苏苏州
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202501014
  CLC： TP242.6
- Received：25 June 2024，
  
  Online First：21 October 2024，
  
  Published：10 January 2025
- 稿件说明：
移动端阅览
XIAO Zhiyi, SHA Liansen, ZOU Xuekun, et al. Lower Limb Exoskeleton Gait Trajectory Tracking Control Based on Udwadia-Kalaba Control Theory[J]. Journal of Xi’an Jiaotong University, 2025, 59(1): 148-158.
DOI：

XIAO Zhiyi, SHA Liansen, ZOU Xuekun, et al. Lower Limb Exoskeleton Gait Trajectory Tracking Control Based on Udwadia-Kalaba Control Theory[J]. Journal of Xi’an Jiaotong University, 2025, 59(1): 148-158. DOI： 10.7652/xjtuxb202501014.

摘要

针对现有轨迹跟踪控制方法较难兼顾控制精度与稳定性的问题，提出一种基于Udwadia-Kalaba（U-K）控制理论的鲁棒控制方法。基于拉格朗日法建立机器人动力学模型，将动力学参数分为确定的名义部分与不确定部分；结合U-K理论与系统名义部分参数确定外骨骼机器人系统理想运动轨迹约束下的名义部分控制力矩；为消除机器人系统不确定部分的影响，引入鲁棒控制器，通过划分不确定性边界确定其应输出的额外控制力矩。仿真结果表明：相较于传统PID算法，基于U-K控制理论的鲁棒控制的外骨骼机器人髋关节、膝关节角度的轨迹跟踪控制精度分别提高了76.4%和96.8%。基于设计的下肢外骨骼机器人样机进行轨迹跟踪对比实验，实验结果表明：基于该方法的下肢外骨骼髋关节、膝关节角度的轨迹跟踪精度为0.467 0°和0.114 1°，相比作为对照的PID算法，分别提高了82.6%和86.8%，同时系统整体控制周期缩短了56.6%，该控制方法具有更高的同步性、控制精度与稳定性。

Abstract

To address the challenge of balancing control precision and stability in existing trajectory tracking control methods

a robust control method based on Udwadia-Kalaba (U-K) control theory is introduced. Using the Lagrangian method

a dynamic model for robots is established

dividing dynamic parameters into a deterministic nominal part and an uncertain part. The nominal control torque under ideal motion trajectory constraints for the exoskeleton robot system is determined based on the U-K theory and the nominal parameters. A robust controller is introduced to mitigate the effects of uncertainty

with uncertainty boundaries defined to establish the necessary additional control torque. The simulation results indicate that

compared to traditional PID algorithms

the trajectory tracking accuracy of the hip and knee joint angles for the exoskeleton robot is enhanced by 76.4% and 96.8%

respectively

using the proposed U-K-based robust control method. The results from trajectory tracking comparative experiments using a prototype of the lower limb exoskeleton robot designed based on this method show that the trajectory tracking accuracy for the hip and knee joint angles are 0.467 0° and 0.114 1° for the lower limb exoskeleton

indicating an 82.6% and 86.8% enhancement over the PID algorithm used as a control. Furthermore

the overall system control period is decreased by 56.6%. That control method exhibits enhanced synchronization

control precision and stability.

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references

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