基于广义Udwadia-Kalaba方法的下肢康复机器人鲁棒约束跟随控制

孙浩; 汪新; 胡澳华; 马超

doi:10.21656/1000-0887.450085

基于广义Udwadia-Kalaba方法的下肢康复机器人鲁棒约束跟随控制

doi: 10.21656/1000-0887.450085

孙浩^{1, 2,},
汪新^{1, 2},
胡澳华^{1, 2},
马超^{1, 2, ,}

1.
合肥工业大学机械工程学院, 合肥 230009
2.
数字化设计与制造安徽省重点实验室, 合肥 230009

基金项目:

国家自然科学基金 52105093

详细信息

作者简介:
孙浩(1989—)，男，副教授，博士(E-mail: sunhao.0806@hfut.edu.cn)

通讯作者:
马超(1992—)，男，博士生(通讯作者. E-mail: machao@hfut.edu.cn)

中图分类号: TH113;TP242
计量
- 文章访问数: 73
- HTML全文浏览量: 19
- PDF下载量: 15
- 被引次数: 0
出版历程
- 收稿日期: 2024-04-07
- 修回日期: 2025-03-08
- 刊出日期: 2025-04-01

Robust Constraint Following Control of Lower Limb Rehabilitation Robots Based on the Generalized Udwadia-Kalaba Method

SUN Hao^{1, 2
,},
WANG Xin^{1, 2},
HU Aohua^{1, 2},
MA Chao^{1, 2
, ,}

1.
School of Mechanical Engineering, Hefei University of Technology, Hefei 230009, P.R.China
2.
Anhui Key Laboratory of Digit Design and Manufacture, Hefei 230009, P.R.China

摘要

摘要: 针对下肢康复机器人系统中同时存在的等式约束和不等式约束问题，提出了一种基于广义Udwadia-Kalaba(U-K)方程的鲁棒约束跟随控制器，能够使系统同时满足等式约束和不等式约束，并解决系统中存在的不确定性，使得机器人达到很好的约束跟随效果. 在机器人工作的过程中，传统的控制方法难以保证机器人的运动范围在边界条件内，可能导致患者在使用时受到二次伤害. 为解决边界问题带来的影响，提出了一种控制方法, 该方法利用微分同胚变换，将等式约束和不等式约束系统地纳入到U-K方程中，从数学上建立了广义U-K方程. 在此基础上，提出了一种鲁棒约束跟踪策略，以确保系统在存在不确定性和各种约束的情况下，仍具有满意的性能. 此外，利用Lyapunov函数对该鲁棒控制方法的稳定性进行了理论证明，并且通过仿真实验，验证了该鲁棒控制方法能够在非理想条件下实现给定轨迹的高精度跟踪控制.
- 广义Udwadia-Kalaba方程 /
- 不等式约束 /
- 鲁棒控制 /
- 下肢康复机器人
Abstract: A robust constraint following controller based on the generalized Udwadia-Kalaba (U-K) equation was proposed for the problem of equality constraints and inequality constraints in the lower limb rehabilitation robot system, to make the system meet the equality constraints and inequality constraints at the same time, solve the uncertainty in the system, and achieve good constraint following effects on the robot. During the working process of the robot, the traditional control method is difficult to ensure that the motion range of the robot is within the boundary conditions, resulting in secondary injury to the patient during use. To solve the influence of boundary problems, a control method was proposed to use the diffeomorphism transformation to incorporate the equality constraint and inequality constraint system into the U-K equation, with the generalized U-K equation established mathematically. On this basis, a robust constraint tracking strategy was presented to ensure satisfactory performances of the system in the presence of uncertainties and various constraints. In addition, the stability of the robust control method was theoretically proved with the Lyapunov function. The simulation results show that, the robust control method has high-precision tracking control of a given trajectory under non-ideal conditions.
- generalized Udwadia-Kalaba equation /
- inequality constraint /
- robust control /
- lower limb rehabilitation robot

HTML全文

图 1 下肢康复机器人二连杆模型

Figure 1. The 2-link model for the lower limb rehabilitation robot

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图 2 康复机器人大腿运动范围

Figure 2. The hip angle boundary

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图 3 有/无鲁棒项的髋关节位移误差

Figure 3. Hip joint tracking errors with and without robust control

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图 4 有/无鲁棒项的膝关节位移误差

Figure 4. Knee joint tracking errors with and without robust control

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图 5 有/无鲁棒项的髋关节位移

Figure 5. Hip joint displacements with and without robust control

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图 6 有/无鲁棒项的膝关节位移

Figure 6. Knee joint displacements with and without robust control

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图 7 有/无鲁棒项的髋关节力矩

Figure 7. Hip joint control torques with and without robust control

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图 8 有/无鲁棒项的膝关节力矩

注为了解释图中的颜色，读者可以参考本文的电子网页版本.

Figure 8. Knee joint control torques with and without robust control

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表 1 动力学参数

Table 1. Dynamics parameters

dynamics parameter	value	dynamics parameter	value
l₁/m	0.5	I₃/(kg·m²)	0.012 2
l₂/m	0.5	m₁/kg	1.2
l_c1/m	0.2	m₂/kg	1.3
l_c2/m	0.3	m₃/kg	2.3
I₁/(kg·m²)	0.023 3	m₄/kg	2
I₂/(kg·m²)	0.023 3

下载: 导出CSV

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