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 哈尔滨工程大学学报  2018, Vol. 39 Issue (12): 1994-2000  DOI: 10.11990/jheu.201706086 0

### 引用本文

CHEN Lingling, SONG Xiaowei, WANG Jie, et al. Design of nonlinear disturbance observer for lower extremity exoskeleton system of swing phase[J]. Journal of Harbin Engineering University, 2018, 39(12), 1994-2000. DOI: 10.11990/jheu.201706086.

### 文章历史

1. 河北工业大学 人工智能与数据科学学院, 天津 300130;
2. 智能康复装置与检测技术教育部工程研究中心, 天津 300130;
3. 国家康复辅具研究中心, 北京 100176

Design of nonlinear disturbance observer for lower extremity exoskeleton system of swing phase
CHEN Lingling 1,2, SONG Xiaowei 1, WANG Jie 1,2, ZHANG Tengyu 3
1. School of Artificial Intelligence, Hebei University of Technology, Tianjin 300130, China;
2. Engineering Research Center of Intelligent Rehabilitation, Ministry of Education, Tianjin 300130, China;
3. National Research Center for Rehabilitation Technical Aids, Beijing 100176, China
Abstract: Considering the uncertainty of the active moments by the wearer's muscles during the lower extremity exoskeleton operation, this study investigates the swing phase control method based on the disturbance observer technology. The physical model was simplified. Lagrange principle was used to analyze the dynamic characteristics, and a swing model of the lower limb exoskeleton was established. The sliding mode controller was designed, considering the nonlinearity and strong coupling characteristics of the model. The active torque of the wearer was estimated based on disturbance observer technology to compensate the sliding mode controller, and the closed-loop system for the observer/controller integrated design was found to be stable. The control system simulation platform was established to control the angle of hip and knee joints. The results demonstrate that this closed-loop system can effectively follow the desired angle and restrain disturbances.
Keywords: lower extremity exoskeleton    system co-driven by human and machine    swing phase    dynamics modeling    disturbance observer    sliding mode control    simulation verification

1 基于拉格朗日的动力学建模

1) 对躯干部分和下肢系统共同建模会增加模型的复杂性，提高了控制器设计的难度。而躯干部分对下肢运动的影响无法忽略，因此对髋关节进行坐标设置。将髋关节的速度和加速度信息建立到模型中，利用髋关节信息作为干扰来代替躯干部分对下肢运动的影响。

2) 气动肌肉在控制过程中长度和质心位置都会发生变化。为了简化气动肌肉在下肢运动过程中造成的影响，假设气动肌肉在控制过程中可以完全跟随人的运动状态，利用腿部的两固定点间的距离代替气动肌肉的长度，并认为气动肌肉的质心始终在气动肌肉的中心位置。

 $\mathit{\boldsymbol{F}}\left( \mathit{\boldsymbol{\theta }} \right)\mathit{\boldsymbol{\ddot \theta }} + \mathit{\boldsymbol{H}}\left( {\mathit{\boldsymbol{\theta }},\mathit{\boldsymbol{\dot \theta }}} \right)\mathit{\boldsymbol{\dot \theta }} + \mathit{\boldsymbol{G}}\left( \mathit{\boldsymbol{\theta }} \right) = \mathit{\boldsymbol{\tau }} + {\mathit{\boldsymbol{\tau }}_h}$ (1)

 $\mathit{\boldsymbol{F}}\left( \mathit{\boldsymbol{\theta }} \right) = \left[ {\begin{array}{*{20}{c}} {{F_{11}}}&{{F_{12}}}\\ {{F_{21}}}&{{F_{22}}} \end{array}} \right]$
 $\begin{array}{*{20}{c}} {{F_{11}} = \frac{1}{4}r_5^2{m_3} + \frac{1}{3}\left( {{m_1}{l_2} + {m_2}{l_3}} \right) + \left( {l_2^2 + r_4^2} \right){m_4} + }\\ {\left[ {2{r_4}{l_2}{m_4} + \frac{1}{2}{r_5}\left( {{r_1} + {l_2}} \right){m_3}} \right]\cos {\theta _2} + \frac{1}{4}r_3^2 + }\\ {\frac{1}{4}\left( {{r_1} + {l_2}} \right)2{m_3}} \end{array}$
 $\begin{array}{*{20}{c}} {{F_{12}} = - \frac{1}{4}{r_5}\left( {{r_1} + {l_2}} \right){m_3}\cos {\theta _1}\cos \left( {{\theta _2} - {\theta _1}} \right) - }\\ {{r_4}{l_2}{m_4}\cos {\theta _1}\cos \left( {{\theta _2} - {\theta _1}} \right) - }\\ {\frac{1}{4}r_5^2{m_3} - r_4^2{m_4} - \frac{1}{3}{m_2}{l_3}} \end{array}$
 $\begin{array}{*{20}{c}} {{F_{21}} = - \frac{1}{4}{r_5}\left( {{r_1} + \frac{1}{2}} \right){m_3}\cos {\theta _1}\cos \left( {{\theta _2} - {\theta _1}} \right) - }\\ {{r_4}{l_2}{m_4}\cos {\theta _1}\cos \left( {{\theta _2} - {\theta _1}} \right) - }\\ {\frac{1}{4}r_5^2{m_3} - r_4^2{m_4} - \frac{1}{3}{m_2}{l_3}} \end{array}$
 ${F_{22}} = \frac{1}{4}r_5^2{m_3} + r_4^2{m_4} + \frac{1}{3}{m_2}{l_3}$
 $\mathit{\boldsymbol{H}}\left( {\mathit{\boldsymbol{\theta }},\mathit{\boldsymbol{\dot \theta }}} \right) = \left[ {\begin{array}{*{20}{c}} {{H_{11}}}&{{H_{12}}}\\ {{H_{21}}}&{{H_{22}}} \end{array}} \right]$
 $\begin{array}{*{20}{c}} {{H_{11}} = {r_5}\left( {{r_1} + {l_2}} \right)\left( {\frac{1}{2}{m_2} + \frac{1}{4}{m_3}} \right)\sin \left( {2{\theta _1} - {\theta _2}} \right){{\dot \theta }_2} + }\\ {3{r_4}{l_2}{m_4}\sin \left( {2{\theta _1} - {\theta _2}} \right){{\dot \theta }_2}} \end{array}$
 $\begin{array}{*{20}{c}} {{H_{12}} = \frac{1}{4}{r_5}\left( {{r_1} + {l_2}} \right){m_3}\cos {\theta _1}\sin \left( {{\theta _2} - {\theta _1}} \right){{\dot \theta }_2} + }\\ {{r_4}{l_2}{m_4}\cos {\theta _1}\sin \left( {{\theta _2} - {\theta _1}} \right){{\dot \theta }_2}} \end{array}$
 ${H_{21}} = \left[ {\frac{1}{4}{r_5}\left( {{r_1} + {l_2}} \right){m_3} + {r_4}{l_2}{m_4}} \right]\sin \left( {2{\theta _1} - {\theta _2}} \right){{\dot \theta }_1}$
 $\begin{array}{*{20}{c}} {{H_{22}} = \frac{1}{4}{r_5}\left( {{r_1} + {l_2}} \right){m_3}\cos {\theta _1}\sin \left( {{\theta _2} - {\theta _1}} \right){{\dot \theta }_1} + }\\ {{r_4}{l_2}{m_4}\cos {\theta _1}\sin \left( {{\theta _2} - {\theta _1}} \right){{\dot \theta }_1}} \end{array}$
 $\mathit{\boldsymbol{G}}\left( \mathit{\boldsymbol{\theta }} \right) = {\left[ {\begin{array}{*{20}{c}} {{G_1}}&{{G_2}} \end{array}} \right]^{\rm{T}}}$
 $\begin{array}{*{20}{c}} {{G_1} = \left\{ {\left[ {{m_1}{r_1} + \frac{1}{2}{r_3}{m_2} + \frac{1}{2}\left( {{r_1} + {l_2}} \right){m_3} + {l_2}{m_4}} \right]\cos {\theta _1} + } \right.}\\ {\left. {\left( {{r_4}{m_4} - \frac{1}{2}{r_5}{m_3}} \right)\cos \left( {{\theta _2} - {\theta _1}} \right)} \right\}{{\ddot x}_0} - }\\ {\left\{ {\left[ {{m_1}{r_1} + \frac{1}{2}{r_3}{m_2} + {l_2}{m_4} + \frac{1}{2}\left( {{r_1} + {l_2}} \right){m_3}} \right]\sin {\theta _1} + } \right.}\\ {\left. {\left( {{r_4}{m_4} + \frac{1}{2}{r_5}{m_3}} \right)\sin \left( {{\theta _2} - {\theta _1}} \right)} \right\}{{\ddot y}_0} - }\\ {\left( {{r_2}{m_1} + {l_2}{m_2}} \right)g\sin {\theta _1} + {r_4}{m_2}g\sin \left( {{\theta _2} - {\theta _1}} \right)} \end{array}$
 $\begin{array}{*{20}{c}} {{G_2} = - \left[ {\frac{1}{2}{r_5}{m_3}\cos \left( {{\theta _2} - {\theta _1}} \right) + {r_4}{m_4}\cos \left( {{\theta _2} - {\theta _1}} \right)} \right]{{\ddot x}_0} - }\\ {\left[ {\frac{1}{2}{r_3}{m_3}\sin \left( {{\theta _2} - {\theta _1}} \right) + {r_4}{m_4}\sin \left( {{\theta _2} - {\theta _1}} \right)} \right]{{\ddot y}_0} - }\\ {{r_4}{m_2}g\sin \left( {{\theta _2} - {\theta _1}} \right)} \end{array}$

 Download: 图 4 髋关节和膝关节的跟随效果 Fig. 4 Tracking effects of hip and knee joints

3.3 实物验证

 $\mathit{\boldsymbol{P}} = \left( {\mathit{\boldsymbol{F}} + 168} \right)/\left( {289 - 1\;528\varepsilon + 2\;468{\varepsilon ^2}} \right)$ (22)

 ${\varepsilon _1} = 1 - \sqrt {5.151\;2 + 3.498\;0\cos {\theta _1}}$ (23)

 ${\varepsilon _2} = 1 - \sqrt {0.504\;8 + 0.495\;3\cos {\theta _2}}$ (24)

 ${F_1} = \frac{{{\tau _1}}}{{\sin \beta \sqrt {1.01 + b\cos {\theta _1}} }}$ (25)
 $\beta = {\theta _1} - \arctan \frac{{a\sin {\theta _1}}}{{0.1 + a\cos {\theta _1}}}$

 ${F_2} = {\tau _2}/\left( {c + a\cos {\theta _2}} \right)$ (26)