Research on decoupling algorithm of six-dimensional force sensor based on polynomial fitting

doi:10.3785/j.issn.1006-754X.2023.00.063

Chin J Eng Design

2023, Vol. 30

Issue (5): 571-578 DOI: 10.3785/j.issn.1006-754X.2023.00.063

Theory and Method of Mechanical Design

Research on decoupling algorithm of six-dimensional force sensor based on polynomial fitting

Zhijun WANG(

),Xiaotao ZHANG,Mengxiang LI

College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China

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Abstract

As an important spatial force sensing element, the six-dimensional force sensor is widely used in robot force/position control, grasping assembly, contour detection, autonomous obstacle avoidance and human-computer interaction. At present, improving the accuracy is one of the main research directions of six-dimensional force sensors. However, due to the influence of own structure and processing error and other factors, the six-dimensional force sensor will produce the interdimensional coupling phenomenon, and the interdimensional coupling is an important factor affecting its accuracy. In order to reduce the influence of coupling error, the decoupling algorithm of six-dimensional force sensor is studied by combining error analysis, theoretical derivation and experimental verification. Firstly, the coupling analysis of the six-dimensional force sensor was carried out, and its coupling model was obtained. Then, the linear decoupling algorithm of the six-dimensional force sensor was studied, and on this basis, the decoupling algorithm based on polynomial fitting was proposed to reduce the coupling error without changing the structure of the six-dimensional force sensor, so as to improve its accuracy. Finally, the orthogonal parallel six-dimensional force sensor was selected to carry out calibration experiments, and two algorithms were used for decoupling solution. The results showed that the decoupling algorithm based on polynomial fitting could reduce the influence of interdimensional coupling on the accuracy of six-dimensional force sensors. The proposed decoupling algorithm effectively improved the accuracy of the six-dimensional force sensor. Compared with the linear decoupling algorithm, the maximum coupling error was reduced by 8.914 percentage points and the linearity error was reduced by 0.111 percentage points. The research results can provide reference for reducing the coupling error and improving the accuracy of six-dimensional force sensors.

Key words： six-dimensional force sensor coupling model decoupling algorithm polynomial fitting calibration experiment decoupling solution

Received: 27 February 2023 Published: 03 November 2023

CLC:

TP 212

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Cite this article:

Zhijun WANG,Xiaotao ZHANG,Mengxiang LI. Research on decoupling algorithm of six-dimensional force sensor based on polynomial fitting. Chin J Eng Design, 2023, 30(5): 571-578.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2023.00.063 OR https://www.zjujournals.com/gcsjxb/Y2023/V30/I5/571

基于多项式拟合的六维力传感器解耦算法研究

六维力传感器作为重要的空间力感知元件，被广泛应用于机器人的力/位置控制、抓取装配、轮廓检测、自主避障和人机交互等。目前，提高精度是六维力传感器的主要研究方向之一。但由于受到自身结构和加工误差等因素的影响，六维力传感器会产生维间耦合现象，而维间耦合是影响其精度的重要因素。为减少耦合误差的影响，采用误差分析、理论推导及实验验证相结合的方法对六维力传感器的解耦算法进行研究。首先，对六维力传感器进行了耦合分析，得到其耦合模型。然后，对六维力传感器的线性解耦算法进行研究，并在此基础上提出了基于多项式拟合的解耦算法，以在不改变六维力传感器结构的前提下减小耦合误差，从而提高其精度。最后，选用正交并联六维力传感器开展标定实验，并分别采用2种算法进行解耦求解。结果表明，基于多项式拟合的解耦算法能减小维间耦合对六维力传感器精度的影响；所提出的解耦算法有效地提高了六维力传感器的精度，与线性解耦算法相比，最大耦合误差减小了8.914个百分点且线性度误差减小了0.111个百分点。研究结果可为六维力传感器维间耦合误差的减小和精度的提高提供参考。

关键词： 六维力传感器, 耦合模型, 解耦算法, 多项式拟合, 标定实验, 解耦求解

Fig.1 Six-dimensional force sensor with cross beam structure

Fig.2 Stewart six-dimensional force sensor with parallel structure

Fig.3 Input-output coupling model of six-dimensional force sensor

Fig.4 Orthogonal parallel six-dimensional force sensor

序号	$F s x / N$	$F c x / N$	$F c y / N$	$F c z / N$	$M c x / (N · m)$	$M c y / (N · m)$	$M c z / (N · m)$
1	10	9.958 4	-0.039 4	0.121 5	-0.005 5	0.014 9	0.014 6
2	20	19.820 2	-0.052 3	0.011 8	-0.012 5	0.031 2	0.030 8
3	30	29.823 4	-0.068 0	-0.106 4	-0.018 9	0.044 6	0.046 7
4	40	39.645 4	-0.121 6	-0.158 9	-0.027 7	0.0553	0.060 1
5	50	49.706 9	-0.159 7	-0.219 7	-0.030 5	0.051 7	0.067 4
6	60	59.837 8	-0.169 5	-0.251 1	-0.032 0	0.055 0	0.068 1
7	70	69.804 1	-0.234 3	-0.398 5	-0.043 3	0.061 7	0.071 2
8	80	79.827 2	-0.304 9	-0.483 5	-0.058 7	0.059 1	0.071 7
9	90	89.772 3	-0.356 8	-0.553 9	-0.060 2	0.049 0	0.069 5
10	100	99.784 8	-0.417 5	-0.725 5	-0.080 7	0.038 3	0.068 2

Table 1 Calibration experiment results of orthogonal parallel six-dimensional force sensor under different

F s x

Fig.5 Coupling relationship between

F c y

and

F s x

Fig.6 Coupling relationship between

F c z

and

F s x

Fig.7 Coupling relationship between

M c x

and

F s x

Fig.8 Coupling relationship between

M c y

and

F s x

Fig.9 Coupling relationship between

M c z

and

F s x

Fig.10 Coupling relationship between

F c x

and

F s y

Fig.11 Coupling relationship between

F c z

and

F s y

Fig.12 Coupling relationship between

M c x

and

F s y

Fig.13 Coupling relationship between

M c y

and

F s y

Fig.14 Coupling relationship between

M c z

and

F s y

解耦方法	误差	$F x$	$F y$	$F z$	$M x$	$M y$	$M z$
线性解耦	线性度误差	0.417	0.925	3.095	0.144	0.084	0.226
线性解耦	最大耦合误差	2.509	1.599	9.867	0.546	0.243	0.313
多项式拟合解耦	线性度误差	0.403	0.904	2.984	0.108	0.076	0.189
多项式拟合解耦	最大耦合误差	1.340	0.472	0.953	0.055	0.059	0.042

Table 2 Comparison of error analysis results of different decoupling algorithms


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