Elsevier

Mechanical Systems and Signal Processing

Volume 110, 15 September 2018, Pages 509-520
Mechanical Systems and Signal Processing

Research on static decoupling algorithm for piezoelectric six axis force/torque sensor based on LSSVR fusion algorithm

https://doi.org/10.1016/j.ymssp.2018.03.015Get rights and content

Highlights

  • Decoupling algorithm of piezoelectric six axis force/torque sensor is presented.

  • The static linear decoupling based on the LS algorithm is developed.

  • The LSSVR fusion decoupling algorithm is first introduced to solve the cross coupling problem.

  • The LSSVR fusion decoupling algorithm can reduce the nonlinear error and cross coupling error.

  • The linear errors and cross coupling errors after LSSVR decoupling are all less than 1%.

Abstract

Six axis force/torque sensors with characteristics of high precision, high reliability, and high dynamic, have become one of the major bottlenecks restricting the development of the robot. Aiming at the existing decoupling problem of piezoelectric six axis force/torque sensor with four point support structure, this paper presents the research and application on static decoupling method. Firstly, initial experimental data for decoupling of piezoelectric six axis force/torque sensor is obtained by making a calibration experiment. And then, experimental data are analyzed according to evaluate indicator. The linear decoupling algorithm based on the least square (LS) method is performed. Fusion decoupling algorithm based on Least Square Support Vector Machine Regression (LSSVR) is adopted to optimize multi-dimensional nonlinear characteristics of sensor output. The mapping relation between input and output of the sensor is identified. After LSSVM fusion algorithm decoupling, the maximum nonlinear error and cross coupling error are 0.89%, and 0.1%, respectively. The results show that the decoupling of LSSVR fusion algorithm can reduce the nonlinear error and cross coupling error of the fabricated piezoelectric six axis force/torque sensor. It has important significance to improve the measurement accuracy of robot force feedback with piezoelectric six axis force/torque sensors.

Introduction

Sensing and measurement is important part of the control system. Six axis force/torque sensors can be used to detect forces Fx, Fy and Fz, and torques Mx, My and Mz in Cartesian coordinate frame simultaneously. It has characteristics of abundant force information and high measuring accuracy. The six axis force/torque sensor is required increasingly in the field of force-position precision compliance control and multi-degree-freedom-coordinated control [1], [2], [3], such as robotics, automotive wheel force testing, aircraft landing force detection, rocket thrust measurement, transient space station docking, and wind tunnel experiments, et al. For example, if the sensor is to be equipped in a robotic wrist, which is being under a constant control to perform variable and flexible tasks, it then requires that the decoupling be one of the important factors. Furthermore, since there have six force components to be measured, it is generally hoped that all these components can be determined with approximately equal measurement sensitivity [4]. At present, the measuring principles of six axis force/torque sensor are mainly including strain and piezoelectric type.

Strain six axis force/torque sensor has high measurement accuracy, and is mainly suitable for static or quasi-static measurement [5], [6], [7]. Its disadvantages are slow measuring speed, easily affected by the strain bridge circuit and environmental factors, large volume, and complex decoupling problem. The decoupling of force sensor is adopting error compensation calculation method to reduce cross coupling. At present, static linear decoupling algorithm and static nonlinear decoupling algorithm are the main decoupling algorithms for six axis force/torque sensor. There are mainly two ways to realize linear decoupling. One is static decoupling based on the traditional linear calibration. The other is the linear decoupling based on the least square method. Yuan [8] made researches on the development and evaluation of a six-axis force/moment sensor used under humanoid robot foot. Simulation results with FEM software (ANSYS) demonstrated that the design of the sensor follows the stress concentration principle. The character test results indicated that the designed sensor has good enough sensitivity, linearity error less than 0.62%F.S., and interference error less than 3.0%F.S. Wang [9] presented Optimal design and experiment research of a fully pre-stressed six-axis force/torque sensor. In order to reduce the interference error, an effective way is using calibration matrix to eliminate inter coupling. Yao [10] presented a 3-D printed redundant six-component force sensor with eight parallel limbs. In order to reduce the influence factor, the least squares minimum norm solution is used for solving the calibration matrix. Kang [11] made shape optimization of a mechanically decoupled six-axis force/torque sensor. As a result of shape optimization, principal coupling of a six-axis F/T sensor was reduced from 35% to 2.5% with good isotropy. The final design of the F/T sensor was fabricated for experimental verification and there was only 0.7% difference in principal coupling and 5.2% difference in the overall strain output between the numerical and experimental results. Palli [12] proposed development of an optoelectronic 6-axis force/torque sensor for robotic applications. The cross coupling errors evaluated on the experimented sensor prototype are reported. From results it can be stated that, even if a considerable coupling error exists, probably due to the aforementioned defects in the sensor implementation, the variation of the output signals are consistent with the expected behavior. In order to obtain the actual calibration matrix and also to evaluate the overall measurement characteristics, S. Liu [4] made research on six-component force sensor with good measurement isotropy and sensitivities. Although high degrees of coupling exist in such a six component force sensor, however, they distribute sparsely only in a few places in the calibration matrix, making the calculations for the force components reasonably easy and quick. Ma [13] researched a robust static decoupling algorithm for 3-axis force sensors based on coupling error model and SVR. Instead of regarding the whole system as a black box in conventional algorithm, six separate Support Vector Regressions (SVRs) are employed for their ability to perform adaptive, nonlinear data fitting. The decoupling performance of the proposed algorithm is compared with the conventional method by utilizing obtained data from the static calibration experiment of a 3-axis force sensor. Xiao [14] analyzed the fundamental principle of the linear decoupling of the six-axis force/torque sensor, and according to the index of isotropy, compared two different linear decoupling algorithms, which were based on the Cramer theorem and the least square method and established non-linear decoupling method of radial basis function neural network.

Compared to strain six axis force/torque sensor, the difference is that quartz crystals are mainly using as the force sensing element in piezoelectric six axis force/torque sensor, which has the characteristics of good dynamic characteristics, high accuracy, high sensitivity, and good stability [15], [16]. Especially, it can meet the application requirement of natural frequency. However, there is less report on the piezoelectric six axis force/torque sensor. Piezoelectric six axis force/torque sensor generally adopts multi point support combined measuring structure. For the development of a six axis force/torque sensor, the cross coupling is an important factor regarding sensor quality [17], [18]. Multi-dimensional output of sensor affected by factors in the structural design, manufacture, assembly, and layout, will cause the coupling. And then, it is particularly important to make decoupling research on piezoelectric six axis force/torque sensors. It is likewise the fundamental research to eliminate the coupling error of the six dimensional force sensors. Liu [19] proposed traditional decoupling matrix for a parallel piezoelectric six-axis force/torque sensor. The coupling interference is less than 3% after using the decoupling matrix.

The essence of decoupling algorithm on six axis force/torque sensors is to obtain accurate functional relationship between the generalized force vectors and the output signals of the sensor, and to achieve accurate measurement of the force/torque. Conventional decoupling algorithm based on calculating the pseudo-inverse matrix requires a 6 × 6 matrix. Usually, the measured output waveform of the sensor is complicated and non-linear. Due to the limitation of the linear assumption, the decoupling effect of linear decoupling algorithm is not ideal. However, the cross coupling is the principal factor to restrict the measurement accuracy of six axis force/torque sensors. Therefore, nonlinear static decoupling research on six axis force/torque sensors is necessary.

This paper first proposes decoupling algorithm research on piezoelectric six dimensional force sensor. Research on linear decoupling algorithm and nonlinear decoupling fusion algorithm is carried out, and the results are analyzed and compared. The paper is organized as follows. In Section 2, the calibration experiment for fabricated piezoelectric six axis force/torque sensor is designed and carried out, and the original data is obtained analyzed. Linear decoupling algorithm based on Least Squares (LS) and fusion decoupling algorithm based on Least Square Support Vector Machine Regression (LSSVR) are studied in Section 3. The paper is concluded in Section 4, summarizing the present work.

Section snippets

Measuring principle of piezoelectric six axis force/torque sensor

The static nonlinear ratio and the static coupling ratio are usually adopted as indexes to evaluate the measurement accuracy of sensors. The static nonlinear ratio reflects the linearity of the sensor. The static coupling ratio reflects the cross coupling strength. When the load is applied on a six-axis force/torque sensor in one direction, other directions will be output force unavoidably, which is named as cross coupling error. And then, the cross coupling error is defined as the ratio of

Linear decoupling algorithm based on least squares method

The six axis force/torque sensor is applied under a certain load F = [Fx, Fy, Fz, Mx, My, Mz]T at the center within its linear elastic range. Assuming that the sensor is a linear measurement system between six dimensional inputs and six dimensional outputs, the relationship between the input force matrix and the output force matrix can be expressed as:F=G·Uwhere F ∈ Rn is the standard loading force matrix, U ∈ Rn is the output voltage matrix of the sensor, G ∈ R6×6 is the calibration matrix

Conclusion

This paper presents research on static linear and nonlinear decoupling algorithms of piezoelectric six axis force/torque sensor. Based on calibration experiment on the piezoelectric six axis force/torque sensor, initial non-decoupling calibration data are obtained. The sensor performance evaluation index is created. The sensor anisotropy linear error is small, but the difference between the actual output load and the theoretical expectations is obvious, and the cross coupling error is also

Acknowledgments

This work is supported by a grant from the National Natural Science Foundation of China (Grant No. 51705200), Shandong Provincial Natural Science Foundation, China (Grant No. ZR2017QEE012), National Natural Science Foundation of China (GrantNo. 51205165), China Postdoctoral Science Foundation (Grant No. 2012M511758).

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