IROS2019国际学术会议论文集1933

Modelling of Uniaxial EGaIn-Based Strain Sensors for Proprioceptive Sensing of Soft Robots Abdullah Al-Azzawi, A. Mounir Boudali, He Kong, Ali H. G okto gan, and Salah Sukkarieh AbstractSoft strain resistive sensors based on eutectic gallium-indium liquid metal can play an important role in proprioceptive sensing for soft robots. However, there are no available mathematical models to accurately estimate the strain as a function of the measured resistance. Furthermore, non- uniform strain in the microchannels has not been analysed yet. In this paper, we introduce a new model to estimate the strain or elongation in sub-millimetre scale, and analyse its accuracy through a customised testing set-up and procedure. The effect of strain rate on the measurement accuracy is also studied. We compare existing theoretical models with our experimental results, and discuss the differences between them. Moreover, we analyse the effect of strain rate on hysteresis caused by the viscoelastic behaviour and introduce a new model for it to be potentially used for future work. This paper demonstrates, among other things, that rational models could provide high accuracy in strain estimation, and might help to enhance proprioceptive sensing and state control of soft robots. I. INTRODUCTION Soft robots play an important role in robotics research and scientifi c innovation. Unlike classical rigid robots with limited degrees of freedom (DoF), soft robots are built from highly deformable materials to produce systems with infi nite DoF. This fl exibility provides the opportunity to design devices capable of performing tasks that cannot be achieved by rigid robots. A challenge coming along with this fl exibility is in the control of soft robots as the entire body can deform, causing more complicated sensing and control problems than rigid robots 1. Various methods have been proposed to measure this deformation, and can be categorised into two groups: external monitoring (external perception) using 2D or 3D motion capture systems 2, and internal monitoring (proprioceptive) 3. While external perception might be capable of providing precise measurements of the deformation 4, it is not so practical to use when deploying robots equipped with soft pneumatic actuators (SPAs) outside the labs. As a result, several proprioceptive sensing techniques were studied in the literature such as optical 5, inertial measurement units 6, inductance 7 and Hall effect 8. Soft strain sensors are another interesting technique 9- 10 to be used for proprio- ceptive sensing. Existing examples include capacitive sensors made of dielectric elastomer to measure surface strain 11, resistive sensors based on Eutectic Gallium-Indium (EGaIn) liquid metal used as embedded sensors 12, and resistive strain sensors based on carbon nanotubes 13, etc. All authors are with the Australian Centre for Field Robotics (ACFR), The University of Sydney, NSW 2006, Australia. Corresponding, email:.au Fig. 1: Geometrical design of selected sensor. The 3D cross- sectional view shows one stretched EGaIn microchannel. Of particular interest in this paper are EGaIn-based strain sensors which have been designed in several types and shapes for both uniaxial 14 and multiaxial 15 measure- ments.These sensors have also been designed to be embedded in the SPAs 16, or mounted externally or as a sensory skin 1720. Our study focuses on using uniaxial EGaIn strain sensors in estimating the strain based on the measured resistance. After reviewing the complexity and manufacturing cost of several EGaIn-based soft sensors in the literature, one design was selected for our study as shown in Figure 1 and was fab- ricated according to the manufacturing technique presented in 17. The contributions of this paper are to 1) introduce a new mathematical model to estimate the strain as a function of resistance and determine the estimation accuracy, 2) study the effect of strain rate on modelling accuracy using a custom procedure designed for analysing hysteresis in soft sensors. The reminder of the paper is organised as follows. Section II presents related work, followed by a description of sensor geometry in Section III. The experimental set-up and testing procedure are explained in Section IV. Analysis of the introduced model based on testing results along with outcome discussion are presented in Section V. Finally, the conclusions and future work are given in Section VI. II. RELATED WORK EGaIn-based sensors are considered highly fl exible and stretchable 21. They experience low hysteresis and have strong bonding capability to soft actuators made from similar silicon material 22. Many simulation studies have been conducted in the literature to analyse these sensors. For example, a 3D simulation tool has been introduced in 23 to characterise the electrical and mechanical responses. 24 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Macau, China, November 4-8, 2019 978-1-7281-4003-2/19/$31.00 2019 IEEE7468 has presented some numerical studies to analyse resistance change with radius of curvature. Moreover, experimental studies for embedded sensors and sensory skins have also been carried out with different characterising techniques. Especially, in 17, an optical motion capture system with spatial accuracy of 0.44 mm has been used to calculate the hysteresis in measurements. In 25, a motorised testing stand with a linear accuracy of 0.05 mm has been utilised to analyse resistance v.s. strain data. Furthermore, 12 has presented a successful integration of EGaIn-based sensor into a soft gripper. Their characterisation of sensors is based on calculating the strain from series of images taken while actuating the gripper, and the resistance measurements have been plotted within 90% confi dence intervals due to noticeable error margins. In addition, a recurrent neural network has been used in 26 for characterising the pressure response of microfl uidic soft sensors with high hysteresis. There exist other studies that estimate the strain based on resistance measurement, and analyse measurement un- certainties of such sensors. A multi-element strain gauge module was presented in 19 where 6.08% error in strain measurement was calculated and used to reconstruct the module triangular shape using a Monte Carlo approach to estimate the uncertainties. Then, a multi-mode strain and curvature sensors module was presented by the same team in 18. The error between experimental and reconstructed data in strain and curvature was found to be 7.00% and 8.75% respectively. The uncertainties in measurements were evaluated then compared to the measured noise in the system, and the electrical noise was found to be an insignifi cant contributor to overall sensor performance. To the best of the authors knowledge, mathematical mod- els of EGaIn-based soft strain sensors to estimate strain with higher accuracy are not available yet. The required model has to be able to achieve an estimation error in sub-millimetre scale. This accuracy is required if the proprioceptive sensing is expected to replace the external perception when detecting SPAs deformation. However, less accuracy might be required depending on the targeted applications 17. We extends the existing literature by introducing a new model, and focus on studying its accuracy limits, and the effect of strain rate (or speed) on hysteresis. This could lead the way to understand the possibility of reconstructing the deformation of soft actuators using a network of sensors in future work. III. SENSOR GEOMETRY The selected sensor, shown in Figure 1, has an active length of Lcc= 76.3mm between the connection centre points where the strain will be applied while the remaining length is inactive. The active length has two main regions. The fi rst region consists of two distinctive subregions in which one represents the sensing element with a length of Ls= 30.0mm and the other contains connection microchan- nels with a length of Le= 18.0mm. This enables the connection of measuring devices to read sensor resistance. The second region represents the remaining length within Lcc that has no microchannels in it, and transfers applied strain from centre points to the sensing element. The microchannel has a rectangular cross section area. Its initial theoretical width and height are w = 0.25mm and h = 0.15mm respectively. As EGaIn is incompressible, its volume is constant and can be represented as: V = LoAo= LA,(1) where, L and A are the length and cross section area of microchannel and the subscript ”o” denoting initial values. When the sensor is stretched, the length increases and the area decreases. This change in dimensions causes a change in the resistance of the sensor. The change in resistance as a function of applied strain was modelled earlier in 17 but a simpler theoretical model was introduced later in 27: R Ro = ?(2 + ?),(2) where, ? is the strain in microchannel length, R is the resistance represented by: R = L/A,(3) in which, is the resistivity of EGaIn (29.4108.m). Ro is calculated at initial microchannel length as: Lo= 6 Ls+ 2 Le= 216mm(4) The deformed length L is calculated later in terms of the active length Lccwhere the input strain is applied. IV. EXPERIMENTAL SET-UP A. Testing Rig To characterise the sensor, we use an affordable custom- built testing rig to generate linear strain at different speeds up to 1000 mm/min approximately. The system consists of a slider mechanism, and two 3D printed brackets A and B mounted on the fi xed and slider ends respectively. The sensor ends are connected to both brackets as shown in Figure 2(a). The mechanism is driven by a NEMA23 stepper motor with step angle of 1.8 deg via a screw that has a theoretical lead of 5mm per rev. The stepper motor is driven by a GeckoDrive (GM215) module connected to a microcontroller (Arduino Mega 2560) to generate the required strain and speeds via hardware generated PWM signal 28 as shown in Figure 2(b). The GM215 module can drive at full, half and micro-stepping (i.e. 200,400 and 2000steps/rev respectively) hence the theoretical linear precision are 25,12.5 and 2.5 m, respectively. B. Data acquisition system (DAQ) A constant current technique was used in 1719 to measure the sensor resistance. However, we found that the method has current stability issues towards slight variations of 100%, due to the excellent extrapolatory power of the rational function. The fi tting parameters of (10) need to be recalculated for each new sensor via a single test at reference speed. D. Strain rate effect Viscoelastic behaviour of silicon-based sensors causes hysteresis which depends on strain rate. Some researcher focus on reducing or eliminating its effects 33 while others focus on modelling it and its effects 26. This work focuses on modelling hysteresis by deriving a relatively simple model to be potentially used in real time applications. We used the measurements of sensor 2 to study the strain rate effect. It can be seen in Figure 3(c) that the sensor has exhibited lower performance for strains 5%, hence we decided to exclude the measurements of this region. To focus on the fi tting accuracy and omitting sensing accuracy, we 020406080100 Strain (%) 0 1 2 3 4 5 Resistance (ohm) 1000 mm/min (Loading) 1000 mm/min (Unloading) 60 60.5 61 2.95 3 3.05 02004006008001000 Speed (mm/min) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Hysteresis (%) Hysteresis vs Speed Power1 fit 0102030405060708090100110 Strain (%) -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 Fitting Error (mm) Fit for Loading Fit for Unloading Fit for Loading/Unloading 5% limit (a)(b) (c) Fig. 6: Strain rate effect in sensor 2 data: (a) loading vs unloading at highest speed, (b) hysteresis percentage, and (c) comparison between separate vs combined fi tting at reference speed. calculated the three runs average for each speed. Then, we calibrated sensor 2 via re-calculating the fi tting parameters of (10) using the measurements at lowest speed to be the reference as stated earlier. Results of the highest speed (test #1) were plotted against strain in Figure 6(a) with a zoomed zone to show the difference between the loading and unloading curves. We followed the procedure in 17 to calculate hysteresis percentage and the results are shown in Figure 6(b). We found that these percentage results can be modelled using the Matlab fi t model (power1) as follow: H = a2 sb2,(11) where, H is the hysteresis percentage, s is the speed, a2= 0.02894, b2= 0.3337 with RMSE = 0.0119 and R2= 0.974. This model can be used in future work to correct estimated strain based on strain rate values. Due to hysteresis, two approaches can be used for calcu- lating fi tting parameters of (10): either two separate models for loading and unloading data, or one combined model. We calculated fi tting parameters at reference speed for both approaches then calculated the fi tting error which is plotted against strain in Figure 6(c). The dotted line represents the excluded 5% region from the data, the blue curve represents the error in fi tting loading data only, the red curve is for unloading data only, the green dots represents a fi tting model generated by using both loading and unloading data. The fi tting error for each separate model is 0.02mm while it is 0.04mm approximately for the combined model. However, using a combined approach is a straight- forward solution if its error margin is acceptable based on each particular application. On the other hand, another algo- rithm is required to determine the direction of the sensors 7472 0204060 Time (min) 51.28 51.30 51.32 51.34 51.36 51.38 Equivalent Elongation (mm) 0204060 Time (min) -0.01 -0.005 0 0.005 0.01 Resistance Derivative (Ohm/sec) dR/dt Linear fit (a)(b) -8-6-4-202468 Derivative of Resistance (Ohm/sec) 10-3 0 100 200 300 400 500 Density -3+3-4+4 Input data Normal distribution (c) (d) Fig. 7: Direction of movement algorithm: (a) Noise in elon- gation measurement, (b) Derivative of measured resistance, (c) Normal distribution of resistance derivative, and (d) Simulink model for the algorithm. movement when using separate models if higher accuracy is required. E. Loading vs Unloading determination A simple way to determine the sensors movement di- rection (i.e. loading, unloading, or holding position) is by checking the sign of resistance derivative. However, noise in the measurement can affect the derivative sign and may give false readings. We found that using a dead zone (around zero) can enhance direction detection. To determine the measurement noise, we connected a suit- able solid resistor to the DAQ and logged the measurements for one hour. The selected value of this solid resistor was based on the results in Figure 6(c) where the maximum error occurred between 6070% strain. By comparing with sensor 2 measurements in Figure 3(b), we selected a resistor with 3.3Ohm nominal value for the test. We then calculated an equivalent elongation via the same approach we used for calculating Figure 6(c) data, i.e. using both loading and unloading data to fi nd fi tting parameters as its similar to a no-movement case. The noise in elongation measurement is shown in Fig- ure 7(a). An error of 0.025mm in elongation can be seen in the entire log, this error is due to measurement noise as well as a decreasing trend in the fi rst half hour of logging. The error trend maintained an approximate position for the next half hour, which we believe it was related to a small change in room temperature during the time required to conduct the test. This error in logging is different than fi tting error discussed earlier. Furthermore, the derivative of the measured resistance and its normal distribution are shown in Figure 7(b) and (c) respectively. We analysed the derivative behaviour and we found that the noise margin has no time-related bias in it as indicated by the red fi t line in Figure 7(b). The analysis outcome suggests three suitable values for dead zone limits, 0.005Ohms/sec as can be seen in Figure 7(b), 3 (or 99.73%) and 4 (or 99.99%) which are equivalent to 0.0036 and 0.0048Ohms/sec respectively as shown in Figure 7(c). Finally, a Simulink model representing the movement direction determination algorithm is shown in Figure 7(d) where resistance derivative can provide three states: negative, zero (dead zone) or positive for unloading, hold position or loading respectively. VI. CONCLUSIONS In this paper, we have introduced a new mathematical model to estimate the strain, in sub-millimetre scale, as a function of measured resistance and analysed its estimation accuracy. The model was able to estimate the strain even with the non-uniform stretching in the microchannels. Moreover, we studied the effect of strain rate on the measurements accuracy through analysing the hysteresis using a custom procedure. The fi ndings showed that the rational model such as rat22 provided desirable accuracy for strain estimation. While this study does not characterise the precision and accuracy of the selected sensor, it analyses the accuracy of modelling the sensor. In addition, we introduced a method for estimating hysteresis percentage as a function of strain rate. Finally, we showed the advantage of using separate models for loading and unloading in fi tting accuracy instead of a combined model. We introduced a new concept of using a dead zone to help in estimating movement direction, and we then developed an algorithm to be used with the separate models. This framework will likely pave the way for a better proprioceptive sensing for soft actuators deformation and state estimation in both 2D and 3D space. Although the proposed model seems to be fairly accurate, it would be desirable to perform extra tests and collect more data samples for further