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 Abstract Soft 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 a alazzawi acfr usyd edu 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 17 20 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 4 10 8 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 17 19 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 sensor s 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 sensor s 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 60 70 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 measurement s 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 validation and potential improve ment of the model In addition extensive analysis of the effect of dead zone limits on the fi tting accuracy should also be conducted Given that there are measurement uncertainties present in soft sensors in our future work we will look into enhancing the sensing accuracy through the use of advanced state estimation techniques 34 36 ACKNOWLEDGEMENT The authors would like to thank all colleagues at the ACFR who helped in producing this work 7473 REFERENCES 1 C Laschi and M Cianchetti Soft robotics New perspectives for robot bodyware and control Fron