谐波传动机器人关节的自适应转矩估计【中文5640字】
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谐波传动机器人关节的自适应转矩估计【中文5640字】,谐波,传动,机器人,关节,自适应,转矩,估计,估量,中文
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Article history:Received 7 June 2015Received in revised form 3 December 2016Accepted 31 March 2017Available online 11 April 2017Robot joint torque estimation using input and output position measurements is a promis-torque sensingWhenare affectedcomputation delays and model errors 5. There are several techniques of direct joint torque sensing, e.g., joint torquesors based on elastic elements that are placed in the output transmission line of each joint of the robot 6,7./10.1016/j.ymssp.2017.03.0410888-3270/C211 2017 Elsevier Ltd. All rights reserved.Corresponding author.E-mail address: gjliuryerson.ca (G. Liu).1The work was conducted at the Systems and Control Laboratory, Department of Aerospace Engineering, Ryerson University, 350 Victoria Street, Toronto,Ontario, Canada.Mechanical Systems and Signal Processing 96 (2017) 115Contents lists available at ScienceDirectMechanical Systems and Signal Processingjournal homepage: /locate/ymsspbe used in the dynamic control of robots without the need of computing the robot inverse dynamics 3. Jointor estimation is also essential for controlling robot force and compliance, as well as for collision detection.Conventionally, joint torque sensors or a multi-axis force/torque (F/T) sensor is utilized in robot force control.mating joint torques using F/T sensor at the robot wrist, extensive calculations are needed, and the resultsesti-bysen-1. IntroductionHarmonic drives, invented in the 1950s 1, are widely used in robotic systems, due to their desirable features of near-zero backlash, compactness, light weight, high torque capacity, high gear ratio and coaxial assembly. These distinctive char-acteristics of harmonic drives vindicate their widespread applications, especially in electrically-driven robot manipulators.Joint torque feedback (JTF) has been widely recognized to improve the performance of robot control in the robotics com-munity 2,3. JTF is typically used in motion control of robot manipulators to suppress the effect of load torques 4 and canKeywords:RobotJoint torque estimationHarmonic drive transmissionKalman filtering technique, but the result may be affected by the load variation of the joint. In this paper,a torque estimation method with adaptive robustness and optimality adjustment accord-ing to load variation is proposed for robot joint with harmonic drive transmission. Basedon a harmonic drive model and a redundant adaptive robust Kalman filter (RARKF), theproposed approach can adapt torque estimation filtering optimality and robustness tothe load variation by self-tuning the filtering gain and self-switching the filtering modebetween optimal and robust. The redundant factor of RARKF is designed as a function ofthe motor current for tolerating the modeling error and load-dependent filtering modeswitching. The proposed joint torque estimation method has been experimentally studiedin comparison with a commercial torque sensor and two representative filtering methods.The results have demonstrated the effectiveness of the proposed torque estimationtechnique.C211 2017 Elsevier Ltd. All rights reserved.Adaptive torque estimation of robot joint with harmonic drivetransmissionZhiguo Shia, Yuankai Lib, Guangjun Liuc,1aSchool of Computer and Communication Engineering, University of Science and Technology, Beijing 100083, ChinabSchool of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, ChinacDepartment of Aerospace Engineering, Ryerson University, Canadaarticle info abstractharmonic drive, which is usually referred to as built-in torque sensing for harmonic drives 911. The torsional compliance2 Z. Shi et al./Mechanical Systems and Signal Processing 96 (2017) 115of harmonic drives lends itself to torque sensing, but it is difficult to achieve durable accurate torque measurement with thistechnique due to signal ripples and amplifier drifts 12.Torque estimation using harmonic drive compliance model provides an effective way of torque estimation for robots withharmonic drives, which is shown in 13, a previous work of our laboratory. The joint torque estimation technique uses link-side position measurement along with a proposed harmonic derive model to realize stiff and sensitive torque estimation,obtaining joint torque with minimal mechanical modifications. However, in 13, a low-pass filter is used to filter the outputof the harmonic drive model. While the low pass filter provides a simple and convenient way to resist high frequency noises,the torque estimation response speed is limited by the filter bandwidth.Kalman optimal filtering technique is commonly used in torque estimation algorithms. However, the filter gain is optimaland cannot be self-adjusted in the standard Kalman filter algorithm, and the external environment is only reflected by thepre-set measurement noise variance, which makes it difficult to adapt to changes in the actual external disturbance andrespond timely. Disturbances are taken into account in real time according to the actual measurement in the robust filteringalgorithms 14,15, where the online estimation of the noise variance 14 and resetting recursive prediction error variance15 are incorporated to adjust the filter gain online, which improves the adaptability of the filters to disturbances andensures the robustness of the algorithm.Traditionally, optimality is mainly considered in controlling robot force and compliance. In 16, a neural network learn-ing using approximate dynamic programming is developed to achieve optimal control. In 10, to cancel the torque measure-ment ripples due to the gear teeth meshing, standard Kalman filter estimation is used. By on-line implementation of theKalman filter, it has been demonstrated with experiments that this method is a fast and accurate way to filter torque ripplesand torque due to misalignment. However, standard Kalman filter only guarantees optimality for the torque estimation,while the robustness is also indispensable.As robustness conflicts with optimality, robust performance improvement is often associated with loss of optimality. Inthe meantime, strong robustness is not essential all the time, and it may cause excessive loss of optimality. In 15, an adap-tive robust extended Kalman filter (AREKF) is proposed to switch the working mode of the filter between robust and optimal,adaptively adjusting the filtering gain with the functions of automatic determination and switching. However, nonlinearmodeling errors in the state and measurement models may cause failure in the switching function of judgment mechanismsof AREKF. To solve this problem, redundant parameters are introduced into the AREKF, and a redundant adaptive robustextended Kalman filter (RAREKF) 17 is proposed to make the switching function work stably to provide capability of tol-erating the modeling error and load-dependent filtering mode switching in torque estimation.Torque estimation represents an efficient, economical and convenient to obtain joint torque with minimal mechanicalmodifications. In 18, joint torque estimation is based on EMG signals, in which matrix modifier is applied to make the con-troller adaptable to every upper-limb posture of any users. In this paper, a torque estimation method is developed for robotjoint with harmonic drive based on a harmonic drive model and a redundant adaptive robust Kalman filter, in that Kalmanfilter based filtering method is commonly used and has been proved to be conveniently realized in practice.The proposed method provides desirable tolerant capability to the modeling error and enables dynamic balance of opti-mality and robustness according to the load variation. The proposed method consists of a modeling part and a filtering part.The modeling part models the harmonic drive compliance on the basis of link-side absolute encoder readings, motor-sideencoder readings and the motor current. In the torque estimation, the motor current and the output of the modeling partprovide the inputs to the filtering part that consists of a redundant adaptive robust Kalman filter. The proposed methodhas been studied experimentally in comparison with a commercial torque sensor and two representative filtering methods,and the experimental results have demonstrated the superior effectiveness of the proposed robot joint torque estimationmethod.A brief version 19 of this approach was published in ICRA 2014. In this paper, the modeling part and experiments setupare briefly presented. The filtering part is redesigned and simplified to improve the performance, using the motor current asan input parameter. Meanwhile, the experimental analyses are extended in detail and comprehensively presented. The com-parisons with several typical commonly used filtering methods are given from the aspects of optimal and robust modes,especially the influence of time delay on the torque estimation. The rest of the paper is organized as follows: the overallstructure of the torque estimation method is presented in Section 2. The system model and torque estimation algorithmare presented in Section 3 and Section 4, respectively. Experimental results are given in Section 5, including comparisonresults. Concluding remarks are in Section 6.2. Overall structure of torque estimationThe overall structure of the proposed torque estimation method is as shown in Fig. 1. The redundant adaptive robust Kal-man filter (RARKF) approach is introduced in the filtering part. Generally, the joint loading is directly reflected by the motorIn 8, a linear encoder is used to measure the torsional deformation of the additional elastic body of a joint torque sensor.As measurement accuracy is in inverse proportion to sensor stiffness, low sensor stiffness is desirable in order to achievehigh measurement resolution, which leads to complicated joint dynamics. Another joint torque sensing technique is basedon the method proposed by Hashimoto et al. 9. Joint torque sensing is achieved by mounting strain gages directly on theZ. Shi et al./Mechanical Systems and Signal Processing 96 (2017) 115 3current, which contains low noise and is fast in response. Therefore, the redundant factor of RARKF is designed as a functionof the motor current to deal with modeling error and disturbances, and more importantly, to balance optimality and robust-ness according to the load variation.As a result of joint load variation, motion control, friction, or external forces, the torque of a robot joint may vary dramat-ically. A robust filter can allow timely joint torque estimation. However, there exists a trade-off between robustness andoptimality. Sometimes it is desirable to smoothen the torque estimation at the sacrifice of robustness. The proposed RARKFbased method adaptively switches the filtering mode between the optimal and robust according to the joint loading, whichcan effectively balance the estimation accuracy and response speed. The RARKF makes the switching function work stablywithin the range of a certain redundancy and switch the filtering mode between the optimal and robust when necessary.3. Modeling of harmonic drive torqueA harmonic drive consists of three main components: wave generator (WG), flex spline (FS) and circular spline (CS). Typ-ically the WG is connected to the motor shaft, the CS is connected to the joint housing, and the FS is sandwiched in between(CS and WG) and connected to the joint output. The WG consists of an elliptical disk (rigid elliptical inner-race), called wavegenerator plug, and an outer ball bearing.The wave generator plug is inserted into the bearing, thereby giving the bearing an elliptical shape as well. The FS fitstightly over WG; when the WG plug is rotated, the FS deforms and molds into the shape of the rotating ellipse but doesnot rotate with WG.3.1. Harmonic drive kinematic modelThe ideal input/output kinematic relationship, as explained in 20, equates the angular positions at the components ofthe harmonic drive:h Nh 1wherecan bewheredrivesreductionture showThethe kinematicdescribeselingThetorsionalthe needconsiderationFig. 1. Overall structure of the torque estimation.MIfowiwfwMIw fhwis the wave generator position, hfis the flexspline output position, and N is the gear ratio. The static force balancedescribed assw1Nsf2swis the torque at the wave generator and sfis the flexspline output torque. Eqs. (1) and (2) represent the harmonicideal linear input/output relationship in which the harmonic drive transmission is treated as a perfectly rigid gearmechanism. However, the empirical measurements of the input/output relationship provided in the cited litera-that the output is not linearly related to the input 21.causes of this nonlinearity are torsional compliance in the harmonic drive components, nonlinear friction forces, anderror that is due to gear meshing and machining errors. Given this ideal kinematic relationship whichthe motion and force constraints present in harmonic drives, the remaining effects can be incorporated by mod-compliance, friction and kinematic error.harmonic drive torsional compliance is due to flexibility in both flexspline and wave generator 13,22. By taking thecompliance of the wave generator into account, the hysteresis behavior of the harmonic drive is captured withoutfor a separate hysteresis model. The compliance behavior of the harmonic drive 13 is illustrated in Fig. 2, withof the flexspline and wave generator compliance.Thewhereat thewhereSubstituting4 Z. Shi et al./Mechanical Systems and Signal Processing 96 (2017) 115Dh DhfDhwh 7Consideringwhereposescompensatiwherelubricant3.2. KinematicThematicdeterminewith noEqs. (3)(5) into Eq. (6), we obtainAs in 13, the total torsional angle of the harmonic drive is written asDh hfoC0hwiN6Ngenerator plug), respectively. Note that hfiand hwoare not available as only hfoand hwiare measured by the link-side encoderand the motor-side encoder, respectively.The kinematic error is defined as the measured flexspline output minus the expected flexspline output (wave generatordisplacement multiplied by the gear ratio) 21. Therefore, the kinematic error,h can be expressed ash hfiC0hwo5Dhw hwoC0 hwi4hwo, hwidenote the positions of the wave generator outside part (ball-bearing outer rim) and the center part (waveThe wave generator torsional angle is defined ashfidenotes the angular position at the flexspline geartoothed circumference, hfodenotes the flexspline angular positionload side which is measured using the linkside encoder.Dhf hfoC0 hfi3torsional angle of the flexspline can be defined asFig. 2. Kinematic representation of a harmonic drive showing the three ports.cwifKfiwowKfoNthe harmonic drive friction, the expression in Eq. (2) becomessw1NsfC0sft 8sftis the harmonic drive friction torque as seen with respect to the output side of the transmission. For practical pur-and simplicity, the Stribeck friction model 23 has been proven useful and validated on a robot arm for joint frictionon 24, which is utilized in harmonic drive torque estimation and written assftFcFsC0 FceC0v=_xsd FvvC138signv 9v is the relative velocity, Fsdenotes static friction, Fcdenotes the minimumvalue of the Coulomb friction,_xsand Fvareand load parameters, and d is an additional empirical parameter.error modeleffective torque estimation can be achieved only if one compensates for the effects of the kinematic error. The kine-error can be measured for one complete output revolution using the high resolution link side absolute encoder. Tothe kinematic error,h, the test joint is rotated clockwise and counterclockwise one complete output revolutionpayload 13. The total torsional deformation Dhcwand Dhccware measured during this process.Dhcw DhfDhwcwNh 10Dhccw DhfDhwccwNh 11where Dhwcwand Dhwccware the wave generator torsional deformation in the clockwise and counterclockwise directionrespectively, which are calculated using both link-side and motor-side encoders measurements by the way of rotating inboth full directions with no payload.Since the output torque is equal to zero, the flexspline torsional deformation is also equal to zero, Dhf 0. With theassumption that the torsional deformation of the wave generator is symmetric, i.e.,DhwcwC0Dhwccw12the kinematic error can be determined from the following equationh DhcwDhccw=2 133.3. Harmonic drive compliance modelA typicalsionalTheplinetorqueTheZ. Shi et al./Mechanical Systems and Signal Processing 96 (2017) 115 5AFig. 3. Typical stiffness and hysteresis curve of a harmonic drive.fBBffKKfKAteresis shape of this stiffness curve, the wave generator local elastic coefficient is approximated asKw Kw0eCwjswj15where Kw0and Cware constants to be determined. The wave generator torsional angle can be calculated using the followingequation:DhwZsw0dswKw16curve is approximated by three straight-line segments with stiffness of K1, K2, and K3. Stiffness K1applies for flexs-torque of 0 to s1; stiffness K2applies for flexspline torque ranging from s1to s2; and stiffness K3applies for flexsplinegreater than s2.harmonic drive torsional deformation can be from C0W/2 to W/2 at zero torque output. In 13, to replicate the hys-function of the output torque.DhfsfK1; sf6s1s1K1sfC0s1K2; s1:14where K1, K2, K3, s1, and s2are given by the manufacture. The slope of the curve shown in Fig. 3 indicates the harmonic pliance. The flexspline torsional compliance is described in 20, where Dhfis approximated by a piecewise linearhysteresis behavior.The total harmonic drive torsional deformation comprises deformation of both the flexspline and the wave generator.Based on experimental observation, the harmonic drive torsional deformation is largely contributed by the flexspline tor-harmonic drive stiffness curve 20 is shown in Fig. 3, which features i
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