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An Extended Friction Model to Capture Load and Temperature Effects in Robot Joints

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An Extended Friction Model to Capture Load and Temperature Effects in Robot Joints Technical report from Automatic Control at Linköpings universitet An Extended Friction Model to capture Load and Temperature effects in Robot Joints André Carvalho Bittencourt, Erik Wernholt, Shiva Sander-Tavallaey, Torgny Brogårdh Division of Automatic Control E-mail: [email protected], [email protected], [email protected], [email protected] 7th April 2010 Report no.: LiTH-ISY-R-2948 Accepted for publication in the 2010 IEEE/RSJ International Confer- ence on Intelligent Robots and Systems (IROS 2010) Taipei International Convention Center, Taipei, Taiwan October 18-22, 2010 Address: Department of Electrical Engineering Linköpings universitet SE-581 83 Linköping, Sweden WWW: http://www.control.isy.liu.se AUTOMATIC CONTROL REGLERTEKNIK LINKÖPINGS UNIVERSITET Technical reports from the Automatic Control group in Linköping are available from http://www.control.isy.liu.se/publications. Abstract Friction is the result of complex interactions between contacting surfaces in a nanoscale perspective. Depending on the application, the dierent models available are more or less suitable. Available static friction models are typically considered to be dependent only on relative speed of interacting surfaces. However, it is known that friction can be aected by other factors than speed. In this work, static friction in robot joints is studied with respect to changes in joint angle, load torque and temperature. The eects of these variables are analyzed by means of experiments on a standard industrial robot. Jus- tied by their signicance, load torque and temperature are included in an extended static friction model. The proposed model is validated in a wide operating range, reducing the average error a factor of 6 when compared to a standard static friction model. Keywords: friction, modeling, identication, industrial robots An Extended Friction Model to capture Load and Temperature effects in Robot Joints Andre´ Carvalho Bittencourt, Erik Wernholt, Shiva Sander-Tavallaey and Torgny Brogardh˚ Abstract— Friction is the result of complex interactions be- found in [17], where the author designs joint friction models tween contacting surfaces in a nanoscale perspective. Depending based on physical models of elementary joint components as on the application, the different models available are more helical gear pairs and pre-stressed roller bearings. or less suitable. Available static friction models are typically considered to be dependent only on relative speed of interacting Empirically motivated friction models have been successfully surfaces. However, it is known that friction can be affected by used in many applications, including robotics [5], [18]– other factors than speed. In this work, static friction in robot joints is studied with [20]. This category of models was developed through time respect to changes in joint angle, load torque and temperature. according to empirical observations of the phenomenon [2]. The effects of these variables are analyzed by means of Considering a set of states, X , and parameters, θ, these experiments on a standard industrial robot. Justified by their models can be described as the sum of N functions that significance, load torque and temperature are included in an describe the behavior of friction, F, extended static friction model. The proposed model is validated N in a wide operating range, reducing the average error a factor X of 6 when compared to a standard static friction model. F(X ; θ) = fi(X ; θ): (M) I. INTRODUCTION i=1 X = [z; q;_ q] gives the set of Generalized empirical Friction Friction exists in all mechanisms to some extent. It can be Model structures (GFM) [1], where z is an internal state defined as the tangential reaction force between two surfaces related to the dynamic behavior of friction and q is a in contact. It is a nonlinear phenomenon which is physically generalized coordinate and q_ = dq=dt. dependent on contact geometry, topology, properties of the Among the GFM model structures, the LuGre model [5], materials, relative velocity, lubricant, etc [1]. Friction has [19] is a common choice in the robotics community. For a been constantly investigated by researchers due to its impor- revolute joint, it can be described as tance in several fields [2]. In this paper, friction has been studied based on experiments on an industrial robot. τf = σ0z + σ1z_ + h(_'m) (ML) One reason for the interest in friction of manipulator joints j'_ mj is the need to model friction for control purposes [3]–[7], z_ =' _ m − σ0 z; g(_' ) where a precise friction model can considerably improve m the overall performance of a manipulator with respect to where τf is the friction torque and 'm is the joint motor accuracy and control stability. Since friction can relate to angle. The state z is related to the dynamic behavior of the wear down process of mechanical systems [8], including asperities in the interacting surfaces and can be interpreted as robot joints [9], there is also interest in friction modeling for their average deflection, with stiffness σ0 and damping σ1. robot condition monitoring and fault detection [9]–[16]. The function h(_'m) represents the velocity strengthening A friction model consistent with real experiments is nec- (viscous) friction, typically taken as h(_'m) = Fv'_ m, and essary for successful simulation, design and evaluation. Due g(_'m) captures the velocity weakening of friction. Motivated to the complexity of friction, it is however often difficult to by the observations of Stribeck [18], [21], g(_'m) is usually obtain models that can describe all the empirical observations modeled as α j '_ m j (see [1] for a comprehensive discussion on friction physics g(_') = Fc + Fse− '_ s : and first principle friction modeling). In a robot joint, the Where F is the Coulomb friction, F is, in this paper, de- complex interaction of components such as gears, bearings c s fined as the standstill friction parameter∗, '_ s is the Stribeck and shafts which are rotating/sliding at different velocities, velocity and α is the exponent of the Stribeck nonlinearity. makes physical modeling difficult. An example of an ap- The model structure M is a GFM with X = [z; '_ ] and proach to model friction of complex transmissions can be L m θ = [σ0; σ1;Fc;Fs;Fv; '_ s; α]. According to [19] it can This work was supported by ABB and the Vinnova Industry Excellence successfully describe many of the friction characteristics. Center LINK-SIC at Linkoping¨ University. Since z is not measurable, a difficulty with ML is the A. C. Bittencourt and E. Wernholt are with the Division of Auto- estimation of the dynamic parameters [σ ; σ ]. In [5], these matic Control, Department of Electrical Engineering, Linkoping¨ University, 0 1 Linkoping,¨ Sweden [andrecb,erikw]@isy.liu.se parameters are estimated in a robot joint by means of open S. Sander-Tavallaey is with ABB Corporate Research, Vaster¨ as,˚ Sweden ∗ [email protected] Fs is commonly called static friction. An alternative nomenclature T. Brogardh˚ is with ABB Robotics, Vaster¨ as,˚ Sweden was adopted to make a distinction between the dynamic/static friction [email protected] phenomena. loop experiments and by use of high resolution encoders. Open-loop experiments are not always possible, and it is common to accept only a static description of ML. For constant velocities, ML is equivalent to the static model MS: τf (_') = g(_'m)sign(_'m) + h(_'m) (MS) which is fully described by the g- and h functions. In fact, ML simply adds dynamics to MS. The typical choice for (a) ABB IRB 6620 robot with (b) Schematics of the 3 first g and h as defined for ML yields the static model structure 150 kg payload and 2:2 m joints including the torque reach. definitions for joint 2. M0: h '_ m α i Fig. 1. The experiments were made on joint 2 of the ABB robot IRB j '_ j τf (_'m) = Fc + Fse− s sign(_'m) + Fv'_ m: (M0) 6620. 'a is the joint angle, T the joint temperature, τm the manipulation torque and τp the perpendicular torque. M0 requires a total of 4y parameters to describe the velocity weakening regime g(_'m) and 1 parameter to capture viscous where T is the joint (more precisely, lubricant) temperature friction h(_'m). See Figure 3 for an interpretation of the parameters. and 'a the joint angle at arm side. Ideally, the chosen model should be coherent with the From empirical observations, it is known that friction can be empirical observations and, simultaneously, with the lowest affected by several factors, dimension of θ, the parameter vector, and with the lowest temperature, velocity, number of describing functions (minimum N). For practical • • force/torque levels, acceleration, purposes, the choice of fi should also be suitable for a useful • • position, lubricant/grease properties. identification procedure. • • A shortcoming of the LuGre model structure, as with any The document is organized as follows. Section II presents GFM, is the dependence only of the states X = [z; q;_ q]. In the method used to estimate static friction in a robot joint, more demanding applications, the effects of the remaining together with the guidelines used during the experiments. variables can not be neglected. For instance in [17], the Section III contains the major contribution of this work, with author observes a strong temperature dependence, while in the empirical analysis, modeling and validation. Conclusions [5] joint load torque and temperature are considered as and future work are presented in Section IV. disturbances and estimated in an adaptive framework. In [9], the influence of both joint load torque and temperature II. STATIC FRICTION ESTIMATION AND are observed. However, more work is needed in order to EXPERIMENTATION understand the influence of different factors on the friction A manipulator is a multivariable, nonlinear system that properties.
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