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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 1 Identification of Industrial Robot Parameters for Advanced Model-Based Controllers Design Basilio BONA and Aldo CURATELLA Dipartimento di Automatica e Informatica Politecnico di Torino, Italy

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 2 1.Introduction 2.Robot model and parameters 3.Closed-loop parameter identification 4.Test case 5.Identification results I.Robot model II.Gravity compensation III.Friction identification IV.Parameter estimation V.Validation 6.Controller design 7.Conclusions and further developments 0 Contents

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 3 Estimation of the model parameters of a COMAU Smart S2 industrial robot for controller design purposes. Challenges controller in-the-loop no sensors to measure joint velocities Suitable trajectories were generated to avoid the excitation of unmodelled plant dynamics The method is applied to a 6 DoF industrial robot, estimating its parameters to design an improved model- based controller 1 Introduction

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 4 Robot Model and Parameters rigid links and joints, i.e. no elastic potential energy storage elements; ideal joint gearboxes are ideal, 100% efficient, no dead bands, friction is modelled as the sum of viscous and Coulomb friction only, no stiction is considered. Assumptions 2.1

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 5 Robot Model and Parameters Lagrange equation where and friction torque is Friction torques 2.2

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 6 Robot Model and Parameters Regressor model where Base (identificable) parameters A subset of inertial parameters Friction parameters k-th link inertial parameters 2.3 k-th link friction parameters

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 7 Robot Model and Parameters SISO closed-loop discrete-time system to be identified The controller is often unknown 2.4

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 8 Closed-loop Parameter Identification Closed-loop Methods 1.Direct methods: no a-priori controller knowledge is necessary 2.Indirect methods: applicable only if the controller is known 3.Joint I/O methods: the controller is identified The Projection Method [Forssell 1999, Forssell & Ljung 2000] has been used (type 3) It estimates the controller influence on the output data to remove its effects 3.1

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 9 Closed-loop Parameter Identification Projection Method (PM) – phase 1 The sensitivity function 3.2 is estimated using a non-causal FIR filter

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 10 Closed-loop Parameter Identification Projection Method (PM) – phase 2 The estimated sensitivity is used to compute 3.3 where which in turn is used to estimate from using an open-loop method chosen so large to avoid correlation between and

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 11 Closed-loop Parameter Identification Maximum Likelihood Estimation (MLE) method was used to estimate 3.4 from MLE needs a properly exciting reference signal (trajectory) measured data are joint positions and torques joint velocities and accelerations are needed friction (nonlinear effect) is to be considered aliasing error is present the observation time is finite white gaussian noise assumed

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 12 Closed-loop Parameter Identification The excitation trajectory is given by a Finite Fourier series 3.5 the fundamental frequency and the number of harmonicsdefine the signal band, that should avoid to excite parasitic (elastic) modes

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 13 Test Case COMAU SMART-3 S2 Robot 4.1

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 14 6 revolute joints driven by 6 brushless motors 6 gearboxes with different reduction rates 1 force-torque sensor on tip (not used) non-spherical wrist: no closed-form inverse kinematics exists power drives are still the original ones, but … the original control and supervision system has been replaced, and is now based on Linux RTAI real-time extension 4.2 Facts Test Case COMAU SMART-3 S2 Robot

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 15 Test Case COMAU SMART-3 S2 Robot 4.3

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 16 Test Case COMAU SMART-3 S2 Robot 4.4

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 17 Sampling frequency is constrained to 1 kHz Resonance frequency for shoulder links is 3 Hz ÷ 20 Hz Resonance frequency for wrist links is 5 Hz ÷ 30 Hz Constraints … 4.5 choice made … Test Case COMAU SMART-3 S2 Robot

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 18 Identification Results 5.1 I – Robot Model Simplified inertial model

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 19 Identification Results Axis 2 and 3 are those mainly affected by gravity, which appears as a sinusoidal torque 5.2 II – Gravity compensation (1) – Model Two velocity ramps, one negative one positive, were used to minimize Coriolis and centripetal torques

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 20 Identification Results 5.3 II – Gravity compensation (2) – Results

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 21 Coulomb + viscous friction Reference trajectory used Coriolis and centripetal effects neglected Identification Results 5.4 III – Friction identification (1) – Model position velocity acceleration

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 22 compensated uncompensated Identification Results 5.5 III – Friction identification (2) – Results Axis 2

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 23 Identification Results 5.6 III – Friction identification (3) – Results

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 24 Identification Results 5.7 IV – Parameter estimation (1) – Trajectory generation Axis 3 Degrees

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 25 Identification Results 5.8 IV – Parameter estimation (2) – Optimization With this trajectory only 11 parameters are estimated for each joint The optimal parameters are solutions of an optimization problem where Max singular value min singular value

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 26 Identification Results Every observation was repeated 25 times The data were filtered with a 8-th order Chebyshev low pass filter (cut-off freq. = 80 Hz) and resampled at 200 Hz The estimated probability distribution of the measurement noise is 5.9 IV – Parameter estimation (3) – Data filtering Position noise gaussian & very small Torque noise gaussian & non-negligible

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 27 Identification Results Measured torque was adjusted for friction compensation 5.10 IV – Parameter estimation (4) – Data filtering Torque [Nm] Original measured torque Friction torque compensated and filtered used for identification

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 28 Identification Results 5.11 IV – Parameter estimation (5) – final results

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 29 Identification Results Position error (PDF) between simulated and measured data 5.12 V – Validation (1)

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 30 Identification Results Torque error (PDF) between simulated and measured data 5.13 V – Validation (2)

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 31 Controller Design Preliminary results on joint-6 controller Controller tracking errors: 6.1

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ICRA 2005 – Barcelona, April 2005Basilio Bona – DAUIN – Politecnico di TorinoPage 32 Conclusions and Further Developments Identification of an industrial manipulator with its original controller PM identification method Exciting signal with suitable frequency band Friction compensation and parameter estimation Inertial parameter estimation Error PDF validation New controller design only for joint 6 Extend controller design to other joints Identification of elastic parameters? 7.1

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