Identification of Industrial Robot Parameters
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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 [email protected] Contents. 0. Introduction Robot model and parameters

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Identification of Industrial Robot Parameters for Advanced Model-Based Controllers Design

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Identification of industrial robot parameters for advanced model based controllers design

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

[email protected]

Basilio Bona – DAUIN – Politecnico di Torino


Contents

Contents

0

  • Introduction

  • Robot model and parameters

  • Closed-loop parameter identification

  • Test case

  • Identification results

    • Robot model

    • Gravity compensation

    • Friction identification

    • Parameter estimation

    • Validation

  • Controller design

  • Conclusions and further developments

Basilio Bona – DAUIN – Politecnico di Torino


Introduction

1

Introduction

  • 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

Basilio Bona – DAUIN – Politecnico di Torino


Robot model and parameters

Robot Model and Parameters

2.1

Assumptions

  • 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.

Basilio Bona – DAUIN – Politecnico di Torino


Robot model and parameters1

Robot Model and Parameters

2.2

Friction torques

Lagrange equation

where

and friction torque is

Basilio Bona – DAUIN – Politecnico di Torino


Robot model and parameters2

Robot Model and Parameters

2.3

Friction parameters

Base (identificable) parameters

A subset of inertial parameters

k-th link inertial parameters

Regressor model

where

k-th link friction parameters

Basilio Bona – DAUIN – Politecnico di Torino


Robot model and parameters3

Robot Model and Parameters

2.4

SISO closed-loop discrete-time system to be identified

  • The controller is often unknown

Basilio Bona – DAUIN – Politecnico di Torino


Closed loop parameter identification

Closed-loop Parameter Identification

3.1

Closed-loop Methods

  • Direct methods: no a-priori controller knowledge is necessary

  • Indirect methods: applicable only if the controller is known

  • 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

Basilio Bona – DAUIN – Politecnico di Torino


Closed loop parameter identification1

Closed-loop Parameter Identification

3.2

Projection Method (PM) – phase 1

The sensitivity function

is estimated using a non-causal FIR filter

Basilio Bona – DAUIN – Politecnico di Torino


Closed loop parameter identification2

Closed-loop Parameter Identification

3.3

Projection Method (PM) – phase 2

The estimated sensitivity is used to compute

chosen so large to avoid correlation

between and

which in turn is used to estimate

from

using an open-loop method

where

Basilio Bona – DAUIN – Politecnico di Torino


Closed loop parameter identification3

Closed-loop Parameter Identification

3.4

Maximum Likelihood Estimation (MLE) method was used to estimate

from

white gaussian noise assumed

  • 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

Basilio Bona – DAUIN – Politecnico di Torino


Closed loop parameter identification4

Closed-loop Parameter Identification

3.5

The excitation trajectory is given by a Finite Fourier series

the fundamental frequency

and the number of harmonics

define the signal band, that should avoid to excite parasitic (elastic) modes

Basilio Bona – DAUIN – Politecnico di Torino


Test case comau smart 3 s2 robot

Test Case COMAU SMART-3 S2 Robot

4.1

Basilio Bona – DAUIN – Politecnico di Torino


Identification of industrial robot parameters for advanced model based controllers design

Test Case COMAU SMART-3 S2 Robot

4.2

Facts

  • 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

Basilio Bona – DAUIN – Politecnico di Torino


Test case comau smart 3 s2 robot1

Test Case COMAU SMART-3 S2 Robot

4.3

Basilio Bona – DAUIN – Politecnico di Torino


Test case comau smart 3 s2 robot2

Test Case COMAU SMART-3 S2 Robot

4.4

Basilio Bona – DAUIN – Politecnico di Torino


Test case comau smart 3 s2 robot3

Test Case COMAU SMART-3 S2 Robot

4.5

  • 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 …

  • choice made …

Basilio Bona – DAUIN – Politecnico di Torino


Identification results

Identification Results

5.1

I – Robot Model

  • Simplified inertial model

Basilio Bona – DAUIN – Politecnico di Torino


Identification results1

Identification Results

5.2

II – Gravity compensation (1) – Model

  • Axis 2 and 3 are those mainly affected by gravity, which appears as a sinusoidal torque

  • Two velocity ramps, one negative one positive, were used to minimize Coriolis and centripetal torques

Basilio Bona – DAUIN – Politecnico di Torino


Identification results2

Identification Results

5.3

II – Gravity compensation (2) – Results

Basilio Bona – DAUIN – Politecnico di Torino


Identification results3

Identification Results

5.4

III – Friction identification (1) – Model

  • Coulomb + viscous friction

  • Reference trajectory used

  • Coriolis and centripetal effects neglected

position

velocity

acceleration

Basilio Bona – DAUIN – Politecnico di Torino


Identification results4

Identification Results

5.5

III – Friction identification (2) – Results

  • compensated

  • uncompensated

Axis 2

Basilio Bona – DAUIN – Politecnico di Torino


Identification results5

Identification Results

5.6

III – Friction identification (3) – Results

Basilio Bona – DAUIN – Politecnico di Torino


Identification results6

Identification Results

5.7

IV – Parameter estimation (1) – Trajectory generation

Degrees

Axis 3

Basilio Bona – DAUIN – Politecnico di Torino


Identification results7

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

Basilio Bona – DAUIN – Politecnico di Torino


Identification results8

Identification Results

5.9

IV – Parameter estimation (3) – Data filtering

  • 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

Position noise

gaussian & very small

Torque noise

gaussian & non-negligible

Basilio Bona – DAUIN – Politecnico di Torino


Identification results9

Identification Results

5.10

IV – Parameter estimation (4) – Data filtering

  • Measured torque was adjusted for friction compensation

Original measured torque

Torque [Nm]

Friction torque

compensated and filtered used for identification

Basilio Bona – DAUIN – Politecnico di Torino


Identification results10

Identification Results

5.11

IV – Parameter estimation (5) – final results

Basilio Bona – DAUIN – Politecnico di Torino


Identification results11

Identification Results

5.12

V – Validation (1)

  • Position error (PDF) between simulated and measured data

Basilio Bona – DAUIN – Politecnico di Torino


Identification results12

Identification Results

5.13

V – Validation (2)

  • Torque error (PDF) between simulated and measured data

Basilio Bona – DAUIN – Politecnico di Torino


Controller design

Controller Design

6.1

  • Preliminary results on joint-6 controller

  • Controller tracking errors:

Basilio Bona – DAUIN – Politecnico di Torino


Conclusions and further developments

Conclusions and Further Developments

7.1

  • 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?

Basilio Bona – DAUIN – Politecnico di Torino


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