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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 basilio.bona@polito.it. Contents. 0. Introduction Robot model and parameters

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Presentation Transcript
slide1
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

basilio.bona@polito.it

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
1Introduction
  • 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

slide14
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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