identification of industrial robot parameters for advanced model-based controllers design

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 1

Identification of Industrial Robot Parameters

for Advanced Model-Based Controllers Design

Basilio BONA and Aldo CURATELLA

Dipartimento di Automatica e InformaticaPolitecnico di Torino, Italy

basilio.bona@polito.it

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 2

1. Introduction2. Robot model and parameters3. Closed-loop parameter identification4. Test case5. Identification results

I. Robot modelII. Gravity compensationIII. Friction identificationIV. Parameter estimationV. Validation

6. Controller design7. Conclusions and further developments

0Contents

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 3

• Estimation of the model parameters of a COMAU Smart S2 industrial robot for controller design purposes.

• Challengescontroller in-the-loopno 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

1Introduction

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 5

Robot Model and Parameters

Lagrange equation

where

and friction torque is

Friction torques

2.2

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 7

Robot Model and Parameters

SISO closed-loop discrete-time system to be identified

The controller is often unknown

2.4

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 8

Closed-loop Parameter Identification

Closed-loop Methods1. Direct methods: no a-priori controller knowledge is

necessary2. Indirect methods: applicable only if the controller

is known3. 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

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 9

Closed-loop Parameter Identification

Projection Method (PM) – phase 1

The sensitivity function

3.2

is estimated using a non-causal FIR filter

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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 correlationbetween and

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 13

Test Case COMAU SMART-3 S2 Robot 4.1

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 15

Test Case COMAU SMART-3 S2 Robot 4.3

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 16

Test Case COMAU SMART-3 S2 Robot 4.4

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 18

Identification Results 5.1

I – Robot Model

• Simplified inertial model

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 20

Identification Results 5.3

II – Gravity compensation (2) – Results

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 21

• Coulomb + viscous friction• Reference trajectory used

• Coriolis and centripetal effects neglected

Identification Results 5.4

III – Friction identification (1) – Model

position

velocity

acceleration

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 22

• compensated• uncompensated

Identification Results 5.5

III – Friction identification (2) – Results

Axis 2

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 23

Identification Results 5.6

III – Friction identification (3) – Results

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 24

Identification Results 5.7

IV – Parameter estimation (1) – Trajectory generation

Axis 3

Degre

es

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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 noisegaussian & very small

Torque noisegaussian & non-negligible

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 27

0 2 4 6 8 10

-1.5

-1

-0.5

0

0.5

1

1.5

t

T

Identification Results

• Measured torque was adjusted for friction compensation

5.10

IV – Parameter estimation (4) – Data filtering

Torq

ue [

Nm

]

Original measured torque

Friction torquecompensated and filtered

used for identification

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 28

Identification Results 5.11

IV – Parameter estimation (5) – final results

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 29

Identification Results

• Position error (PDF) between simulated and measured data

5.12

V – Validation (1)

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 30

Identification Results

• Torque error (PDF) between simulated and measured data

5.13

V – Validation (2)

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 31

Controller Design

• Preliminary results on joint-6 controller• Controller tracking errors:

6.1

0 2 4 6 8 10

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Ang

le [

de

gre

es]

t

original controllernew controller

ICRA 2005 – Barcelona, 18-21 April 2005 Basilio Bona – DAUIN – Politecnico di Torino

Page 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