Download - 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
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