Presentazione di PowerPoint

1
Identification of Industrial Robot Parameters
for Advanced Model-Based Controllers
Design Basilio BONA and Aldo CURATELLA Dipartime
nto di Automatica e Informatica Politecnico di
Torino, Italy basilio.bona_at_polito.it
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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

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Introduction
1

• 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

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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.

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Robot Model and Parameters
2.2

• Lagrange equation

Friction torques
where
and friction torque is
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Robot Model and Parameters
2.3
Regressor model
where
k-th link friction parameters
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Robot Model and Parameters
2.4

• SISO closed-loop discrete-time system to be
  identified

• The controller is often unknown

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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

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Closed-loop Parameter Identification
3.2

• Projection Method (PM) phase 1
• The sensitivity function

is estimated using a non-causal FIR filter
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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
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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

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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
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Test Case COMAU SMART-3 S2 Robot
4.1
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4.2
Test Case COMAU SMART-3 S2 Robot
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

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Test Case COMAU SMART-3 S2 Robot
4.3
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Test Case COMAU SMART-3 S2 Robot
4.4
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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

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Identification Results
5.1
I Robot Model

• Simplified inertial model

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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

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Identification Results
5.3
II Gravity compensation (2) Results
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Identification Results
5.4
III Friction identification (1) Model

• Coulomb viscous friction
• Reference trajectory used
• Coriolis and centripetal effects neglected

position
velocity
acceleration
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Identification Results
5.5
III Friction identification (2) Results

• compensated
• uncompensated

Axis 2
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Identification Results
5.6
III Friction identification (3) Results
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Identification Results
5.7
IV Parameter estimation (1) Trajectory
generation
Degrees
Axis 3
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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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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
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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
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Identification Results
5.11
IV Parameter estimation (5) final results
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Identification Results
5.12
V Validation (1)

• Position error (PDF) between simulated and
  measured data

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Identification Results
5.13
V Validation (2)

• Torque error (PDF) between simulated and measured
  data

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Controller Design
6.1

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

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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?