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Vision-Based Motion Control of Robots

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Title: Vision-Based Motion Control of Robots


1
Vision-Based Motion Control of Robots
  • Azad Shademan
  • Guest Lecturer
  • CMPUT 412 Experimental Robotics
  • Computing Science, University of Alberta
  • Edmonton, Alberta, CANADA

2
Vision-Based Control
B
B
A
A
A
B
3
Vision-Based Control
Left Image
Right Image
B
B
B
4
Vision-Based Control
  • Feedback from visual sensor (camera) to control a
    robot
  • Also called Visual Servoing
  • Is it any difficult?
  • Images are 2D, the robot workspace is 3D 2D data
    ? 3D geometry

5
Where is the camera located?
  • Eye-to-Hand
  • e.g.,hand/eye coordination
  • Eye-in-Hand

6
Visual Servo Control law
  • Position-Based
  • Robust and real-time pose estimation robots
    world-space (Cartesian) controller
  • Image-Based
  • Desired image features seen from camera
  • Control law entirely based on image features

7
Position-Based
Desired pose
Estimated pose
8
Image-Based
Desired Image feature
Extracted image feature
9
Visual-motor Equation
Visual-Motor Equation
10
Visual-motor Jacobian
Joint space velocity
Image space velocity
11
Image-Based Control Law
  1. Measure the error in image space
  2. Calculate/Estimate the inverse Jacobian
  3. Update new joint values

12
Image-Based Control Law
13
Jacobian calculation
  • Analytic form available if model is known. Known
    model ? Calibrated
  • Must be estimated if model is not known
  • Unknown model ? Uncalibrated

14
Image Jacobian (calibrated)
  • Analytic form depends on depth estimates.

Camera Velocity
  • Camera/Robot transform required.
  • No flexibility.

15
Image Jacobian (uncalibrated)
  • A popular local estimator
  • Recursive secant method (Broyden update)

16
Calibrated vs. Uncalibrated
  • Relaxed model assumptions
  • Traditionally
  • Local methods
  • No global planning ?
  • Difficult to show asymptotic stability condition
    is ensured ?
  • The problem of traditional methods is the
    locality.
  • Model derived analytically
  • Global asymptotic stability ?
  • Optimal planning is
  • possible ?
  • A lot of prior knowledge on the model ?
  • Global Model Estimation (Research result)
  • Optimal trajectory planning ?
  • Global stability guarantee ?

17
Synopsis of Global Visual Servoing
  • Model Estimation (Uncalibrated)
  • Visual-Motor Kinematics Model
  • Global Model
  • Extending Linear Estimation (Visual-Motor
    Jacobian) to Nonlinear Estimation
  • Our contributions
  • K-NN Regression-Based Estimation
  • Locally Least Squares Estimation

18
Local vs. Global
  • Key idea using only the previous estimation to
    estimate the Jacobian
  • RLS with forgetting factor Hosoda and Asada 94
  • 1st Rank Broyden update Jägersand et al. 97
  • Exploratory motion Sutanto et al. 98
  • Quasi-Newton Jacobian estimation of moving
    object Piepmeier et al. 04
  • Key idea using all of the interaction history to
    estimate the Jacobian
  • Globally-Stable controller design
  • Optimal path planning
  • Local methods dont!

19
K-NN Regression-based Method
q2
q1
20
Locally Least Squares Method
(X,q)
21
Experimental Setup
  • Puma 560
  • Eye-to-hand configuration
  • Stereo vision
  • Features projection of the end-effectors
    position on image planes (4-dim)
  • 3 DOF for control

22
Measuring the Estimation Error
23
Global Estimation Error
24
Noise on Estimation Quality
KNN
LLS
25
Effect of Number of Neighbors
26
Conclusions
  • Presented two global methods to learn the
    visual-motor function
  • LLS (global) works better than the KNN (global)
    and local updates.
  • KNN suffers from the bias in local estimations
  • Noise helps system identification

27
Eye-in-Hand Simulator
28
Eye-in-Hand Simulator
29
Eye-in-Hand Simulator
30
Eye-in-Hand Simulator
31
Mean-Squared-Error
32
Task Errors
33
Questions?
34
Position-Based
  • Robust and real-time relative pose estimation
  • Extended Kalman Filter to solve the nonlinear
    relative pose equations.
  • Cons
  • EKF is not the optimal estimator.
  • Performance and the convergence of pose
    estimates are highly sensitive to EKF parameters.

35
Overview of PBVS
2D-3D nonlinear point correspondences
T. Lefebvre et al. Kalman Filters for Nonlinear
Systems A Comparison of Performance, Intl. J.
of Control, vol. 77, no. 7, pp. 639-653, May 2004.
36
EKF Pose Estimation
yaw
pitch
roll
State variable
Process noise
Measurement noise
Measurement equation is nonlinear and must be
linearized.
37
Visual-Servoing Based on the Estimated Global
Model
38
Control Based on Local Models
39
Estimation for Local Methods
  • In practice Broyden 1st-rank estimation, RLS
    with forgetting factor, etc.

40
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