Feedback Control and Visual Servoing Lecture 11
What will you take home today? Introduction to Control Recap - PD Controllers PID Controllers Visual Servoing Different Formulations Interaction Matrix Control Law Case-Study: Learning-based approach
Joint Space - PD Controller Proportional – Derivative control law in joint space
Joint Space Control
Passive Natural Systems - Conservative k m x
Passive Natural Systems - Conservative = 1 2 V kx 2 x t
Passive Natural System – Dissipative k m x Friction x x x x
Passive Natural System – Dissipative + + = 0 !! ! mx bx kx k m x Friction x b k x x x + + = 0 !! ! x m x m x Natural frequency damping x x x t t t Over Oscillatory Critically damped damped damped
Critically Damped System – Choose B + + = 0 !! ! mx bx kx b k + + = 0 !! ! x m x m x bm w n m 2 m × w 2 2 n w w 2 2 n n Natural damping ratio as a reference value b b Critically = 2 x = 2 damped n w m km when m b/m=2 w n n Critically damped system: x n = = 1 ( b 2 km )
1 DOF Robot Control V(x) f m x x d x 0 x 0 x d
Asymptotic Stability – Converging to a value f m x 0 x d
Test yourself
Control Partitioning
Non-Linearity f m x d x 0 f ¢ f + ( , ! ) m ˆ x x System +
Disturbance rejection f dist x ¢ f f d ¢ k p + + System - + ¢ k v + -
Steady-State Error f + ¢ + ¢ = !! ! e k e k e dist v p m The steady-state
Example f f dist m k p f dist m k v x x x x
PID controller
Test yourself
What will you take home today? Introduction to Control Recap - PD Controllers PID Controllers Visual Servoing Different Formulations Interaction Matrix Control Law Case-Study: Learning-based approach
Camera-Robot Configurations Image from: CHANG, W., WU, C.. Hand-Eye Coordination for Robotic Assembly Tasks. International Journal of Automation and Smart Technology ,
Image-based visual servoing Current Image Goal Image
Camera Motion to Image Motion ω x ω z v x v z ω y v y Slides adapted from Peter Corke
The Image Jacobian ω f = f v ) T ( ˙ u, ˙ ˆ ρ ( X, Y, Z ) T 0 1 v x v v y ✓ ˙ B C ✓ − ˆ uv/ ˆ − ( ˆ f + u 2 / ˆ ◆ ◆ B C u f/Z 0 u/Z f f ) v v z B C = − ˆ f + u 2 / ˆ ˆ − uv/ ˆ B C v ˙ 0 f/Z v/Z f f − u ω x B C B C ω y @ A ω z Slides adapted from Peter Corke
f = [ u, v ] T Camera Motion to Image Motion r = [ v x , x y , v z , ω x , ω y , ω z ] T ˙ ω x ω z v x v z ω y v y Slides adapted from Peter Corke
Optical flow Patterns Slides adapted from Peter Corke
Image-based visual servoing Getting a camera velocity to minimize the error between the current and goal image Current Image Goal Image
Image-based visual servoing Current Image Goal Image J ( u, v, Z ) 0 1 v x v y B C − ˆ uv/ ˆ − ( ˆ f + u 2 / ˆ ✓ ◆ ✓ ◆ B C u ˙ f/Z 0 u/Z f f ) v v z B C = − ˆ f + u 2 / ˆ ˆ − uv/ ˆ B C v ˙ 0 f/Z v/Z f f − u ω x B C B C ω y @ A ω z Slides adapted from Peter Corke
Image-based visual servoing ˙ u 1 v x Current Image Goal Image ˙ v 1 v y J ( u 1 , v 1 , Z 1 ) ˙ u 2 v z J ( u 2 , v 2 , Z 2 ) = ˙ v 2 ω x J ( u 3 , v 3 , Z 3 ) ˙ u 3 ω y ˙ v 3 ω z
Image-based visual servoing ˙ u 1 v x ˙ v 1 v y J ( u 1 , v 1 , Z 1 ) ˙ u 2 v z = J ( u 2 , v 2 , Z 2 ) ˙ v 2 ω x J ( u 3 , v 3 , Z 3 ) ˙ u 3 ω y ˙ v 3 ω z ˙ v x u 1 ˙ v y v 1 − 1 J ( u 1 , v 1 , Z 1 ) ˙ v z u 2 J ( u 2 , v 2 , Z 2 ) = ˙ v 2 ω x J ( u 3 , v 3 , Z 3 ) ˙ u 3 ω y ˙ v 3 ω z
Desired Pixel Velocity Slides adapted from Peter Corke
Simulation Slides adapted from Peter Corke
Point Correspondences How to find them? Features, Markers
What will you take home today? Introduction to Control Recap - PD Controllers PID Controllers Visual Servoing Different Formulations Interaction Matrix Control Law Case-Study: Learning-based approach
Training Deep Neural Networks for Visual Servoing Bateux et al. ICRA 2018 1. Instead of using features, use the whole image to compare to given goal image a. Challenge: Small convergence region due to non-linear cost function
Training Deep Neural Networks for Visual Servoing Bateux et al. ICRA 2018
Training Deep Neural Networks for Visual Servoing Bateux et al. ICRA 2018
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