Introduction to Control Lecture 10 Announcement - Feedback for - PowerPoint PPT Presentation

Introduction to Control Lecture 10

Announcement - Feedback for Project proposal latest tonight - Given erroneous data provided for Q3, we extended the submission deadline till tonight - Kevin Zakka started course notes (see Piazza) - bonus points for contributing - No time after class today – CS300 Lecture at 4:30pm

What will you take home today? Differentiable Filters Backpropagation through a Particle Filter Introduction to Control PD Controllers PID Controllers Gain tuning

Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.

Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.

Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.

Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.

Particle Filter Networks with Application to Visual Localization. Karkus et al. CORL 2018.

Differentiable Particle Filter – Loss Function

Differentiable Particle Filter – Experiments and Baselines

Differentiable Particle Filter – Experiments and Baselines

Differentiable Particle Filter – Experiments and Baselines

What will you take home today? Differentiable Filters Backpropagation through a Particle Filter Introduction to Control PID Controllers Feedforward Controllers

Introduction to Control

Open-Loop Control

Feedback Control

Joint Space Control

Task Space Control Å x desired

Joint Space Control d q 1 q 1 Control Joint 1 d q 2 q 2 x d q d Joint 2 Control q Inv. Kin. d q n q n Control Joint n

Task Space Control F t = T J F Å x desired

Joint Space - PD Controller

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

No Damping By Pasimi - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=65465311

Underdamped By Pasimi - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=65465311

Overdamped By Pasimi - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=65465311

Critically Damped By Pasimi - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=65465311

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 Position gain = stiffness

Asymptotic Stability – Converging to a value f m x 0 x d

Proportional Derivative Controller !! = f = - - - ! mx f k ( x x ) k x p v d 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 +

Motion control x ¢ f f d ¢ k p + + System - + ¢ k v + - + ¢ + ¢ = 0 !! ! e k e k e v p

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