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
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