SLIDE 1
Introduction to Control
Lecture 10
SLIDE 2 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
SLIDE 3 What will you take home today?
Differentiable Filters Backpropagation through a Particle Filter Introduction to Control PD Controllers PID Controllers Gain tuning
SLIDE 4
Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.
SLIDE 5
Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.
SLIDE 6
Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.
SLIDE 7
Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.
SLIDE 8 Particle Filter Networks with Application to Visual
- Localization. Karkus et al. CORL 2018.
SLIDE 9
Differentiable Particle Filter – Loss Function
SLIDE 10
Differentiable Particle Filter – Experiments and Baselines
SLIDE 11
Differentiable Particle Filter – Experiments and Baselines
SLIDE 12
Differentiable Particle Filter – Experiments and Baselines
SLIDE 13 What will you take home today?
Differentiable Filters Backpropagation through a Particle Filter Introduction to Control PID Controllers Feedforward Controllers
SLIDE 14
Introduction to Control
SLIDE 15
Open-Loop Control
SLIDE 16
Feedback Control
SLIDE 17
SLIDE 18
Joint Space Control
SLIDE 19
Task Space Control
desired
x
Å
SLIDE 20 Joint Space Control
Inv. Kin. xd qd q
Control Control Control Joint n Joint 2 Joint 1 dq1 dqn dq2 q2 qn q1
SLIDE 21
Task Space Control
T
J F t =
F
desired
x
Å
SLIDE 22
Joint Space - PD Controller
SLIDE 23 Passive Natural Systems - Conservative
x
k
m
SLIDE 24 Passive Natural Systems - Conservative
V kx = 1 2
2 x t
SLIDE 25 Passive Natural System – Dissipative
x
k
m
x x x x Friction
SLIDE 26 Passive Natural System – Dissipative
x
k
m
x x x x Friction
mx bx kx !! ! + + = 0
!! ! x b m x k m x + + = 0
x t
Oscillatory damped
x t
Critically damped
x t
Over damped
Natural frequency damping
SLIDE 27 By Pasimi - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=65465311
No Damping
SLIDE 28 By Pasimi - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=65465311
Underdamped
SLIDE 29 By Pasimi - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=65465311
Overdamped
SLIDE 30 By Pasimi - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=65465311
Critically Damped
SLIDE 31 Critically Damped System – Choose B
m
n n
2 2 w w ×
mx bx kx !! ! + + = 0
!! ! x b m x k m x + + = 0
bm
m
n
2 2 w
w n
2
Natural damping ratio as a reference value
Critically damped when b/m=2wn
x w
n n
b m = 2 m b km = 2
Critically damped system: x n
b km = = 1 2 ( )
SLIDE 32 1 DOF Robot Control
m
f
x0 xd
V(x)
x0 xd
x Position gain = stiffness
SLIDE 33 Asymptotic Stability – Converging to a value
m
f
x0 xd
SLIDE 34 Proportional Derivative Controller
mx f !! = f
k x x k x
p d v
= -
) !
m
f
x0 xd
SLIDE 35
Test yourself
SLIDE 36
Control Partitioning
SLIDE 37 Non-Linearity
m
f
x0 xd System f
( , !) x x
+ +
ˆ m
f ¢
SLIDE 38 Motion control
!! ! e k e k e
v p
+ ¢ + ¢ = 0
+
+
d
x
¢ kp
¢ kv
¢ f
System
f
SLIDE 39 Disturbance rejection
+
+
d
x
¢ kp
¢ kv
¢ f
System
f
fdist
SLIDE 40 Steady-State Error The steady-state
!! ! e k e k e f m
v p dist
+ ¢ + ¢ =
SLIDE 41 Example
m
f
fdist
kp
m
x x x x
kv
fdist
SLIDE 42
PID controller
