Lecture 4 Part 4xa

8/17/2019 Lecture 4 Part 4xa

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Computer Vision Group

Prof. Daniel Cremers

Autonomous Navigation for Flying R

Lecture 4.4 :

PID Control

Jürgen Sturm

Technische Universität München


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Rigid Body Kinematics

Consider a rigid body

Free floating in 1D space, no gravity

Jürgen Sturm Autonomous Navigation for Flying Robots


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System model

Initial state



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In each time instant, we can apply a force

Results in acceleration Desired position

What will happen if we apply P-control?



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P Control

Control law



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PD Control

Proportional-derivative control



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PD Control


What if we set lower gains for ?



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PD Control


What if we set higher gains for ?



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PD Control

What happens when we add gravity?



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Gravity compensation

Add as an additional term in the control law

Any known (inverse) dynamics can be included



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PD Control

What happens when we have systematic errors?

(control/sensor noise with non-zero mean) Example: unbalanced quadrotor, wind, …



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PID Control

Idea: Estimate the system error (bias) by integrati



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PID Control

Idea: Estimate the system error (bias) by integrati

For steady state systems, this can be reasonable

Otherwise, it may create havoc or even disaster (w

effect)



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Example: Wind-up effect

Quadrotor gets stuck in a tree does not reach s

state What is the effect on the I-term?



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De-coupled Control

So far, we considered only single-input, single-ou

systems (SISO) Real systems have multiple inputs + outputs

MIMO (multiple-input, multiple-output)

In practice, control is often de-coupled


Controller 1

Controller 2

System


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How to Choose the Coefficients?

Gains too large: overshooting, oscillations

Gains too small: long time to converge Heuristic methods exist

In practice, often tuned manually



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Cascaded Control


Localization

Robot

Sensors Actuators

Quadrotor

Physical World

Kinematics

Dynamics

Position Control

Trajectory

Attitude Estimation Attitude Control

RPM Estimation Motor Speed Control10

R

1

10

0.1


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Assumptions of Cascaded Control

Dynamics of inner loops is so fast that it is not vis

outer loops Dynamics of outer loops is so slow that it appears

to the inner loops



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Example: Ardrone

Cascaded control

Inner loop runs on embedded PC and controls at Outer loop runs externally and implements positio


Inner loop MotorsOuter loop

Ardrone (=seen as the system by the ouLaptop

wireless, approx. 15Hz

onboard, 1000Hz


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Mechanical Equivalent

PD Control is equivalent to adding spring-dampe

the desired values and the current position

Run the demo from http://wiki.ros.org/tum_ardronJürgen Sturm Autonomous Navigation for Flying Robots


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Lessons Learned

P – proportional term

I – integral term D – derivative term

De-coupled control

Cascaded control


Lecture 4 Part 4xa

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