1. Computer Vision Group Prof. Daniel Cremers Autonomous Navigation for Flying Robots Lecture 4.2 : Feedback Control Jürgen Sturm Technische Universität München

2. Motivation: Position Control  Move the quadrotor to a desired location  How can we generate a suitable control signal ?  Current location (observed through sensors) Jürgen Sturm Autonomous Navigation for Flying Robots 2

3. Controller (you!) Sensor (you!) Feedback Control – Generic Idea Jürgen Sturm Autonomous Navigation for Flying Robots 3 Desired value 35° Turn hotter (not colder) System 25° 35° 45° 25° 35° 45° Measured temperature error

4. Feedback Control – Block Diagram Jürgen Sturm Autonomous Navigation for Flying Robots 4 ControllerSystem Sensor Reference Measured error +-+- Control State Measured state

5. Proportional Control  P-Control: Jürgen Sturm Autonomous Navigation for Flying Robots 5

6. Effect of Noise  What effect has noise in the process/measurements?  Poor performance for K=1  How can we fix this? Jürgen Sturm Autonomous Navigation for Flying Robots 6

7. Proper Control with Noise  Lower the gain… (K=0.15) Jürgen Sturm Autonomous Navigation for Flying Robots 7

8. What do High Gains do?  High gains are always problematic (K=2.15) Jürgen Sturm Autonomous Navigation for Flying Robots 8

9. What happens if sign is messed up?  Check K=-0.5 Jürgen Sturm Autonomous Navigation for Flying Robots 9

10. Saturation  In practice, often the set of admissible controls u is bounded  This is called (control) saturation Jürgen Sturm Autonomous Navigation for Flying Robots 10

11. Delays  In practice most systems have delays  Can lead to overshoots/oscillations/de-stabilization  One solution: lower gains (why is this bad?) Jürgen Sturm Autonomous Navigation for Flying Robots 11

12. Delays  What is the total dead time of this system?  Can we distinguish delays in the measurement from delays in actuation? Jürgen Sturm Autonomous Navigation for Flying Robots 12 Measurement Controller – System 1000ms delay in water pipe 200ms delay in sensing

13. Smith Predictor  Allows for higher gains  Requires (accurate) system model Jürgen Sturm Autonomous Navigation for Flying Robots 13 Controller – System with delay Delay-free system model Delay model – – Sensor

14. Smith Predictor  Assumption: System model is available, 5 seconds delay  Smith predictor results in perfect compensation  Why is this unrealistic in practice? Jürgen Sturm Autonomous Navigation for Flying Robots 14

15. Smith Predictor  Time delay (and system model) is often not known accurately (or changes over time)  What happens if time delay is overestimated? Jürgen Sturm Autonomous Navigation for Flying Robots 15

16. Smith Predictor  Time delay (and plant model) is often not known accurately (or changes over time)  What happens if time delay is underestimated? Jürgen Sturm Autonomous Navigation for Flying Robots 16

17. Lessons Learned  Control problem  Feedback control  Proportional control  Delay compensation  Next video:  PID control  Position control for quadrotors Jürgen Sturm Autonomous Navigation for Flying Robots 17