1. Introduction to RoboticsCourse Summary…or all you need to know in 75min December 6, 2011

2. Retrospective Introduction Locomotion Kinematics Sensors Overview Vision-based ranging Features & Uncertainty Localization and Mapping Overview Markov Localization Kalman filter Midterm

3. Ratslife

4. Locomotion: Control Actuators are controlled by a periodic signal Think about the desired phase difference, not about the desired angle

5. Locomotion: Stability Dynamically stable: has to keep moving in order not to fall Statically stable: does not fall when resting 3-Point rule 3 legs : static stability 6 legs : static walking

6. Kinematics Forward kinematics Calculate impact of actuators on world coordinates Inverse kinematics Calculate actuation based on desired change in world coordinates

7. Wheel kinematic constraints Wheel cannot slide (in this class) Exception: Castor, swedish and spherical wheels

8. Recipe: Forward and Inverse Kinematics Start with forward kinematics Focus on actuated wheels Check constraints Keep all but one wheel fixed Add wheels up Inverse kinematics: solve equation system

9. Exam preparation: Kinematics Solve differential wheel drive (textbook) on paper Revisit Midterm example (tricyle)

10. Sensors What can be sensed? How can be sensed? Navigation Distance Position Vision

11. Laser Range Scanner Measures phase-shift of reflected signal Example: f=5MHz -> wavelength 60m

12. Sensor performance Dynamic range: lowest and highest reading Resolution: minimum difference between values Linearity: variation of output as function of input Bandwidth: speed with which measurements are delivered Sensitivity: variation of output change as function of input change Cross-Sensitivity: sensitivity to environment Accuracy: difference between measured and true value Precision: reproducibility of results Hokuyo URG

13. Example: Position Sensing Gyroscope Odometry Control input GPS Landmarks

14. Exam preparation: Sensors Get an overview over robotic sensors Reason about what the different sensor properties, e.g. bandwidth mean for this specific sensor

15. Uncertainty: The Gaussian Distribution

16. Key concept: Error Propagation Intuition: the more sensitive the estimated quantity is to perception error, the more this sensor should be weighted Covariance matrix Representing output uncertainties Function relating sensor input to output quantities Covariance matrix representing input uncertainties

17. Differential Wheel Robot Odometry

18. How does the error build up? Ingredient 1: variance on wheel-speed / slip Ingredient 2: variance on previous position estimate Relation between wheel-speed and position Derivative wrt error Derivative wrt position

19. Error propagation Wheel-Slip f=

20. Localization p(A^B) =p(A|B)p(B) =p(B|A)p(A) p(loc|sensing)=p(sensing|loc)p(loc)

21. Example 1: topological map Detect open/close doors using sonar p(n|i)=p(i|n)p(n)

22. Example 1: topological map

23. Kalman Filter: Intuition 1. Predict 2. Update

24. Basics: Fuse two Measurements Multiple measurements Actual value Mean-square error Weights 1/ Optimal error

25. Kalman Filter Measurement Kalman Filter Gain

26. Exam preparation No need to derive any of the equations Understand what they mean and what the intuition is Understand Bayes formula and how it maps to localization

27. A* Shortest Path Routing Heuristic path cost biases search toward goal Heuristic here: Manhattan distance Extra rule: Always start from cell with lowest cost

28. Organization Wednesday: Q&A in the CSEL Final exam:Wednesday, December 15,7:30 p.m. - 10:00 p.m, CAETE classroom.