Lecture 10: Summary


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Lecture 10: Summary

  1. 1. Introduction to RoboticsCourse Summary…or all you need to know in 75min<br />December 6, 2011<br />
  2. 2. Retrospective<br />Introduction<br />Locomotion<br />Kinematics<br />Sensors<br />Overview<br />Vision-based ranging<br />Features & Uncertainty<br />Localization and Mapping<br />Overview<br />Markov Localization<br />Kalman filter<br />Midterm<br />
  3. 3. Ratslife<br />
  4. 4. Locomotion: Control<br />Actuators are controlled by a periodic signal<br />Think about the desired phase difference, not about the desired angle<br />
  5. 5. Locomotion: Stability<br />Dynamically stable: has to keep moving in order not to fall<br />Statically stable: does not fall when resting<br />3-Point rule<br />3 legs : static stability<br />6 legs : static walking<br />
  6. 6. Kinematics<br />Forward kinematics<br />Calculate impact of actuators on world coordinates<br />Inverse kinematics<br />Calculate actuation based on desired change in world coordinates <br />
  7. 7. Wheel kinematic constraints<br />Wheel cannot slide (in this class)<br />Exception: Castor, swedish and spherical wheels<br />
  8. 8. Recipe: Forward and Inverse Kinematics<br />Start with forward kinematics<br />Focus on actuated wheels<br />Check constraints<br />Keep all but one wheel fixed<br />Add wheels up<br />Inverse kinematics: solve equation system<br />
  9. 9. Exam preparation: Kinematics<br />Solve differential wheel drive (textbook) on paper<br />Revisit Midterm example (tricyle)<br />
  10. 10. Sensors<br />What can be sensed?<br />How can be sensed?<br />Navigation<br />Distance<br />Position<br />Vision<br />
  11. 11. Laser Range Scanner<br />Measures phase-shift of reflected signal<br />Example: f=5MHz -> wavelength 60m<br />
  12. 12. Sensor performance<br />Dynamic range: lowest and highest reading<br />Resolution: minimum difference between values<br />Linearity: variation of output as function of input<br />Bandwidth: speed with which measurements are delivered<br />Sensitivity: variation of output change as function of input change<br />Cross-Sensitivity: sensitivity to environment<br />Accuracy: difference between measured and true value<br />Precision: reproducibility of results<br />Hokuyo URG<br />
  13. 13. Example: Position Sensing<br />Gyroscope<br />Odometry<br />Control input<br />GPS<br />Landmarks<br />
  14. 14. Exam preparation: Sensors<br />Get an overview over robotic sensors<br />Reason about what the different sensor properties, e.g. bandwidth mean for this specific sensor<br />
  15. 15. Uncertainty: The Gaussian Distribution<br />
  16. 16. Key concept: Error Propagation<br />Intuition: the more sensitive the estimated quantity is to perception error, the more this sensor should be weighted<br />Covariance matrix<br />Representing output<br />uncertainties<br />Function relating sensor input<br />to output quantities<br />Covariance matrix<br />representing input<br />uncertainties<br />
  17. 17. Differential Wheel Robot Odometry<br />
  18. 18. How does the error build up?<br />Ingredient 1: variance on wheel-speed / slip<br />Ingredient 2: variance on previous position estimate<br />Relation between wheel-speed and position<br />Derivative wrt error<br />Derivative wrt position<br />
  19. 19. Error propagation<br />Wheel-Slip<br />f=<br />
  20. 20. Localization<br />p(A^B) =p(A|B)p(B)<br />=p(B|A)p(A)<br />p(loc|sensing)=p(sensing|loc)p(loc)<br />
  21. 21. Example 1: topological map<br />Detect open/close doors using sonar<br />p(n|i)=p(i|n)p(n)<br />
  22. 22. Example 1: topological map<br />
  23. 23. Kalman Filter: Intuition<br />1. Predict<br />2. Update<br />
  24. 24. Basics: Fuse two Measurements<br />Multiple measurements<br />Actual value<br />Mean-square error<br />Weights 1/<br />Optimal error<br />
  25. 25. Kalman Filter<br />Measurement<br />Kalman Filter Gain<br />
  26. 26. Exam preparation<br />No need to derive any of the equations<br />Understand what they mean and what the intuition is<br />Understand Bayes formula and how it maps to localization<br />
  27. 27. A* Shortest Path Routing<br />Heuristic path cost biases search toward goal<br />Heuristic here: Manhattan distance<br />Extra rule: Always start from cell with lowest cost<br />
  28. 28. Organization<br />Wednesday: Q&A in the CSEL<br />Final exam:Wednesday, December 15,7:30 p.m. - 10:00 p.m, CAETE classroom.<br />