Lecture 10: Navigation

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Lecture 10: Navigation

  1. 1. Introduction to RoboticsNavigation<br />April 5, 2010<br />
  2. 2. Review: Localization<br />Localization is probabilistic<br />Error propagation law<br />Markov localization and Kalman Filter<br />Simultaneous Localization and Mapping<br />
  3. 3. Last Exercise<br />Beacon-based<br />Line-based<br />Maps are used for LOCALIZATION<br />
  4. 4. Today: Navigation<br />How to find a collision-free, shortest path from A to B?<br />Two approaches:<br />Local planning: go towards goal while avoiding obstacles<br />Global planning: calculate shortest path offline<br />
  5. 5. Global Planning<br />Workspace<br />Configuration Space<br />
  6. 6. Graph-based and Potential-field Planning<br />Grid-decomposition<br />Visibility Graph<br />Potential field<br />
  7. 7. Configuration Space<br />Grow obstacles at least by radius of robot<br />
  8. 8. Voronoi Decomposition<br />
  9. 9. Exact Cell Decomposition<br />
  10. 10. Adaptive Cell Decomposition<br />
  11. 11. Graph-based planning<br />Dijkstra/<br />Wavefront<br />A*<br />
  12. 12. Rapidly Exploring Random Trees<br />Select a random point in the configuration space<br />Grow tree into this direction from the closest point already in the graph<br />Explores space quickly, and eventually completely<br />
  13. 13. Potential-field based Planning<br />Potential given by <br />Distance to obstacles<br />Direction to goal<br />Possible to construct more complex behaviors<br />
  14. 14. Calculate virtual force pulling at the robot<br />Differential wheel robot<br />Left wheel = Fx – Fy<br />Right wheel = Fx + Fy<br />Potential-Field based Planning<br />x<br />y<br />
  15. 15. Reactive Obstacle Avoidance<br />Goal<br />Braitenberg behavior not sufficient (U-obstacle)<br />Classic: bug-algorithms<br />Easy to construct sub-optimal results<br />
  16. 16. Vector Field Histogram<br />
  17. 17. Practice<br />Localization, actuation and obstacles are uncertain<br />Combination of Local and Global Techniques<br />
  18. 18. Debate Outline<br />Constructive speeches<br />10 minutes pro<br />10 minutes contra<br />Rebuttal <br />3 minutes affirmative<br />3 minutes negative<br />Discussion and cross examination<br />5-10 minutes<br />4 Debates total<br />
  19. 19. Debates<br />Social:<br />Robots putting humans out of work is a risk that needs to be mitigated.<br />Robots should not have the capability to autonomously discharge weapons.<br />Robotic cars should not be allowed to participate in urban traffic.<br />…<br />Technical:<br />Swarms of simple robots are more attractive than monolithic, more capable robots.<br />Robots do not need to be as cognitive as humans in order to be useful as making the environment intelligent is sufficient.<br />Robots need to be made differently than from links, joints, and gears in order to reach the agility of people.<br />…<br />In both cases: debates should be driven by verifiable, technical arguments!<br />
  20. 20. Debates<br />Social:<br />D1: Robots putting humans out of work is a risk that needs to be mitigated.<br />D2: Robots should not have the capability to autonomously discharge weapons / drive around in cities (autonomous cars).<br />Technical:<br />D3: Robots do not need to be as cognitive as humans in order to be useful as making the environment intelligent is sufficient.<br />D4: Robots need to be made differently than from links, joints, and gears in order to reach the agility of people.<br />…<br />In both cases: debates should be driven by verifiable, technical arguments!<br />
  21. 21. Random assignments<br />
  22. 22. Organization<br />Week 12 + 13: Debates<br />http://courses.csail.mit.edu/6.141/spring2009/pub/debates/Debates.html<br />Week 14: Graduate student presentations<br />Week 15: Final presentations<br />Final exam: Monday, May 3 7:30 p.m. - 10:00 p.m.<br />

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