Lecture 07: Localization and Mapping I
- 1. Introduction to RoboticsLocalization and Mapping IOctober 18, 2010
- 2. MidtermHarder than last finalLess time than finalNo recitalBut: less than 3/3.5 need to work!Understand midterm => good shape for finals
- 3. Last 2 week’s exercisesRatslifeTasksVisionMappingNavigationPlanningStrategyShare the load: 1 or 2 tasks per studentPresent your plan in 2 weeks in class – be specific
- 4. Last lecture: The Gaussian Distribution
- 5. Error PropagationIntuition: the more sensitive the estimated quantity is to perception error, the more this sensor should be weightedCovariance matrixRepresenting outputuncertaintiesFunction relating sensor inputto output quantitiesCovariance matrixrepresenting inputuncertainties
- 6. TodaySensors for localizationError propagation for localizationPosition representationPlanning
- 7. Localization
- 8. LocalizationGyroscopeOdometryControl inputGPSLandmarksSensor input with different uncertainties. What is the overall uncertainty of the estimate?
- 9. Differential Wheel Robot Odometry
- 10. Step-by-Step
- 11. How does the error build up?Ingredient 1: variance on wheel-speed / slipIngredient 2: variance on previous position estimateRelation between wheel-speed and positionDerivative wrt errorDerivative wrt position
- 13. Step-by-Step
- 15. Belief representationParametric, single hypothesisParametric, multi hypothesisNon-parametric, multi hypothesis(particle filter)
- 17. Example: Google MapsContinuous, Discrete or Topological?
- 18. Belief representation in topological maps
- 20. From Sensor Data to Topological MapsExact Decomposition
- 21. Voronoi DecompositionPoints on lines have the same distance to neighboring obstaclesVoronoi edges correspond to the safest path
- 23. Reactive vs. Deliberative PlanningSo farMove randomlyUse heuristics (follow wall, spiral, …)Use landmarks (infrared beacons, magnet wire)Use gradients / feedback control (Exercise 2)TodayDeliberative planningReason on abstract representation
- 24. Exercise: Navigation AlgorithmsFind the shortest path from A to BChoose the map representationDevise an algorithm to extract path
- 25. Dijkstra’s Shortest Path Routing
- 26. A* Shortest Path RoutingHeuristic path cost biases search toward goalHeuristic here: Manhattan distanceExtra rule: Always start from cell with lowest cost
- 27. HomeworkSection 5.6 (pages 212-244)