Lecture 8

1. Lecture 8 Mapping 5 April, 2005

2. Quiz 5 • What is the most significant integration error in dead reckoning? • State two requirements for a good landmark. • Give two examples of navigation in nature. Are these examples using dead-reckoning, landmarks, or other techniques? • What is perceptual aliasing? What are some methods to combat it? • Name one issue each with single position, and multiple position, belief representations.

3. Overview • Why do we map? • Spatial decomposition • Representing the robot • Current challenges

4. Mapping • Represent the environment around the robot • Impacted by robot position representation • Relationships • Map precision must match application • Precision of features on map must match precision of robots data (and hence sensor output) • Map complexity directly affects computational complexity, and reasoning about localization and navigation • Two basic approaches • Continuous • Decomposition (discretization)

5. Environment representation • Continuous metric -> x, y, theta • Discrete metric -> metric grid • Discrete topological -> topological grid • Environmental modeling • Raw sensor data • Large volume, uses all acquired information • Low level features (e.g. lines, etc) • Medium volume, filters out useful information, still some ambiguities • High level features (e.g. doors, car) • Low volume, few ambiguities, not enough information

6. Continuous representation • Exact decomposition of environment • Closed-world assumption • Map models all objects • Any area of map without objects has no objects in corresponding environment • Map storage proportional to density of objects in environment • Map abstraction and selective capture of features to ease computational burden

7. Continuous representation • Match map type with sensing device • For laser ranger finder, may represent map as series of infinite lines • Fairly easy to fit laser range data to series of lines

8. Continuous representation • In conjunction with position representation • Single hypothesis: extremely high accuracy possible • Multiple hypothesis: • Either, depict as geometric shape • Or, as discrete set of possible positions • Benefits of continuous • High accuracy possible • Dangers • Can be computationally expensive • Typically only 2D

9. Decomposition • Capture only useful features of world • Computationally better for reasoning, particularly if map is hierarchical

10. Exact cell decomposition • Model empty areas with geometrical shapes • Can be extremely compact (18 nodes in this figure) • Assumption: robot position within each area of free space does not matter

11. Fixed cell decomposition • Tessellate world: discrete approximation • Each cell is either empty or full • Inexact (note loss of narrow passageway on right)

12. Adaptive cell decomposition • Multiple types of adaptation: quadtree, BSP, exact • Recursively decompose until a cell is completely free or completely an object • Very space efficient compared to fixed cell approach

13. Occupancy grid • Typically fixed decomposition • Each cell is either filled or free • Counter for cell: 0 indicates free, above a certain threshold is considered to be filled with an object • Particularly useful with range-based sensors • If sensor strikes something in a cell, increase cell counter • If sensor goes over cell and strikes something else, decrease cell counter (presuming is free space) • By also discounting cell values over time, can deal with transient obstacles • Disadvantages • Map size a function of size of environment and size of cell • Imposes a priori geometric grid on world

14. Occupancy grid • Darkness of cell proportional to cell counter value

15. Topological decomposition • Use environment features most useful to robots • A graph specifying nodes and the connectivity between them • Nodes not of fixed size nor specify free space • A node is an area the robot can recognize its entry to and exit from

16. Topological example • For this example, robot must be able to detect intersections between halls, and halls and rooms.

17. Topological decomposition • To robustly navigate with a topological map a robot • Must be able to localize relative to nodes • Must be able to travel between nodes • These constraints require the robot’s sensors to be tuned to the particular topological decomposition • Major advantage is ability to model non-geometric features (like artificial landmarks) that benefit localization

18. Map updates: occupancy grids • Occupancy grid • Each cell indicates probability is free space and probability is occupied • Need method to update cell probabilities given sensor readings at time t • Update methods • Sensor model • Bayesian • Dempster-Shafer

19. Representing the robot • How represent the robot itself on a map? • Point-robot assumption • Represent the robot as a point • Assume it is capable of omnidirectional motion • Robot in reality is of nonzero size • Dilation of obstacles by robot’s radius • Resulting objects are approximations • Leads to problems with obstacle avoidance

20. Current challenges • Real world is dynamic • Perception still very error prone • Hard to extract useful information • Occlusion • Traversal of open space • How to build up topology • Sensor fusion

21. Summary • Decomposition • Continuous • Discrete • Map updating • Bayes • Dempster-Shafer • Robot representation • Current challenges

22. References • “Introduction to Autonomous Mobile Robots”, R Siegwart and I Nourbaksh, Bradford • “Mobile Robotics: A Practical Introduction”, U Nehmzow, Springer • “Computational Principles of Mobile Robotics”, G Dudek, M Jenkin, Cambridge University Press • “Introduction to AI Robotics”, R Murphy, Bradford • “Rover Localizaton Results for the FIDO Rover”, E Baumgartner, H Aghazarian, A Trebi-Ollennu, SPIE Photinics East Conference, October, 2001.