Robotic Mapping: A Survey

1. Robotic Mapping: A Survey Sebastian Thrun, 2002 Presentation by David Black-Schaffer and Kristof Richmond

2. Historical Overview • Metric Mapping • Geometric representations • Occupancy Grids • Larger maps much more computationally intensive • Topological Mapping • Milestones with connections • Require navigation information • Hard to scale

3. The Problems • Measurement noise • Sensor and Position noise is not independent • Map size • High resolution maps can be very large • Correspondence • Do multiple measurements at different times correspond to the same object? • Dynamic environments • Most current algorithms assume a static environment

4. Current State of Mapping • Algorithms • Robust for static, structured, and limited-size environments • Probabilistic • Correspondence Problem • Incremental vs. Multi-pass • Unsolved Areas • Dynamic environments • Planning exploration paths of unknown environments

5. Odometry Errors: heading and distance measurements accumulate errors with time Command Noise

6. Sensor Noise • Sensor probability model depends on the characteristics of the sensor and the object being sensed Basic sonar probability model for angle of incidence = 0. Z-axis = P(s|d at angle = 0) sigma - std. Deviation for gaussian return from ideal surface. lambdaF - false positive rate lambdaS - missed rate d - distance to target on map s - measured distance from sonar

7. p(x|d) =  p(d|x) p(x) p(x|d) is the probability of (the map) x being true given the (sensor) measurement d p(d|x) is the probability of the (sensor) measurement being being d given (an object at) x p(x) is the prior probability (of the map) Bayes Rule

8. Bayes Rule in time • Notation • s = pose of robot (x, y, ) • u = command given to robot • z = sensor measurment • m = map • All are functions of time • zt = sensor measurements at time t • zt = all sensor measurements up to time t • (same for s, u, and m)

9. Bayes Filter • Assume static world (map m constant) • p(zt|st, m) is the sensor model • p(st|ut, st-1) is the motion model • p(st-1, m|zt-1, ut-1) is the probability we were where we thought we were last time • Generally the sensor model and the motion model are static

10. SLAM • SLAM • Simultaneous Localization And Mapping • Figure out where we are and what our world looks like at the same time • Localization • Where are we? • Position error accumulates with movement • Mapping • What does the environment look like? • Sensor error (not independent of position error)

11. SLAM Example Thrun, Sebastian. “Animation of On-line mapping with Monte Carlo Localization”

12. Mapping Methods

13. Kalman Filter (SLAM) • Assume Gaussian noise • Linear motion model: x(t+1) = Ax(t) + Bu(t) + d • Linear sensor model: y(t) = Cx(t) + w • x includes robot and map states

14. Kalman Filter Performance • Pros: • Full (Gaussian) posterior probabilities • Incremental • Good convergence • Cons: • Limited model • Correspondence problem • Limited map size • Improvements: Lu/Milios • Improves correspondence • Non-incremental

15. Newman, Paul. “Navigating in a Building Site - Closed Loop CML”

16. Expectation Maximization (EM) • Find most likely map (and poses) • Expectation step (E-step) • Calculate probabilities of robot poses for current guess of map • Maximization step (M-step) • Calculate single most likely map for distribution of robot poses • Iterate

17. EM Performance • Pros: • Resolves correspondences • Cons: • Non-incremental • No posterior probabilities for map • Slow • Greedy • Improvements: Hybrid approaches • Incremental computation • Maintain a few possible robot poses

18. Occupancy Grids • Impose grid on space to be mapped • Find inverse sensor model p(mx,y|zt,st) • Update odds that grid cells are occupied

19. Occupancy Grid Example Moravec, Hans. “Robust Navigation by Probabilistic Volumetric Sensing’’

20. Occupancy Grid Example Moravec, Hans. “Robust Navigation by Probabilistic Volumetric Sensing’’

21. Pros Simple Accurate Incremental Cons Require known poses Independence assumptions Occupancy Grids • Extensions: Object Maps • Reduced memory requirements • Better for dynamic environments • Limited by available object models

22. Object Maps

23. Dynamic Environments • Kalman filters • Decaying occupancy grids • Dogma • Dynamic occupancy grid mapping algorithm