1. Navigation Strategies for Exploring Indoor Environments Hector H Gonzalez-Banos and Jean-Claude Latombe The International Journal of Robotics Research October 1, 2002 vol. 21 no. 10-11 829-848

2. Overview Abstract & Introduction Part I : Concepts and Algorithms Part II : Experimental System Conclusion

3. Abstract & Introduction Problem Description Equipped with a range sensor, a mobile robot is tasked with mapping a previously unknown indoor environment. The robot would iteratively explore different sections of the map and patch together local data into a global map. However, at any given time, using only partial data collected thus far, how does the robot decide where to go next?

4. Abstract & Introduction Mapping and Model building Simultaneous Localization and Mapping (SLAM) Next Best View (NBV) problem

5. Part I : Concepts and Algorithms Safe Region  Largest region guaranteed to be safe given the history of sensor readings.  Iteratively build a map by executing union operations over successive safe regions.  Anticipate the overlap between future images and the current partially-built map  Enables the NBV algorithm to estimate the Information Gain

6. Part I : Concepts and Algorithms Definition of Visibility  The workspace is defined as the open subset W ⊂ R 2, with ∂W as the boundary of W.  A set of constraints are defined to determine the visibility of a point w on ∂W from sensor location q

7. Visibility Constraints Line-of-sight constraint: The open line segment S(w, q) joining q and w does not intersect ∂W. Range constraint: d(q,w) ≤ rmax rmax > 0 Incidence constraint: L(n, v) ≤ τ τ ∈ [0, π/2] Part I : Concepts and Algorithms

8. Visible section as a continous function  r = r i (θ; a i, b i ) ∀ θ ∈ (a i, b i ) Range Sensor output (π)  {r(θ; a, b)} ∈ π  θ ∈ (−π, π]

9. Part I : Concepts and Algorithms A Solid Curve is a visible section of ∂W, and is represented by an entry in the list π A Free Curve is a curve that joins two successive solid curves

10. Part I : Concepts and Algorithms Constructing a Local Safe Region s l (q)

11. Next-Best-View Algorithm Incorporating Model Alignment and Merging  M g (q k−1 ) =  m l (q k ) = ALIGN algorithm (assumed to be given)  Transform T to align m l (q k ) with M g (q k−1 )  S g (q k ) = T(S g (q k-1 )) U s l (q k )  M g (q k ) =  Imperfect, requires minimum overlap

12. Next-Best-View Algorithm Candidate Generation and Selection

13. Next-Best-View Algorithm Evaluating Candidates g(q) = A(q) exp(−λL(q)) Computing A(q)  Area of maximal outside region visible through free curves in S g (q k ) Termination Condition  Boundary of S g (q k ) has no free curves  Minimum length of free curves not met

14. Part II : Experimental System Polyline Generation Safe Region Computation Model Alignment Model Merging Detection of small obstacles

15. Part II : Experimental System Polyline Generation  Transform L points obtained by the sensor into a set of polygonal lines π l called polylines.  Usage of clustering allows a group of points to be traced back to single object surface

16. Part II : Experimental System Polyline Generation

17. Part II : Experimental System Safe Region Computation  Using Polyline set π l (q), a safe region s l (q) is computed.  The region will be constructed as a polygon bounded by solid edges(derived from polylines) and free edges(derived from approximated free curves)

18. Part II : Experimental System Safe Region Computation

19. Model Alignment  Using model information in M g (q k-1 ) and M l (q k ), a transform T is obtained that aligns together pairs of line segments in π g (q k-1 ) and π l (q k ) Part II : Experimental System

20. Model Merging  S g (q k ) = T(S g (q k-1 )) U s l (q k )  M g (q k ) = π g (q k ), S g (q k )

21. Dealing with small objects  The “apex” of narrow spikes created by small objects are used to create a small-object-map Part II : Experimental System

22. Example Runs

23. Part II : Experimental System Example Runs

24. Conclusion Reduced processing required Fixed height problem Error recovery Multiple robots

25. Questions?