Navigation Strategies for Exploring Indoor Environments Hector H. González-Baños

1. CS 326A: Motion Planning Navigation Strategies for Exploring Indoor Environments Hector H. González-Baños Jean-Claude Latombe Presented by Miler Lee, 6 May 2002

2. Automatic model building • Task: • Build a representation of an unknown environment relying only on robotic sensors • Next-best-view problem: • What path should the robot take to optimize sensing operations

3. Challenges to next-best view • Avoid obstacle collision, given that the robot is moving through an unknown environment and the sensors are on the robot • Localize to the map-so-far, robustness despite odometry errors (require minimum overlap between senses) Thrun 2001

4. NBV algorithm overview • Given sensor information at the current position and the map-so-far, • Compute the local safe region • Align with the map-so-far • Generate a list of candidate NBVs • Sample points near the edge of the safe region • Remove candidates not adequately visible from the boundaries of the safe region • Remove candidates without a collision-free path • Select NBV maximizing visibilitygain vs. path length

5. NBV algorithm overview • Given sensor information at the current position and the map-so-far, • Compute the local safe region • Align with the map-so-far • Generate a list of candidate NBVs • Sample points near the edge of the safe region • Remove candidates not adequately visible from the boundaries of the safe region • Remove candidates without a collision-free path • Select NBV maximizing visibility gain vs. path length

6. Safe region • Largest region the robot can safely occupy, given map-so-far • Compute visibility region • Extrapolate safe region

7. Visibility • W 2 is the actual workspace • W is the boundary of W • w W is visible from qW if the following constraints are satisfied:

8. Visibility • W 2 is the actual workspace • W is the boundary of W • w W is visible from qW if the following constraints are satisfied: • 1. Line-of-sight constraint: the open line segment S(w, q) does not intersect W W w W w q q

9. Visibility • W 2 is the actual workspace • W is the boundary of W • w W is visible from qW if the following constraints are satisfied: • 2. Range constraint: Euclidean distance d(q, w) rmax for some rmax > 0 w W q

10. Visibility • W 2 is the actual workspace • W is the boundary of W • w W is visible from qW if the following constraints are satisfied: • 3. Incidence constraint: (n,v)   for some [0, /2], for n  W at w and v the vector from w to q w w W W n  n  q q

11. Solid curves • Visible contour described in polar coordinates as piecewise continuous function r( ) with respect to robot origin • r( ) can be decomposed into non-overlapping, continuously visible solid curves, defined by r( ; a,b ) over (a,b), where a and b are critical values of  W a b  q • Let  contain all solid curves in the boundary

12. Free curves • Each pair of succeeding solid curves <r1( ; a1,b1 ), r2( ; a2,b2 )> is connected with a free curve f( ; b1,a2 ), s.t.: f • Any ray from the robot origin in the polar region b1 <  < a2 will intersect the curve before any obstacle • The area defined by f is as large as possible Gonzalez-Banos / Latombe 2002

13. Solid curve approximation • Finite resolution: rather than visible curves, sensor returns a list of visible points • Solution: • group points into clusters • fit a conservative (minimal number of vertices) polyline to each cluster, such that every point lies within  of a line segment

14. NBV algorithm overview • Given sensor information at the current position and the map-so-far, • Compute the local safe region • Align with the map-so-far • Generate a list of candidate NBVs • Sample points near the edge of the safe region • Remove candidates not adequately visible from the boundaries of the safe region • Remove candidates without a collision-free path • Select NBV maximizing visibility gain vs. path length

15. Model alignment / merging • Define the partial global model at qk-1 to be Mg(qk-1 ) = < g(qk-1 ), Sg(qk-1 )> • g(qk-1 ) is the union of the solid curves in Wup to stage k-1 (subject to transform) • Sg(qk-1 ) is the safe region defined by g(qk-1 ) and the connecting free curves • Let the local model be ml (qk ) = < l (qk ), sl(qk )>

16. Model alignment / merging Given Mg(qk-1 ) = < g(qk-1 ), Sg(qk-1 )> and ml (qk ) = < l (qk ), sl(qk )> Calculate the transform T by matching the line segments in g(qk-1 ) andl (qk ) with an alignment algorithm Create the new safe region Sg(qk )=T(Sg(qk-1 ))  sl(qk )

17. Model alignment / merging • Example ALIGN algorithm: • Randomly select pairs of segments from l • For each pair (u1, u2) in l , find (v1, v2) in g with the same relative angle • Look for the best fit transform that results • Not perfect…can use some odometric / distance information as well

18. NBV algorithm overview • Given sensor information at the current position and the map-so-far, • Compute the local safe region • Align with the map-so-far • Generate a list of candidate NBVs • Sample points near the edge of the safe region • Remove candidates not adequately visible from the boundaries of the safe region • Remove candidates without a collision-free path • Select NBV maximizing visibilitygain vs. path length

19. Feasible set of NBV candidates 1. Randomly pick points within the visibility range of the free curves bounding Sg(qk-1 ) 2. Rule out points that are too far away from the visible solid curves of g(qk-1 ), to allow for accurate model alignment 3. Rule out points for which a path planner does not generate a collision-free path

20. Scoring NBV candidates Score is defined for an NBV candidate q by g(q) = A(q) exp{ -L(q) } • A(q ) measures visibility gain of new position • L(q) is the length of the path generated by the planner •  weights path cost against information gain; small  if motion is cheap

21. Visibility gain metric A • Example A(q) calculation: • Cast a set of equally-spaced rays from q • For each ray: • if the segment between 0 and rmax distance from q hits a solid edge, ignore the portion of the ray beyond the intersection • compute the length len of the remaining segment that falls outside of Sg(qk ) • set A(q) = len

22. NBV computation

23. Remarks • Experimentally, showed moderately low number of motions / sense operations required to build map • Ability to tweak parameters to implement cautious detailed mapper or high-exploration rough mapper • Can be extended to multiple robots, efficient if they could work relative to each other

24. Limitations • 2D model only • Lack of error-recovery or retroactive adjustment • Feature-poor environments • Future work: integrate NBV algorithm with other simultaneous localization and mapping (SLAM) techniques