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

Navigation Strategies for Exploring Indoor

Environments

Hector H. González-BañosJean-Claude Latombe

Presented by Miler Lee, 6 May 2002

CS 326A: Motion Planning

Automatic model buildingTask:

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

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

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

Safe region

Largest region the robot can safely occupy, given map-so-far

• Compute visibility region

• Extrapolate safe region

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:

Visibility




1. Line-of-sight constraint: the open line segment S(w, q) does not intersect W

W

q

w W

q

w

Visibility




2. Range constraint: Euclidean distanced(q, w) rmax for some rmax > 0

Ww

q

Visibility




3. Incidence constraint: (n,v) for some [0, /2], for n W at w and v the vector from w to q

W w

q

Ww

q

n

n

Solid curves

• Visible contour described in polar coordinates as piecewise continuous function r( ) with respect to robot origin

W

q

ab

• 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

• Let contain all solid curves in the boundary

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.:

• 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

f

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

Model alignment / mergingDefine 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 W up 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 )>

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 )

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

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

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

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

NBV computation

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

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

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

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