Navigation Strategies for Exploring Indoor Environments

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
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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
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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
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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

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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

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Safe region

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

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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

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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
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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 gt 0

w
?W
q
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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
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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

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Free curves

• Each pair of succeeding solid curves lt r1(?
  a1,b1 ), r2(? a2,b2 )gt is connected with a
  free curve f(? b1,a2 ), s.t.

f

• Any ray from the robot origin in the polar
  region b1 lt ? lt a2 will intersect the curve
  before any obstacle
• The area defined by f is as large as possible

Gonzalez-Banos / Latombe 2002
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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

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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

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Model alignment / merging

• Define the partial global model at qk-1 to be
  Mg(qk-1 ) lt ? g(qk-1 ), Sg(qk-1 )gt
• ? 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 ) lt ? l (qk
  ), sl(qk )gt

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Model alignment / merging
Given Mg(qk-1 ) lt ? g(qk-1 ), Sg(qk-1 )gt and
ml (qk ) lt ? l (qk ), sl(qk )gt 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 )
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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 perfectcan use some odometric / distance
  information as well

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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

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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
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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

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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

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NBV computation
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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

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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