Bug Algorithms
Shmuel Wimer
Bar Ilan Univ., School of Engineering
April 2011
1
Bug1 and Bug2 Algorithm
• Move towards the goal, unless an obstacle is
encountered.
• Circumnavigate the obstacle until motion toward the goal
is again allowable.
• Robot is assumed to be a point with perfect positioning.
• Robot has a contact sensor which detects the obstacle
boundary if it touches it.
• The robot can measure the distance d(x,y) between any
two points.
• The workspace is bounded.
April 2011
2
The Bug1 algorithm
successfully finds the
goal.
April 2011
3
• Bug1 exhibits two behaviors:
– motion to goal, and
– boundary following.
• The robot moves along a line from qstart to qgoal until it hits
an obstacle at a hit point - q1,hit.
• It circumnavigate the obstacle until it returns the hit point.
• It then determines the nearest point to qgoal and traverses
along the boundary to that leave point - q1,leave.
• From q1,leave it heads straight to qgoal again.
• The algorithm terminates when qgoal is reached or the
planner determines that qgoal is not reachable.
April 2011
4
The Bug1 algorithm reports the goal is unreachable.
April 2011
5
The Bug2 algorithm
successfully finds the
goal.
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6
The Bug2 algorithm reports the goal is unreachable.
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• Bug2 also exhibits two behaviors:
– motion to goal, and
– boundary following.
• The motion line is fixed, connecting qstart to qgoal.
• From a hit point qi,hit it circumnavigate an obstacle until it
reaches a new point along the motion line, closer to qgoal.
• If it returns to qi,hit the goal is not reachable.
• At first glance it seems that Bug1 is more effective than
Bug2, yielding a shorter path.
• This is not always the case.
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For Bug1, when the robot hits an obstacle it completely
circumnavigate the boundary and then returns to the
leave point, traversing it 1.5 times in the worst case. If
there are n obstacles then:
LBug1  d  qstart , qgoal   1.5 i 1 pi
n
Let the motion line connecting qstart to qgoal intersects and
obstacle ni times. Bug2 may perform a complete traversal
of the boundary on half of those point. Therefore:
LBug2
1 n
 d  qstart , qgoal    i 1 ni pi
2
LBug2 can be arbitrarily longer than LBug1.
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10
Tangent Bug
The robot has an azimuth distance sensor with infinitesimal
angular resolution. For every point of an obstacle, azimuth
distance is defined:
 : R 2   0,360  R..
For   cos  ,sin   
T

i
WO i , . define

  x,    min d x    cos  ,sin   .
 0,  
T
The range of the sensor is usually limited.
   x,  , if   x,   R
 R  x,   
, otherwise.

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11
ρR is piecewise continuous.
The tangent Bug planner
assumes that the robot can
detect discontinuities in ρR.
April 2011
Intervals of continuity:
[O1,O2] , [O3,O4],
[O5,O6] and [O7,O8]
12
• Like Bug1 and Bug2, Tangent Bug has motion-to-goal
and boundary-following behaviors.
• Unlike Bug1 and Bug2, its motion-to-goal behavior may
have both straight and boundary following phases.
Similarly, in boundary-following behavior it may have a
straight motion phase.
• The robot starts in a motion-to-goal by moving straight
towards the goal until it senses an obstacle at distance
of R units.
• By definition, the line connecting the robot to the goal
must intersect an interval of continuity.
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13
The robot is sensing
WO1 and WO2, but
ignores WO1.
After touching WO2
the first time, an
interval [O1,O2] of
continuity is defined.
The robot then moves towards Oi that maximally decreases
a heuristic distance to goal, for example, d(x,Oi)+d(Oi,qgoal).
April 2011
14
t 1
t2
t 3
Motion-to-goal is also following boundary
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