Download - Sensor Based Planners
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Sensor Based PlannersBug algorithms
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Bug Algorithms World:
The world is , has obstacles, starting point {S} and target point {T}
The obstacles are closed and simple. Each point belongs at most to one
obstacle. The world contains a finite number of
obstacles locally.
2R
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Bug Algorithms Robot
The robot is a point (Configuration Space)
The robot knows his position The robot knows the target position Equipped with a sensor Infinite memory (though not
necessary..)
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Bug Behaviors Bug behaviors are simple:
Move in a straight line to the target Follow a wall (right or left)
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Definitions Start point Target point “Hit point” “Leave point”
sq
goalq
Hiq
Liq
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Bug 0 (No memory)1. Head toward goal2. Follow obstacle until you can head
toward goal again (left or right but not both)
3. continue
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Bug 0 - Example Assuming a left t
turning robot
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What map will foil bug 0?
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What map will foil bug 0?
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Bug 11. Head toward goal2. If an obstacle is encountered,
circumnavigate it and remember how close you get to the goal
3. Return to the closest point (by wall-following and continue)
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Bug 1 - Example
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Bug 2 Call the line from the starting point
to the goal the m-line1. Head toward goal on the m-line2. If an obstacle in the way, follow it
until you encounter the m-line again.
3. Leave the obstacle and continue toward goal.
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Bug1 vs Bug2 Bug1 is an exhaustive search
algorithm It looks all the choices before
committing Bug2 is a greedy algorithm
It takes the first thing that looks better
In many cases Bug2 will outperform bug 1
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Tangent Bug Assume we have a range sensor
(with a finite resolution and is noisy)
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Tangent Bug
[0, ]( , ) min ( , [cos ,sin ]
such that [ ,
,
]
)T
Ti
x d x x
x cos siniwo
( , ), if ( , ))
, other(
wis,
eR
x xx
R
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Tangent Bug Tangent bug relies on finding
endpoints of finite, continuous segments of
R
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Tangent Bug Tangent bug relies on finding
endpoints of finite, continuous segments of
R
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Tangent Bug – Motion to Goal1. Move to in a straight line toward
goal2. If you “see” something in front of
you1. For any such that
choosethe point that minimizes
iO ( , ) ( , ),i goal goald O q d x q
iO ( ) (, ),i i goald d O qx O
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Motion to Goal Example
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What if the distance starts to go up?
M is the point with shortestdistance to goal
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What if the distance starts to go up?
M is the point with shortestdistance to goal
Start to act like a BUG! And follow boundary
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d_reach and d_follow d_follow: is the shortest distance
between the boundary which had been sensed and the goal. (observed thus far)
d_reach: let A be all the points within line of sight of x with range R that are on the followed obstacle. , )min (
creach goalAd d q c
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Tangent Bug – terminate boundary-following behavior When
We found a point on the obstacle, which is closer to the goal than any point we sensed so far (on the currently followed obstacle).
reach followedd d
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Example – Zero Sensor Range
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Example – Finite Sensor Range
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Example – Infinite Sensor Range
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d_followed (M) is constantly updated