Sensor Based PlannersBug algorithms

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

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..)

Bug Behaviors Bug behaviors are simple:

Move in a straight line to the target Follow a wall (right or left)

Definitions Start point Target point “Hit point” “Leave point”

sq

goalq

Hiq

Liq

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

Bug 0 - Example Assuming a left t

turning robot

What map will foil bug 0?

What map will foil bug 0?

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)

Bug 1 - Example

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.

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

Tangent Bug Assume we have a range sensor

(with a finite resolution and is noisy)

Tangent Bug

[0, ]( , ) min ( , [cos ,sin ]

such that [ ,

,

]

)T

Ti

x d x x

x cos siniwo

( , ), if ( , ))

, other(

wis,

eR

x xx

R

Tangent Bug Tangent bug relies on finding

endpoints of finite, continuous segments of

R

Tangent Bug Tangent bug relies on finding

endpoints of finite, continuous segments of

R

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

Motion to Goal Example

What if the distance starts to go up?

M is the point with shortestdistance to goal

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

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

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

Example – Zero Sensor Range

Example – Finite Sensor Range

Example – Infinite Sensor Range

d_followed (M) is constantly updated