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Chapter 2 : Bug Algorithms. Hyoekjae Kwon Sungmin Lee. contents. <Part 1> 1. About Bug 2. Bug1 Algorithms 3. Bug2 Algorithms <Part 2> 4. Tangent Bug Algorithm <Part 3> 5. Implementation 6. Q & A. <Part 1> (Bug1, Bug2). What’s Special About Bugs. Bug 1. Goal. Start.

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Chapter 2 : Bug Algorithms

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Chapter 2 : Bug Algorithms

Hyoekjae Kwon

Sungmin Lee


contents

<Part 1>

1. About Bug

2. Bug1 Algorithms

3. Bug2 Algorithms

<Part 2>

4. Tangent Bug Algorithm

<Part 3>

5. Implementation

6. Q & A


<Part 1>

(Bug1, Bug2)


What’s Special About Bugs


Bug 1

Goal

Start


Bug 1 More formally


Bug 1 analysis

Goal

Start


Bug 2

Goal

Start


The Spiral

Goal

Goal

Start

Start


Bug 2 More formally


Bug 2 analysis

Start

Goal


head-to-head comparison

Start

Goal

Goal

Start


BUG 1 vs. BUG 2


<Part 2>

(Tangent Bug)


The Basic Ideas

• A motion-to-goal behavior as long as way is clear or there is a visible obstacle boundary pt that decreases heuristic distance

• A boundary following behavior invoked when heuristic distance increases.

• A value dminwhich is the shortest distance observed thus far between the sensed boundary of the obstacle and the goal

• A value dleavewhich is the shortest distance between any point in the currently sensed environment and the goal

• Terminate boundary following behavior when dleave< dmin


Tangent Bug Algorithm

Goal

Start

H : hit pointD : depart point

M : minimum pointL : leave point


Tangent Bug Algorithm

  • 1) repeat

    • a) Compute continuous range segments in view

    • b) Move toward n {T,Oi} that minimizes h(x,n) = d(x,n) + d(n,qgoal)

      until

    • a) goal is encountered, or

    • b) the value of h(x,n) begins to increase

  • 2) follow boundary continuing in same direction as before repeating

    a) update {Oi}, dleaveand dmin

    until

    • a) goal is reached

    • b) a complete cycle is performed (goal is unreachable)

    • c) dleave< dmin


Raw Distance Function

Saturated raw distance function


Intervals of Continuity

Tangent Bug relies on finding endpoints of finite, continued segments

of ρR


Motion-to-Goal Transitionfrom Moving Toward goal to “following obstacles”

Currently, the motion-to-goal behavior “thinks” the robot can get to the goal


Transition from Motion-to-Goal


Motion To Goal Example


Motion To Goal Example


Minimize Heuristic Example

At x, robot knows only what it sees and where the goal is,

so moves toward O2. Note the line

connectingO2 and goal pass through

obstacle

so moves toward O4. Note some

“thinking” was involved and the line

connectingO4 and goal pass through

obstacle

For any Oi such that d(Oi,qgoal) < d(x,qgoal),

choose the part Oithat minimizes d(x,Oi) + d(Oi,qgoal)


dminand dleave

• A value dminwhich is the shortest distance observed thus far between the sensed boundary of the obstacle and the goal

• A value dleavewhich is the shortest distance between any point in the currently sensed environment and the goal


Example: Zero Sensor Range

H : hit pointD : depart point

M : minimum pointL : leave point


Example: Finite Sensor Range

Goal

Start

H : hit pointD : depart point

M : minimum pointL : leave point

H : hit pointD : depart point

M : minimum pointL : leave point


Example: Infinite Sensor Range

Start

Goal

There is no boundary-following


dminis constantly updated

Goal

Start


<Part 3>

(Implementation)


What Information: The Tangent Line

safe distance

The dashed line represents the tangent to the offset curve at x.


How to Process Sensor Information

The dashed line is the actual path, but the robot follows the thin black lines, predicting and correcting along the path. The black circles are samples along the path.


Sensors


Tactile sensors

  • Tactile sensors are employed wherever interactions between a contact surface and the environment are to be measured and registered.

A tactile sensor is a device which receives and responds to a signal or stimulus having to do with force.

<daVinci medical system>


Ultrasonic sensors

  • Ultrasonic sensors generate high frequency sound waves and evaluate the echo which is received back by the sensor. Sensors calculate the time interval between sending the signal and receiving the echo to determine the distance to an object.


Polaroid ultrasonic transducer

The disk on the right is the standard Polaroid ultrasonic transducer found on many mobile robots; the circuitry on the left drives the transducer.


Beam pattern for the Polaroid transducer.

This obstacle can be located anywhere along the angular spread of the sonar sensor's beam pattern. Therefore, the distance information that sonars provide is fairly accurate in depth, but not in azimuth.


Centerline model

The beam pattern can be approximated with a cone. For the commonly used Polaroid transducer, the arc base is 22.5degrees


Reference

http://blog.daum.net/pg365/115

http://www.cs.cmu.edu/~motionplanning/student_gallery/2006/st/hw2pub.htm

HowieChoset with slides from G.D. Hager and Z. Dodds (Bug Algorithms)

Book : Principles of Robot Motion


Question

&

Answer


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