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Chapter 2 : Bug AlgorithmsPowerPoint Presentation

Chapter 2 : Bug Algorithms

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Presentation Transcript

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

(Bug1, Bug2)

What’s Special About Bugs

Bug 1 More formally

Bug 2 More formally

(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

- 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

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

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: Finite Sensor Range

Goal

Start

H : hit point D : depart point

M : minimum point L : leave point

H : hit point D : depart point

M : minimum point L : leave point

(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.

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

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