Chapter 2 : Bug Algo-rithms

Hyoekjae KwonSungmin Lee

contents<Part 1>1. About Bug2. Bug1 Algorithms3. Bug2 Algorithms<Part 2>4. Tangent Bug Algorithm<Part 3>5. Implementation6. 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

Start

Goal

Start

Bug 2 More formally

Bug 2 analysis

Start

Goal

head-to-head comparison

Goal

Start

Start

Goal

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 dis-tance increases.

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

• A value dleave which 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

H : hit point D : depart point M : minimum point L : leave point

GoalStart

Tangent Bug Algorithm1) 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}, dleave and 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 ContinuityTangent Bug relies on finding end-points of finite, continued segmentsof ρR

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

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

Transition from Motion-to-Goal

Motion To Goal Example

Motion To Goal Example

Minimize Heuristic Exam-pleAt x, robot knows only what it sees

and where the goal is,

so moves toward O2. Note the lineconnectingO2 and goal pass throughobstacle

so moves toward O4. Note some“thinking” was involved and the lineconnectingO4 and goal pass throughobstacle

For any Oi such that d(Oi,qgoal) < d(x,qgoal),choose the part Oi that minimizes d(x,Oi) + d(Oi,qgoal)

dmin and dleave

• A value dmin which is the shortest dis-tance observed thus far between the sensed boundary of the obstacle and the goal

• A value dleave which is the shortest dis-tance between any point in the cur-rently sensed environment and the goal

Example: Zero Sensor Range

H : hit point D : depart point M : minimum point L : leave point

Example: Finite Sensor Range

H : hit point D : depart point M : minimum point L : leave point

H : hit point D : depart point M : minimum point L : leave point

GoalStart

Example: Infinite Sensor Range

There is no boundary-following

Start

Goal

dmin is constantly updated

Goal

Start

<Part 3>(Implementation)

What Information: The Tangent Line

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

safe distance

How to Process Sensor Informa-tion

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 sam-ples along the path.

Sensors

Tactile sensorsTactile sensors are employed wherever

interactions between a contact surface and the environment are to be mea-sured and registered.

<daVinci medical system>

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

Ultrasonic sensors Ultrasonic sensors generate high fre-

quency sound waves and evaluate the echo which is received back by the sensor. Sensors calculate the time in-terval between sending the signal and receiving the echo to determine the distance to an object.

Polaroid ultrasonic trans-ducer

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

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

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

Howie Choset with slides from G.D. Hager and Z. Dodds (Bug Algo-rithms)

Book : Principles of Robot Motion

Question &

Answer