Optimal Arrangement of Ceiling Cameras for Home Service

Robots Using Genetic AlgorithmsStefanos Nikolaidis*,** and Tamio Arai**

*R&D Division, Square Enix Co., Ltd., Japan**Department of Precision Engineering, The University of Tokyo, Japan

Contribution to Real-World Environment

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Results from this research have been used for the Kanagawa House Square Model Room, as part of the Universal Design Project

Virtual 3D Model of the Kanagawa Room

Camera Placement Optimization

Kanagawa House Square Model Room

Placement of Cameras according to simulation results

　　 Background

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Use of robots in home environments

EXTERNAL SENSORS PLACED ON THE ENVIRONMENT ARE NEEDED

Problem: Cost of sensor placement, network delay

As few sensors as possible

arrange sensors supporting different kinds of robots ceiling cameras are used in this study

Purpose: place the cameras considering robot localization

Robots need to be localized to perform home service tasks

Goal of this Study

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Robot should be visible

Robots need to be localized with a certain

precision

MAXIMIZE AREA COVERAGE

MINIMIZE LOCALIZATION ERROR

Objectives

Place the cameras considering area covered and average

localization error of visible area

Purpose: place the cameras considering robot localization

Camera Placement Optimization

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Objectives

Maximize the area covered by

the cameras

Minimize Localization

Error

Multi-Objective Optimization

NSGA (Non-dominated Sorting Algortihm [Srinivas 1995])

multi-pareto genetic algorithm

Single-Objective Optimization

genetic – algorithm probabilistic global optimization algorithm

COVERAGE ACCURACY

Past Research• Optimal Camera Placement

COVERAGE:Art Gallery Problem : find the minimum number

of guards covering an art gallery (NP-hard [Lee

1986] ) [O’Rourke 1987], [Schermer 1992]

Every guard: two degrees of freedom, 360º FOV

ACCURACY:Intelligent Space Project [Lee 2002], [Hashimoto 2005]

Limited for two cameras, symmetric arrangement is assumed

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This study:• four degrees of freedom for each camera• different FOVs, no symmetric arrangement assumption

Conditions of Optimization Problem

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3D model of room Camera pose [x, y, pan,

tilt]

2D cut at a specific height

Calculation of FOV of camera and Projection at a specific height

Occlusion calculated from obstacles

Single-Objective Optimization:Maximize the Area Covered

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initial population

selection

crossover

mutation

evaluation

new population

gen=gen+1

final population

elitism

MAXgen

MAXgen

• individual: [x0, y0, pan0, tilt0, … , xn, yn, pann, tiltn ]

n: number of cameras• selection: according to the fitness

of each individual• fitness: visible ratio

genetic algorithm

Comparison to Past Research:Results GA – Steepest Descent

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• 100% of the area is visible for three cameras (GA)• GA gives better results than steepest descent but slower (Pentium D CPU 3.20GHz used)• GA is recommended, as computational time not significant

Discussion (Single-Objective Optimization)

• number of cameras changed in order to achieve required visible ratio

• genetic algorithm gives better results than steepest descent (used in past research)

• using three cameras the robot is visible at 100% of the area (Kanagawa Model House environment)

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Localization error should also be considered, as the robot needs to be localized with a certain precision

due to:• safety reasons• complexity of home environment• complexity of home-service tasks

Localization Error due to Image Resolution

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3D localization with triangulation

localization uncertainty due to image resolution

P

Pixel P’ corresponding to Point P

Image Plane

Area of uncertainty Ω

Ground Area covered by vision sensor

П

errorsmall

large

Multi-Objective Optimization

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Place the cameras considering area covered and average localization

error of visible area

A set of optimal solutions minimizing the objective conflict between the

objectives needs to be found

A multi-pareto genetic algorithm, the NSGA Algorithm [Srinivas 1995]

is proposed for this problem

NSGA Algorithm

NSGA is proposed, because it:

can solve optimization problem of multiple objectives

gives set of optimal solutions with only one execution

can perform at the same time both maximization and minimization of objectives

However, it

has a large computational load

has dependence on the sharing parameter 13

Multi-Objective Optimization with NSGA Algorithm

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Constraints: Visible Ratio > 0.8 AND Localization Error < 70 [mm2 ]

Set of optimal

solutions

Discussion

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Single-Objective Optimization (GA)

Multi-Objective Optimization (NSGA)

visible area considered both visible area and average localization error considered

one optimal solution set of pareto optimal solutions

relatively fast convergence slow convergence

GA (single-objective) is faster, simpler and it is recommended if localization accuracy is not

important

Conclusion

• Single-objective case robot is visible at 100% of the room area

genetic algorithm implemented

• Multi-objective case found set of optimal solutions minimizing the objective conflict.

arrangement where robot is visible at 85% of the area and average localization error below 65 [mm2] found

• Single-objective approach simpler and recommended if localization accuracy not important

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Better Results than Steepest -descent method

used in past research

Future Research

• improve sharing efficiency of NSGA algorithm (dynamic niching, clustering analysis)

• apply SPEA (Strength Pareto Evolutionary Algorithm) [Zitzler 1999], a variation of NSGA the SPEA is proven to perform better than NSGA

on the 0/1 knapsack problem

• Generalize the problem for different kinds of sensors range sensors, RFID technology etc.

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on the camera placement problem?

Thank you for your attention

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Challenging Point:Occlusion Estimation

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Pareto Front – NSGA Algorithm

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A

f1

f2

C

B

f1(A)>f1(B)

f2(A)<f2(B)

f1

f2

RANK 1RANK 2

NSGA (Non-dominated Sorting Genetic Algorithm) [Srinivas 1995]

sharing

Multi-Objective Optimization: Common Approach

• Evaluation function of linear combination of objectives

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)(1

xfkF i

N

ii

Gives one solution only with one execution

Weight-dependent

Determining the appropriate weights is a difficult problem itself