Optimal Arrangement of Ceiling Cameras for Home Service Robots Using Genetic Algorithms Stefanos 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 2 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 3 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 4 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 5 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 6 This study: four degrees of freedom for each camera different FOVs, no symmetric arrangement assumption

Conditions of Optimization Problem 7 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 8 initial population selection crossover mutation evaluation new population gen=gen+1 final population elitism individual: [x 0, y 0, pan 0, tilt 0, …, x n, y n, pan n, tilt n ] 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 9 100% 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) 10 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 11 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 error small large

Multi-Objective Optimization 12 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 14 Constraints: Visible Ratio > 0.8 AND Localization Error < 70 [mm 2 ] Set of optimal solutions

Discussion 15 Single-Objective Optimization (GA) Multi-Objective Optimization (NSGA) visible area consideredboth visible area and average localization error considered one optimal solutionset of pareto optimal solutions relatively fast convergenceslow 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 [mm 2 ] found Single-objective approach simpler and recommended if localization accuracy not important 16 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. 17 on the camera placement problem?

Thank you for your attention 18

Challenging Point: Occlusion Estimation 19

Pareto Front – NSGA Algorithm 20 A f1f1 f2f2 C B f 1 (A)>f 1 (B) f 2 (A)<f 2 (B) f1f1 f2f2 RANK 1 RANK 2 NSGA (Non-dominated Sorting Genetic Algorithm) [Srinivas 1995] sharing

Multi-Objective Optimization: Common Approach Evaluation function of linear combination of objectives 21  Gives one solution only with one execution  Weight-dependent  Determining the appropriate weights is a difficult problem itself