Sensor Localization and Target Estimation in Visual Sensor Networks

Transcription

1 Annual Schedule of my Research Sensor Localization and Target Estimation in Visual Sensor Networks Survey and Problem Settings Presented in the FL seminar on May th First Trial and Evaluation of Proposed Method Would like to finish by June Takayuki Nishi FL-8-8 th, June, Simulation (Experimental Verification) Would like to finish by the middle presentation on July 5 th Introduction Introduction Visual Sensor Networks A network consisting of spatially distributed smart cameras Application Environmental monitoring Surveillance The information of the location of the sensor is needed Network Localization Determining the relative poses of each sensor in sensor networks Localization in Camera Networks [5] Distributed estimation of the pose of cameras Use feature points to get the neighboring pose Apply only in static scene Nonsimultaneous measure and estimation ive of my Research Use an object to get the relative pose of the camera Not only determine the relative pose of each sensor but also estimate the pose of the object [5] R. Tron and R. Vidal, Distributed Image-based -D Localization of Camera Sensor Networks, Proc. of the 48th IEEE Conference on Decision and Control, pp. 9-98, 9. 4 Outline Introduction First Trial in a Simple Model Analysis of the Trial 5 Preliminaries Consider a Visual Sensor Network with s Communication graph G = ( V, E) Set of cameras: V= {, L, N} Edge:( i, j) E j can get i s information Neighbor set: Undirected graph Pose Representation Pose of camera i : Position: World frame w Orientation: Pose of object : Pose of object relative to camera i: Relative pose of the camera i and j: Camera Camera4 Camera i s frame i Camera Camera frame Camera j s frame j o 6

2 Preliminaries Definition of Localization Rigid Body Motion Relative Rigid Body Motion (RRBM) Visual Measurements Position of feature points relative to object frame Position of feature points relative to camera frame Perspective projection Estimate from by Visual Motion Observer [8] Estimated pose: " " : wedge : body velocity :focal length Rigid Body Motion RRBM Image Plane Camera Frame 7 Definition of Localization Consider a visual sensor network. Let the world frame be the camera frame. The network is localized when the relative poses of the camera for all i {, L, N} are uniquely determined. (Inspired by Bullo et al. [4] and Vidal et al. [5]) Motivation of Localization Problem Camera Estimates are taken from their own camera frame Estimates (measurements) are corrupted by noise pose needs to be expressed in a common frame (world frame) Camera = World frame pose relative to world frame must be unique Camera Camera4 8 ive Problem Settings ive Determine the poses of the camera and object relative to the camera which are. As close as the estimates Satisfy the uniqueness of the object pose Cost Function Euclidean distance: Optimization Problem such that and are known Procedure of minimization: Gradient method : Pose of the object estimated by camera i To avoid the solution will be trivial Division into Position and Orientation Parts Position Fix variables (known pose): Decision variables: 9 Orientation Introduction Outline Trial with Simple Models Consider cameras and estimate only orientation Graph settings First Trial in a Simple Model Gradient of the cost function : Orientation of the object estimated by camera i Analysis of the Trial Update the estimates (discrete) : Estimates at iteration l ε : Step size

3 z Simulation Settings & Cameras : Stationary Exponential expression Coordinates Plot of orientation Estimated by VMO (measurements). Fixed orientation.5.. Cameras Estimated orientation Step size :. + Random constant noise (Gaussian with mean variance.) Plot of orientation Estimated by VMO (measurements) e-6 5 ξ x Plot of orientation ξ y Discussion & Problems Outline. What are the physical meanings of the estimates? Distance between true and measured orientation Distance between true and calculated orientation seem to reduce the effectiveness of the noise. The pose of cameras change when the object moves Cameras: Stationary :Move Introduction First Trial in Simple Models Analysis of the Trial 7 8

4 Regard cost function as Lyapunov candidate function Lyapunov function considering only position (Orientation fixed) Time derivative of the Lyapunov function Straightforward interpretation Gradient method 9 Analysis in the case Let be the element of () () Let V= {, L, N} L : Graph Laplacian () () Since, substitute () to () () Ex.) 4 4 L= ( I + L) = L = ( I + L) = Checked by the simulation (Appendix) Weighted average Conclusion Characteristic of Assumption The graph is connected and balanced Ex.) 4 7 ( I + L) = (Inspired by Hatanaka [7], []) L ( αi + L) M O M α n L heuristic ( I + L) = Not balanced Conclusion Setting the cost function Orientation Simulation in a Simple Model Future Works The cost function is minimized Question about what is the meaning of the converge value Analysis of the position cost function Converge values are weighted average of the estimates Analysis of the orientation cost function Analytical simulations 4

5 References References [] S. Thrun, W. Burgard and D. Fox, Probabilistic Robotics, The MIT Press, 6. [] N. Trwmy, X. S. Zhou, K. X. Zhou and S. I. Roumeliotis, D Relative Pose Estimation from Distance-only Measurements, Proc. of the 7 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 7-78, 7. [] J. Aspnes, T. Eren, D. K. Goldenberg, A. S. Morse, W. Whiteley, Y. R. Yang, B. D. O. Anderson and P. N. Belhumeur, A Theory of Network Localization, IEEE Transactions on Mobile Computing, Vol. 5, No., pp , 6. [4] G. Piovan, I. Shames, B. Fidan, F. Bullo and B. D. O. Anderson, On Frame and Orientation Localization for Relative Sensing Networks, Automatica,. (submitted) [5] R. Tron and R. Vidal, Distributed Image-based -D Localization of Camera Sensor Networks, Proc. of the 48th IEEE Conference on Decision and Control, pp. 9-98, 9. [7] T. Hatanaka, T. Nishi and M. Fujita, Passivity-based Cooperative Estimation Algorithm for Networked Visual Motion Observers, Proc. of the SICE Annual Conference,. (submitted) [8] M. Fujita, H. Kawai and M. W. Spong, Passivity-based Dynamic Visual Feedback Control for Three Dimensional Target Tracking: Stability and L-gain Performance Analysis, IEEE Transactions on Control Systems Technology, Vol.5, No., pp. 4-5, 7. [9] P. A. Absil, R. Mahony and R. Sepulchre, Optimization Algorithms on Matrix Manifolds, Princeton Press, 8. [] Y. Igarashi, T. Hatanaka, M. Fujita and M. W. Spong, Passivity-based Attitude Synchronization in SE(), IEEE Transactions on Control Systems Technology, Vol. 7, No. 5, pp.9 4, 9. [6] R. Tron, R. Vidal and A. Terzis, Distributed Pose Averaging in Camera Sensor Networks via Consensus on SE(), Proc. of the International Conference on Distributed Smart Cameras, 8. 5 [] T. Hatanaka and M. Fujita, Passivity-based Cooperative Estimation of D Target Motion for Visual Sensor Networks: Analysis on Averaging Performance, Proc. of the American Control Conference,. (to be presented) 6 Definition of Localization Appendix Definition of localization Problem 6 (Frame localizability) [4] Given a relative sensing network with reference node. The reference frame transformation for all i {, L, n} are uniquely determined by the relative measurements :i s orientation relative to node :i s position Definition (Localized network) [5] A network is said to be localized if there is a set of relative transformations such that, when the reference frame of the first node is fixed to, the other absolute poses are uniquely determined. For any path l from node to node i, we have 7 8 Calculation of the Gradient Calculation of the Gradient Consider SO() is submanifold of Define Directional derivative From () and () () () Projection: Tangent space: () : Inner product 9

6 Simulation Settings Cameras : Stationary :Move Estimated by VMO Simulation : Moving Simulation Settings: Only Position True position Fixed position and orientation z Simulation: Only Position.5 Lyapunov Method (Orientation) Lyapunov function considering only orientation.5 p x [m] p x [m] Time derivative of the Lyapunov function Gradient method -. 4 Lyapunov Method (Orientation) Lyapunov Method (Orientation) From Lemma4 in [] if 5 6

7 Lyapunov Method (Orientation) Time Derivative of Orientation Lyapunov Function Consideration if Converge to the set?? Simple model (Ex.) Graph settings Simple model (Ex.) Graph settings 7 8