Identifying maximal rigid components in bearing-based localization

We present an approach for sensor network localization when provided with a set of angular constraints. This problem arises in camera networks when angles between nearby points can be measured but depth measurements are not readily available. We provide contributions for two different variations on this problem. First, when each node is aware of a global coordinate frame, we present a novel method for identifying the components of the problem that are rigidly constrained. Second, in the more difficult case where only relative angles are known, we propose a novel spectral solution that achieves a globally-optimal embedding under transitively-triangular constraints, which we show encompass a wide range of real-world conditions. We demonstrate the utility of our algorithm on both synthetic data and data from quadrotor robot formations.

[1]  Anthony Man-Cho So,et al.  Theory of semidefinite programming for Sensor Network Localization , 2005, SODA '05.

[2]  R. V. Kumar,et al.  Necessary and sufficient conditions for localization of multiple robot platforms , 2004 .

[3]  Camillo J. Taylor,et al.  A bounded uncertainty approach to multi-robot localization , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[4]  Seth J. Teller,et al.  Spectral Solution of Large-Scale Extrinsic Camera Calibration as a Graph Embedding Problem , 2004, ECCV.

[5]  Frank Dellaert,et al.  Linear 2D localization and mapping for single and multiple robot scenarios , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[6]  Franck Petit,et al.  Deterministic Robot-Network Localization is Hard , 2010, IEEE Transactions on Robotics.

[7]  Brian D. O. Anderson,et al.  A Theory of Network Localization , 2006, IEEE Transactions on Mobile Computing.

[8]  Takeo Kanade,et al.  Affine structure from line correspondences with uncalibrated affine cameras , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  W. Torgerson.  Multidimensional scaling: I. Theory and method , 1952 .

[10]  David C. Moore,et al.  Robust distributed network localization with noisy range measurements , 2004, SenSys '04.

[11]  L. El Ghaoui,et al.  Convex position estimation in wireless sensor networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[12]  Camillo J. Taylor,et al.  A bounded uncertainty approach to cooperative localization using relative bearing constraints , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[13]  Andrew Howard,et al.  Multi-robot Simultaneous Localization and Mapping using Particle Filters , 2005, Int. J. Robotics Res..

[14]  Walter Whiteley,et al.  Constraining Plane Configurations in Computer-Aided Design: Combinatorics of Directions and Lengths , 1999, SIAM J. Discret. Math..

[15]  Peter N. Belhumeur,et al.  A Theoretical Analysis of the Conditions for Unambiguous Node Localization in Sensor Networks , 2004 .

[16]  Stergios I. Roumeliotis,et al.  Interrobot Transformations in 3-D , 2010, IEEE Transactions on Robotics.

[17]  C. Lanczos.  An iteration method for the solution of the eigenvalue problem of linear differential and integral operators , 1950 .

[18]  Brian D. O. Anderson,et al.  On frame and orientation localization for relative sensing networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[19]  Francesco Bullo,et al.  On frame and orientation localization for relative sensing networks , 2013, Autom..

[20]  Vijay Kumar,et al.  Towards a swarm of agile micro quadrotors , 2012, Autonomous Robots.

[21]  G. Laman.  On graphs and rigidity of plane skeletal structures , 1970 .

[22]  Brian D. O. Anderson,et al.  Rigidity, computation, and randomization in network localization , 2004, IEEE INFOCOM 2004.

[23]  Walter Whiteley,et al.  CONSTRAINING PLANE CONFIGURATIONS IN CAD: COMBINATORICS OF DIRECTIONS AND LENGTHS , 1999 .

[24]  Meera Sitharam,et al.  Combinatorial decomposition, generic independence and algebraic complexity of geometric constraints systems: applications in biology and engineering , 2006 .