Performance Bounds for Cooperative Simultaneous Localization and Mapping (C-SLAM)

In this Technical Report we study the time evolution of the position estimates’ covariance in Cooperative Simultaneous Localization and Mapping (C-SLAM), and obtain analytical upper boundsfor the positioning uncertainty. The derived bounds provide descriptions of the asymptotic positioning performance of a team of robots in a mapping task, as a function of the characteristics of the proprioceptive and exteroceptive sensors of the robots, and of the graph of relative position measurements recorded by the robots. A study of the properties of the Riccati recursion which describes the propagation of uncertainty through time, yields (i) the guaranteed accuracyfor a robot team in a given C-SLAM application, as well as (ii) the maximum expected steady state uncertainty of the robots and landmarks, when the spatial distribution of features in the environment can be modeled by a known distribution.

[1]  Hugh F. Durrant-Whyte,et al.  Simultaneous Mapping and Localization with Sparse Extended Information Filters: Theory and Initial Results , 2004, WAFR.

[2]  Andrea Garulli,et al.  Simultaneous localization and map building for a team of cooperating robots: a set membership approach , 2003, IEEE Trans. Robotics Autom..

[3]  Lynne E. Parker,et al.  Incremental multi-agent robotic mapping of outdoor terrains , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[4]  J. W. Fenwick,et al.  Collaborative concurrent mapping and localization , 2001 .

[5]  Jeffrey K. Uhlmann,et al.  Simultaneous localisation and map building using split covariance intersection , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[6]  Andrew Howard,et al.  Multi-robot mapping using manifold representations , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[7]  Raja Chatila,et al.  Stochastic multisensory data fusion for mobile robot location and environment modeling , 1989 .

[8]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

[9]  Lynne E. Parker,et al.  Distributed Cooperative Outdoor Multirobot Localization and Mapping , 2004 .

[10]  Stergios I. Roumeliotis,et al.  Distributed multirobot localization , 2002, IEEE Trans. Robotics Autom..

[11]  Ingemar J. Cox,et al.  Autonomous Robot Vehicles , 1990, Springer New York.

[12]  Sebastian Thrun,et al.  A Probabilistic On-Line Mapping Algorithm for Teams of Mobile Robots , 2001, Int. J. Robotics Res..

[13]  Alonzo Kelly.  General solution for linearized systematic error propagation in vehicle odometry , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[14]  John J. Leonard,et al.  Explore and return: experimental validation of real-time concurrent mapping and localization , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[15]  Sebastian Thrun,et al.  FastSLAM: a factored solution to the simultaneous localization and mapping problem , 2002, AAAI/IAAI.

[16]  Gregory Dudek,et al.  Multi-robot cooperative localization: a study of trade-offs between efficiency and accuracy , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[17]  Stefan B. Williams,et al.  An efficient approach to the simultaneous localisation and mapping problem , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[18]  Peter C. Cheeseman,et al.  Estimating uncertain spatial relationships in robotics , 1986, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[19]  Ryo Kurazume,et al.  Cooperative positioning with multiple robots , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[20]  Lynne E. Parker,et al.  Distributed heterogeneous outdoor multi-robot localization , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[21]  Stergios I. Roumeliotis,et al.  Analysis of positioning uncertainty in reconfigurable networks of heterogeneous mobile robots , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[22]  Sebastian Thrun,et al.  Results for outdoor-SLAM using sparse extended information filters , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[23]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[24]  Babak Hassibi.  Indefinite metric spaces in estimation, control and adaptive filtering , 1996 .

[25]  John J. Leonard,et al.  Cooperative concurrent mapping and localization , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).