A scalable information theoretic approach to distributed robot coordination

This paper presents a scalable information theoretic approach to infer the state of an environment by distributively controlling robots equipped with sensors. The robots iteratively estimate the environment state using a recursive Bayesian filter, while continuously moving to improve the quality of the estimate by following the gradient of mutual information. Both the filter and the controller use a novel algorithm for approximating the robots' joint measurement probabilities, which combines consensus (for decentralization) and sampling (for scalability). The approximations are shown to approach the true joint measurement probabilities as the size of the consensus rounds grows or as the network becomes complete. The resulting gradient controller runs in constant time with respect to the number of robots, and linear time with respect to the number of sensor measurements and environment discretization cells, while traditional mutual information methods are exponential in all of these quantities. Furthermore, the controller is proven to be convergent between consensus rounds and, under certain conditions, is locally optimal. The complete distributed inference and coordination algorithm is demonstrated in experiments with five quad-rotor flying robots and simulations with 100 robots.

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  George J. Pappas,et al.  On trajectory optimization for active sensing in Gaussian process models , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[3]  Claire J. Tomlin,et al.  Mobile Sensor Network Control Using Mutual Information Methods and Particle Filters , 2010, IEEE Transactions on Automatic Control.

[4]  Jorge Cortés,et al.  Distributed Kriged Kalman Filter for Spatial Estimation , 2009, IEEE Transactions on Automatic Control.

[5]  J. P. Lasalle.  Some Extensions of Liapunov's Second Method , 1960 .

[6]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[7]  J. Shamma,et al.  Belief consensus and distributed hypothesis testing in sensor networks , 2006 .

[8]  Mac Schwager,et al.  A Scalable Information Theoretic Approach to Multi-robot Coordination , 2011 .

[9]  Hugh F. Durrant-Whyte,et al.  A Bayesian Approach to Optimal Sensor Placement , 1990, Int. J. Robotics Res..

[10]  Ben Grocholsky,et al.  Information-Theoretic Control of Multiple Sensor Platforms , 2002 .

[11]  Vijay Kumar,et al.  A Multi-robot Control Policy for Information Gathering in the Presence of Unknown Hazards , 2011, ISRR.

[12]  Alexei Makarenko,et al.  Information-theoretic coordinated control of multiple sensor platforms , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[13]  Han-Lim Choi,et al.  Continuous trajectory planning of mobile sensors for informative forecasting , 2010, Autom..

[14]  Alexei Makarenko,et al.  Information based adaptive robotic exploration , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[15]  Randy A. Freeman,et al.  Decentralized Environmental Modeling by Mobile Sensor Networks , 2008, IEEE Transactions on Robotics.

[16]  Andreas Krause,et al.  Efficient Planning of Informative Paths for Multiple Robots , 2006, IJCAI.

[17]  R.M. Murray,et al.  On a decentralized active sensing strategy using mobile sensor platforms in a network , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[18]  Daniel Pérez Palomar,et al.  Representation of Mutual Information Via Input Estimates , 2007, IEEE Transactions on Information Theory.