Cooperative Filters and Control for Cooperative Exploration

Autonomous mobile sensor networks are employed to measure large-scale environmental fields. Yet an optimal strategy for mission design addressing both the cooperative motion control and the cooperative sensing is still an open problem. We develop strategies for multiple sensor platforms to explore a noisy scalar field in the plane. Our method consists of three parts. First, we design provably convergent cooperative Kalman filters that apply to general cooperative exploration missions. Second, we present a novel method to determine the shape of the platform formation to minimize error in the estimates and design a cooperative formation control law to asymptotically achieve the optimal formation shape. Third, we use the cooperative filter estimates in a provably convergent motion control law that drives the center of the platform formation to move along level curves of the field. This control law can be replaced by control laws enabling other cooperative exploration motion, such as gradient climbing, without changing the cooperative filters and the cooperative formation control laws. Performance is demonstrated on simulated underwater platforms in simulated ocean fields.

[1]  Francesco Bullo,et al.  Optimal sensor placement and motion coordination for target tracking , 2006, Autom..

[2]  Yang Liu,et al.  Stability analysis of M-dimensional asynchronous swarms with a fixed communication topology , 2003, IEEE Trans. Autom. Control..

[3]  R. Millman,et al.  Elements of Differential Geometry , 2018, Applications of Tensor Analysis in Continuum Mechanics.

[4]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

[5]  Xiaoming Hu,et al.  A control Lyapunov function approach to multiagent coordination , 2002, IEEE Trans. Robotics Autom..

[6]  Mireille E. Broucke,et al.  Local control strategies for groups of mobile autonomous agents , 2004, IEEE Transactions on Automatic Control.

[7]  Andrea L. Bertozzi,et al.  Tracking Environmental Level Sets with Autonomous Vehicles , 2004 .

[8]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[9]  Fumin Zhang,et al.  Control of small formations using shape coordinates , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[10]  Littlejohn,et al.  Internal or shape coordinates in the n-body problem. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[11]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[12]  C. Samson Control of chained systems application to path following and time-varying point-stabilization of mobile robots , 1995, IEEE Trans. Autom. Control..

[13]  Naomi Ehrich Leonard,et al.  Control of coordinated patterns for ocean sampling , 2007, Int. J. Control.

[14]  Naomi Ehrich Leonard,et al.  Coordinated patterns of unit speed particles on a closed curve , 2007, Syst. Control. Lett..

[15]  William M. Spears,et al.  Swarms for chemical plume tracing , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[16]  R. Olfati-Saber,et al.  Distributed Kalman Filter with Embedded Consensus Filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[17]  Mani Srivastava,et al.  Overview of sensor networks , 2004 .

[18]  Naomi Ehrich Leonard,et al.  Collective Motion, Sensor Networks, and Ocean Sampling , 2007, Proceedings of the IEEE.

[19]  F. Bullo,et al.  Monitoring environmental boundaries with a robotic sensor network , 2006 .

[20]  C. Jacobi,et al.  Vorlesungen über dynamik , 1866 .

[21]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[22]  Nicholas M. Patrikalakis,et al.  Adaptive Coupled Physical and Biogeochemical Ocean Predictions: A Conceptual Basis , 2004, International Conference on Computational Science.

[23]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[24]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[25]  John Baillieul,et al.  Data-rate requirements for nonlinear Feedback control , 2004 .

[26]  C. Samson,et al.  Trajectory tracking for unicycle-type and two-steering-wheels mobile robots , 1993 .

[27]  Petter Ögren,et al.  Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment , 2004, IEEE Transactions on Automatic Control.

[28]  Andrea L. Bertozzi,et al.  Determining Environmental Boundaries: Asynchronous Communication and Physical Scales , 2005 .

[29]  G. Goodwin,et al.  Convergence properties of the Riccati difference equation in optimal filtering of nonstabilizable systems , 1984 .

[30]  H. G. Schaeffer,et al.  Book Reviews : Computer Methods for Mathematical Computations: G.E. Forsythe et al. Englewood Cliffs, NJ, Prentice-Hall, Inc., 1977 , 1979 .

[31]  R. Littlejohn,et al.  Gauge fields in the separation of rotations and internal motions in the n-body problem , 1997 .

[32]  I.I. Hussein A Kalman Filter-Based Control Strategy for Dynamic Coverage Control , 2007, 2007 American Control Conference.

[33]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[34]  Gregory J. Pottie,et al.  Wireless integrated network sensors , 2000, Commun. ACM.

[35]  Richard S. Bucy,et al.  Global Theory of the Riccati Equation , 1967, J. Comput. Syst. Sci..

[36]  Naomi Ehrich Leonard,et al.  Generating contour plots using multiple sensor platforms , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[37]  Jiwoong Park,et al.  Tip steering for fast imaging in AFM , 2005, Proceedings of the 2005, American Control Conference, 2005..

[38]  Deborah Estrin,et al.  Guest Editors' Introduction: Overview of Sensor Networks , 2004, Computer.

[39]  A. E. Bryson,et al.  Estimation using sampled data containing sequentially correlated noise. , 1967 .

[40]  R. E. Kalman,et al.  When Is a Linear Control System Optimal , 1964 .

[41]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[42]  S. Martinez Distributed representation of spatial fields through an adaptive interpolation scheme , 2007, 2007 American Control Conference.

[43]  A. Bicchi,et al.  Path-following with a bounded-curvature vehicle: a hybrid control approach , 2005 .

[44]  Jerrold E. Marsden,et al.  Foundations of Mechanics: 2nd Edition , 1980 .

[45]  Edward Belbruno Book Review: CAPTURE DYNAMICS AND CHAOTIC MOTIONS IN CELESTIAL MECHANICS / Princeton University Press , 2004 .

[46]  R. Olfati-Saber,et al.  Consensus Filters for Sensor Networks and Distributed Sensor Fusion , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[47]  R. Fierro,et al.  Cooperative hybrid control of robotic sensors for perimeter detection and tracking , 2005, Proceedings of the 2005, American Control Conference, 2005..

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

[49]  Ralph Abraham,et al.  Foundations Of Mechanics , 2019 .

[50]  Naomi Ehrich Leonard,et al.  Exploring scalar fields using multiple sensor platforms: Tracking level curves , 2007, 2007 46th IEEE Conference on Decision and Control.

[51]  A. Jazwinski Stochastic Processes and Filtering Theory , 1970 .

[52]  Naomi Ehrich Leonard,et al.  Preparing to predict: The Second Autonomous Ocean Sampling Network (AOSN-II) experiment in the Monterey Bay , 2009 .

[53]  B. Anderson,et al.  Detectability and Stabilizability of Time-Varying Discrete-Time Linear Systems , 1981 .

[54]  R.M. Murray,et al.  Experimental validation of an algorithm for cooperative boundary tracking , 2005, Proceedings of the 2005, American Control Conference, 2005..

[55]  W. Hager,et al.  Convergence and Stability Properties of the Discrete Riccati Operator Equation and the Associated Optimal Control and Filtering Problems , 1976 .

[56]  M. Ani Hsieh,et al.  Pattern generation with multiple robots , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[57]  Uwe R. Zimmer,et al.  Control of Open Contour Formations of Autonomous Underwater Vehicles , 2005 .

[58]  Eric W. Justh,et al.  Boundary following using gyroscopic control , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[59]  Randy A. Freeman,et al.  Distributed Cooperative Active Sensing Using Consensus Filters , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.