A geometric extension design for spherical formation tracking control of second-order agents in unknown spatiotemporal flowfields

This article proposes a solution to the problem of directing multiple second-order agents sphere landing, orbit tracking and formation moving around a family of given concentric spheres in unknown spatiotemporal flowfields. The flowfields put stress on each agent’s velocity and acceleration at once, and the specification of each one is composed of three known base vectors and unknown responding coefficients. First, our pervious two-dimensional geometric extension design is extended to deal with the extension of surface in three-dimensional space. Then, two new adaptive estimators and the cooperative control law are constructed to accomplish the robust spherical formation tracking motion by using the tools of adaptive backstepping, geometric extension and consensus. The asymptotic stability of system is proved when the bidirectional communication topology is connected. The effectiveness of the analytical result is verified by numerical simulations.

[1]  Yu Zhao,et al.  Finite-time containment control without velocity and acceleration measurements , 2015 .

[2]  Manfredo P. do Carmo,et al.  Differential Geometry of Surfaces , 1994 .

[3]  Zhouhua Peng,et al.  Robust adaptive formation control of underactuated autonomous surface vehicles with uncertain dynamics , 2011 .

[4]  I. Kaminer,et al.  Coordinated Path Following Control of Multiple Wheeled Robots with Directed Communication Links , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[5]  Derek A. Paley,et al.  Multivehicle Coordination in an Estimated Time-Varying Flowfield , 2011 .

[6]  Y. Zhang,et al.  Coordinated orbit-tracking control of second-order non-linear agents with directed communication topologies , 2016, Int. J. Syst. Sci..

[7]  Fumin Zhang,et al.  Cooperative exploration of level surfaces of three dimensional scalar fields , 2011, Autom..

[8]  Derek A. Paley,et al.  Stabilization of Collective Motion in a Time-Invariant Flowfield , 2009 .

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

[10]  Yu-Ping Tian,et al.  Coordinated path following control of multi-unicycle formation motion around closed curves in a time-invariant flow , 2015, Nonlinear Dynamics.

[11]  Ahmed Rahmani,et al.  Distributed finite-time consensus tracking for nonlinear multi-agent systems with a time-varying reference state , 2016, Int. J. Syst. Sci..

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

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

[14]  Jawhar Ghommam,et al.  Coordinated Path-Following Control for a Group of Underactuated Surface Vessels , 2009, IEEE Transactions on Industrial Electronics.

[15]  James G. Bellingham.  Autonomous Ocean Sampling Networks , 2006 .

[16]  Yu-Ping Tian,et al.  Formation tracking and attitude synchronization control of underactuated ships along closed orbits , 2015 .

[17]  Tyler H. Summers,et al.  Coordinated Standoff Tracking of Moving Targets: Control Laws and Information Architectures , 2008 .

[18]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[19]  Derek A. Paley,et al.  Backstepping control design for motion coordination of self-propelled vehicles in a flowfield , 2011 .

[20]  Guangfu Ma,et al.  Distributed Coordinated Tracking With a Dynamic Leader for Multiple Euler-Lagrange Systems , 2011, IEEE Transactions on Automatic Control.

[21]  Hao Zhang,et al.  Multirate parallel distributed compensation of a cluster in wireless sensor and actor networks , 2016, Int. J. Syst. Sci..

[22]  Carlos Silvestre,et al.  Non‐linear co‐ordinated path following control of multiple wheeled robots with bidirectional communication constraints , 2007 .

[23]  Jiandong Zhu.  Synchronization of Kuramoto model in a high-dimensional linear space , 2013 .

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

[25]  Yu-Ping Tian,et al.  A curve extension design for coordinated path following control of unicycles along given convex loops , 2011, Int. J. Control.

[26]  W. H. Clohessy,et al.  Terminal Guidance System for Satellite Rendezvous , 2012 .

[27]  Zhiyong Geng,et al.  Finite-time formation control for linear multi-agent systems: A motion planning approach , 2015, Syst. Control. Lett..

[28]  Derek A. Paley,et al.  Distributed Estimation for Motion Coordination in an Unknown Spatially Varying Flowfield , 2013 .

[29]  Guanghui Wen,et al.  Distributed finite-time tracking of multiple non-identical second-order nonlinear systems with settling time estimation , 2016, Autom..

[30]  Yu Zhao,et al.  Distributed average computation for multiple time‐varying signals with output measurements , 2016 .

[31]  Timothy W. McLain,et al.  Decentralized Cooperative Aerial Surveillance Using Fixed-Wing Miniature UAVs , 2006, Proceedings of the IEEE.

[32]  Andrew G. Sparks,et al.  Spacecraft formation flying: dynamics and control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[33]  Yu Zhao,et al.  Finite‐time formation tracking control for multiple vehicles: A motion planning approach , 2016 .