Distributed finite-time attitude containment control of multi-rigid-body systems

Abstract In this paper, we study the distributed finite-time attitude containment control problem for multi-rigid-body systems with multiple stationary and dynamic leaders under directed graphs. Based upon two sliding mode observation vectors, the input torque is designed to achieve the control goal. In the regulation case, all the followers will converge into the attitude convex hull spanned by the leaders in finite time, while in the dynamic leaders case, not only the attitudes but also the attitude derivatives of the followers will converge into the convex hull of the leaders in finite time. Necessary and sufficient criteria are established for both the two protocols. Finally, all the theoretical results are illustrated by numerical simulations.

[1]  Ziyang Meng,et al.  Distributed Containment Control for Multiple Autonomous Vehicles With Double-Integrator Dynamics: Algorithms and Experiments , 2011, IEEE Transactions on Control Systems Technology.

[2]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[3]  Wang Feng.  Distributed attitude cooperative control with multiple leaders , 2013 .

[4]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[5]  Magnus Egerstedt,et al.  Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks , 2012, Autom..

[6]  Magnus Egerstedt,et al.  Containment in leader-follower networks with switching communication topologies , 2011, Autom..

[7]  Yiguang Hong,et al.  Target containment control of multi-agent systems with random switching interconnection topologies , 2012, Autom..

[8]  Riccardo Scattolini,et al.  A hybrid model predictive control scheme for containment and distributed sensing in multi-agent systems , 2013, Syst. Control. Lett..

[9]  Ziyang Meng,et al.  Distributed finite-time attitude containment control for multiple rigid bodies , 2010, Autom..

[10]  Panagiotis Tsiotras.  Further passivity results for the attitude control problem , 1998, IEEE Trans. Autom. Control..

[11]  Guangfu Ma,et al.  Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph , 2012, Autom..

[12]  P. Olver.  Nonlinear Systems , 2013 .

[13]  Guangming Xie,et al.  Necessary and sufficient conditions for containment control of networked multi-agent systems , 2012, Autom..

[14]  P.R. Lawson.  The Terrestrial Planet Finder , 2001, 2001 IEEE Aerospace Conference Proceedings (Cat. No.01TH8542).

[15]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[16]  Shengyuan Xu,et al.  Distributed Containment Control with Multiple Dynamic Leaders for Double-Integrator Dynamics Using Only Position Measurements , 2012, IEEE Transactions on Automatic Control.

[17]  J. Wen,et al.  Robust attitude stabilization of spacecraft using nonlinear quaternion feedback , 1995, IEEE Trans. Autom. Control..

[18]  Shihua Li,et al.  Finite-Time Attitude Tracking Control of Spacecraft With Application to Attitude Synchronization , 2011, IEEE Transactions on Automatic Control.

[19]  Wei Kang,et al.  Co-ordinated attitude control of multi-satellite systems† , 2002 .

[20]  Steven P. Neeck,et al.  NASA's small satellite missions for Earth observation , 2005 .

[21]  P. Tsiotras.  Stabilization and optimality results for the attitude control problem , 1996 .

[22]  Giancarlo Ferrari-Trecate,et al.  Containment Control in Mobile Networks , 2008, IEEE Transactions on Automatic Control.

[23]  Dimos V. Dimarogonas,et al.  Leader-follower cooperative attitude control of multiple rigid bodies , 2008, ACC.

[24]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[25]  Yiguang Hong,et al.  Adaptive finite-time control of nonlinear systems with parametric uncertainty , 2006, IEEE Transactions on Automatic Control.

[26]  M. Shuster.  A survey of attitude representation , 1993 .

[27]  John Bristow,et al.  NASA's Autonomous Formation Flying Technology Demonstration, Earth Observing-1(EO-1) , 2002 .

[28]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.