Autonomous rigid body attitude synchronization

This paper studies some extensions to the decentralized attitude synchronization of identical rigid bodies. Considering fully actuated Euler equations, the communication links between the rigid bodies are limited and the available information is restricted to relative orientations and angular velocities. In particular, no leader nor external reference dictates the swarm's behavior. The control laws are derived using two classical approaches of nonlinear control - tracking and energy shaping. This leads to a comparison of two corresponding methods which are currently considered for distributed synchronization - consensus and stabilization of mechanical systems with symmetries.

[1]  Naomi Ehrich Leonard,et al.  Symmetry and Reduction for Coordinated Rigid Bodies , 2006, Eur. J. Control.

[2]  Naomi Ehrich Leonard,et al.  Stable Synchronization of Mechanical System Networks , 2008, SIAM J. Control. Optim..

[3]  E. W. Justh,et al.  Natural frames and interacting particles in three dimensions , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[4]  R. Murray,et al.  Graph rigidity and distributed formation stabilization of multi-vehicle systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[5]  Jerrold E. Marsden,et al.  Stabilization of relative equilibria , 2000, IEEE Trans. Autom. Control..

[6]  J.N. Tsitsiklis,et al.  Convergence in Multiagent Coordination, Consensus, and Flocking , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[7]  Sujit S. Nair,et al.  Stabilization and synchronization of networked mechanical systems , 2006 .

[8]  Naomi Ehrich Leonard.  Stabilization of underwater vehicle dynamics with symmetry-breaking potentials , 1997 .

[9]  L. Moreau,et al.  Stability of continuous-time distributed consensus algorithms , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[10]  Hal L. Smith,et al.  Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions , 1995 .

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

[12]  D. Bertsekas,et al.  Distributed asynchronous optimal routing in data networks , 1984, The 23rd IEEE Conference on Decision and Control.

[13]  Naomi Ehrich Leonard,et al.  Group Coordination and Cooperative Control of Steered Particles in the Plane , 2006 .

[14]  F. Bullo,et al.  Coordinated deployment of mobile sensing networks with limited-range interactions , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[15]  W. Ren.  Distributed attitude consensus among multiple networked spacecraft , 2006, 2006 American Control Conference.

[16]  Naomi Ehrich Leonard,et al.  Stable synchronization of rigid body networks , 2007, Networks Heterog. Media.

[17]  Panagiotis Tsiotras,et al.  TRACKING RIGID BODY MOTION USING THRUSTERS AND MOMENTUM WHEELS , 1998 .

[18]  E. W. Justh,et al.  A Simple Control Law for UAV Formation Flying , 2002 .

[19]  K.Y. Pettersen,et al.  Leader/Follower synchronization of satellite attitude without angular velocity measurements , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[20]  P. S. Krishnaprasad,et al.  Equilibria and steering laws for planar formations , 2004, Syst. Control. Lett..

[21]  Jan Tommy Gravdahl,et al.  Coordinated Attitude Control of Satellites in Formation , 2006 .

[22]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[23]  D. Izzo,et al.  EQUILIBRIUM SHAPING: DISTRIBUTED MOTION PLANNING FOR SATELLITE SWARM , 2005 .

[24]  Jerrold E. Marsden,et al.  Stabilization of rigid body dynamics by internal and external torques , 1992, Autom..

[25]  Steven H. Strogatz,et al.  Sync: The Emerging Science of Spontaneous Order , 2003 .

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

[27]  F. Bullo.  Nonlinear control of mechanical systems : a Riemannian geometry approach , 1999 .

[28]  Maher Moakher,et al.  To appear in: SIAM J. MATRIX ANAL. APPL. MEANS AND AVERAGING IN THE GROUP OF ROTATIONS∗ , 2002 .

[29]  Naomi Ehrich Leonard,et al.  Coordinated control of networked mechanical systems with unstable dynamics , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[30]  R. Sepulchre,et al.  Collective optimization over average quantities , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[31]  Naomi Ehrich Leonard,et al.  COOPERATIVE ATTITUDE SYNCHRONIZATION IN SATELLITE SWARMS: A CONSENSUS APPROACH , 2007 .

[32]  G. Gal'perin.  A concept of the mass center of a system of material points in the constant curvature spaces , 1993 .

[33]  J.N. Tsitsiklis,et al.  Convergence Rates in Distributed Consensus and Averaging , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[34]  Naomi Ehrich Leonard,et al.  Stabilization of collective motion in three dimensions: A consensus approach , 2007, 2007 46th IEEE Conference on Decision and Control.

[35]  Naomi Ehrich Leonard,et al.  Stabilization of Planar Collective Motion With Limited Communication , 2008, IEEE Transactions on Automatic Control.

[36]  Naomi Ehrich Leonard,et al.  Stabilization of Planar Collective Motion: All-to-All Communication , 2007, IEEE Transactions on Automatic Control.

[37]  Oussama Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1986 .

[38]  Alain Sarlette,et al.  Synchronization and balancing on the N-torus , 2007, Syst. Control. Lett..

[39]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.

[40]  A. Jadbabaie,et al.  Distributed Geodesic Control Laws for Flocking of Nonholonomic Agents , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[41]  N.E. Leonard,et al.  Orientation control of multiple underwater vehicles with symmetry-breaking potentials , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[42]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

[43]  Jordan M. Berg,et al.  Almost-global tracking of simple mechanical systems on a general class of Lie Groups , 2006, IEEE Transactions on Automatic Control.

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

[45]  John N. Tsitsiklis,et al.  Problems in decentralized decision making and computation , 1984 .

[46]  Vijay Kumar,et al.  Modeling and control of formations of nonholonomic mobile robots , 2001, IEEE Trans. Robotics Autom..

[47]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

[48]  P. Oprocha.  Topological approach to chain recurrence in continuous dynamical systems , 2005 .

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

[50]  Naomi Ehrich Leonard,et al.  Stabilization of a coordinated network of rotating rigid bodies , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[51]  Alain Sarlette,et al.  Consensus Optimization on Manifolds , 2008, SIAM J. Control. Optim..

[52]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1987, SIGGRAPH.

[53]  Randal W. Beard,et al.  Synchronized multiple spacecraft rotations , 2002, Autom..

[54]  Christopher D. Hall,et al.  Decentralized Coordinated Attitude Control Within a Formation of Spacecraft , 2006 .