Symmetry and reduction for coordinated rigid bodies

European Journal of Control

Volumn 12, Issue 2, 2006, Pages 176-194

  Hanßmann, Heinz ^a   Leonard, Naomi Ehrich ^b   Smith, Troy R ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b Princeton University   (United States)

Author keywords

Coordinated control; Hamiltonian systems; Multi body dynamics; Reduction; Rigid bodies; Stability

Indexed keywords

AUTONOMOUS AGENTS; HAMILTONIANS; NETWORKED CONTROL SYSTEMS; RIGID STRUCTURES;

% REDUCTIONS; CO-ORDINATED CONTROL; COLLECTIVE BEHAVIOUR; CONTROL INPUTS; COORDINATED CONTROL; HAMILTONIAN SYSTEMS; MULTIBODY DYNAMIC (MBD); NETWORKED SYSTEMS; RELATIVE POSITIONS; RIGID BODY;

AUTOMOBILE BODIES;

EID: 39549090024     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.3166/ejc.12.176-194     Document Type: Article

References (20)

1. Bullo F. Nonlinear control of mechanical systems: a Riemannian geometry approach, PhD Thesis, California Institute of Technology,2001
2. Holmes PH, Jenkins J, Leonard NE. Dynamics of the Kirchhoff equations I: coincident centers of gravity and buoyancy. Physica D 1998; 118: 311-342
3. Jadbabaie A, Lin J, Morse AS. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom Control 2003; 48: 988-1001
4. Justh E, Krishnaprasad PS. Steering laws and continuum models for planar formations. In: Proceedings of the 42nd IEEE conference on decision and control, pp. 3609-3614, 2003
5. Leonard NE. Stability of a bottom-heavy underwater vehicle. Automatica 1997: 33(3): 331-346
6. Leonard NE. Stabilization of underwater vehicle dynamics with symmetry-breaking potentials. Syst Control Lett 1997: 32, 35-42
7. Leonard NE, Fiorelli E. Virtual leaders, artificial potentials and coordinated control of groups. In: Proceedings of the 40th IEEE conference on decision and control, pp. 2968-2973, 2001
8. Marsden JE, Ratiu T. Introduction to mechanics and symmetry. 2nd edn. Springer-Verlag, New York, NY
9. Marsden JE, Ratiu T, Weinstein A. Semidirect products and reduction in mechanics. Trans Am Math Soc 1984; 281(1): 147-177
10. McInnes CR. Potential function methods for autonomous spacecraft guidance and control. Adv. Astronautical Sci. 1996: 90: 2093-2109
11. Murray RM, Li Z, Sastry SS. A mathematical introduction to robotic manipulation, CRC Press, Boca Raton, FL,1994
12. Nair S, Leonard NE, Moreau L. Coordinated control of networked mechanical systems with unstable dynamics. In: Proceedings of the 42nd IEEE conference on decision and control, 2003, 550-555
13. Nair S, Leonard NE. Stabilization of a coordinated network of rotating rigid bodies. In: Proceedings of the 43rd IEEE conference on decision and control. 4690-4695
14. Okubo A. Dynamical aspects of animal grouping: swarms, flocks, schools and herds. Adv Biophy 1985; 22: 1-94
15. Olfati-Saber R. Nonlinear control of under actuated mechanical systems with application to robotics and aerospace vehicles, PhD Thesis, Massachusetts Institute of Technology, 2001
16. Partridge BL. The structure and function of fish schools. Scientific Am 1982; June: 114-123
17. Sastry S. Nonlinear systems: analysis, stability and control, Springer-Verlag, New York, NY,1999
18. th IEEE conference on decision and control. 2001; pp. 4598-4603
19. Toner J, Tu Y. Flocks, herds and schools: A quantitative theory of flocking, Phys Rev E 1998; 58(4): 4828-4858
20. th IEEE conference on decision and control. 1999; 2527-2532