Title :
Steering laws and continuum models for planar formations
Author :
Justh, E.W. ; Krishnaprasad, P.S.
Author_Institution :
Inst. for Syst. Res., Maryland Univ., College Park, MD, USA
Abstract :
We consider a Lie group formulation for the problem of control of formations. Vehicle trajectories are described using the planar Frenet-Serret equations of motion, which capture the evolution of both vehicle position and orientation for unit-speed motion subject to curvature (steering) control. The Lie group structure can be exploited to determine the set of all possible (relative) equilibria for arbitrary G-invariant curvature controls, where G=SE(2) is a symmetry group for the control law. The main result is a convergence result for n vehicles (for finite n), using a Lyapunov function which for n=2, has been previously shown to yield global convergence. A continuum formulation of the basic equations is also presented.
Keywords :
Lie groups; Lyapunov methods; convergence; numerical analysis; stability; vehicles; Lie group formulation; Lyapunov function; arbitrary G-invariant curvature control; continuum formulation; convergence; numerical simulation; planar Frenet-Serret equations of motion; steering control; steering laws; vehicle trajectories; Biological system modeling; Control systems; Convergence; Educational institutions; Equations; Evolution (biology); Lyapunov method; Motion control; Unmanned aerial vehicles; Vehicle dynamics;
Conference_Titel :
Decision and Control, 2003. Proceedings. 42nd IEEE Conference on
Print_ISBN :
0-7803-7924-1
DOI :
10.1109/CDC.2003.1271708