The Virtual Filament Model

In the present work, a framework is proposed for studying autonomous agents which interact locally yet effect a globally coherent behavior. This problem of locally induced organization is ubiquitous in decentralized multi-robot environments and …


1 A Continuum Approach to Formation Control
2 The Geometry and Calculus of Continua
2.1 Differential Geometry
2.2 The Oriented Virtual Filament
3 A Class of Virtual Filament Models
3.1 Oriented Filament Kinematics
3.2 The Lagrangian Density Formulation
3.3 Lagrange D’AlembertMechanics
3.4 The Euler-Lagrange Equations
3.5 A Comparative Analysis of Variational Calculus
4 A Virtual Filament Model with Nonholonomic Constraints
4.1 The Lagrangian Density
4.2 The Lagrangian Force
4.3 External Forcing and Constraints
4.4 The Virtual Filament Equations
4.5 The Orientation Field
4.5.1 A Elementary Orientation Field
4.5.2 A Non-trivial Orientation Field
5 Analysis and Future Directions

Author: Klemm, Sandy Lee

Source: University of Maryland

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