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Geometric decompositions of collective motion
Matteo Mischiati1,2,3, P S Krishnaprasad1,2
1Institute for Systems Research, University of Maryland, College Park, MD 20742, USA.
Proceedings. Mathematical, Physical, and Engineering Sciences
|May 10, 2017
Summary
We present a novel geometric method to analyze collective motion by decomposing movement into kinematic modes. This approach quantizes group behaviors, offering insights into natural systems like pigeon flocks and potential applications in robotics.
Area of Science:
- Physics
- Mathematics
- Biology
Background:
- Collective motion is a widespread phenomenon in nature with significant biological and theoretical implications.
- Understanding the mechanisms driving collective motion requires advanced analytical techniques.
Purpose of the Study:
- To introduce a novel geometric framework for analyzing collective motion.
- To develop a method for decomposing complex movements into fundamental kinematic modes.
Main Methods:
- Representing collective motion as tangent vectors on configuration space.
- Utilizing fibre bundle geometry and connections to decompose motion into orthogonal components.
- Integrating with shape space construction to categorize kinematic modes.
Main Results:
- A novel decomposition of collective motion into kinematic modes: rigid translations, rotations, inertia tensor transformations, expansions, and compressions.
- Quantitative measures derived from kinetic energy fractions to characterize collective behavior.
- Successful application to analyze pigeon flocking behavior.
Conclusions:
- The geometric framework provides a powerful tool for analyzing and quantifying collective motion in natural systems.
- This method offers potential for understanding the driving goals of collectives and for controlling artificial systems of interacting agents.
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