Collective Motion, Applications of Dynamical Systems to Formation Control

Carl's Trident project is focused on the study of dynamical systems and their asymptotic behavior, and is motivated by applications to the control theory of autonomous multi-agent systems such as swarms of UAVs. The goal of the project is to design a new class of controllers for pattern formation that would rely on asymptotic properties of dynamical systems. This project is mostly of mathematical nature, but it has a significant experimental component. The algorithms are implemented and tested in GazeboSim, a high fidelity physics robotics simulator.

• Trident Report: Download pdf

• Trident Presentation (slides): Download pdf

Path Planning and Obstacle Avoidance

Examples below use harmonic functions for obstacle avoidance and path planning for robots in a room. The figures show surfaces of harmonic functions. The robots follow the negative gradient of these surfaces.

Controlling swarms in gazebo world from wolfram mathematica

Swarm Dynamics on Manifolds

The following videos show simulations of swarms whose dynamics is governed by the parabolic model r_i''=(1-|r_i'|^2)r_i'-(r_i-R) adjusted to reflect the geometry of the surface of interest. In this model, R represents the center of mass of the system. We simulated swarms on the hyperbolic plane (1st video), sphere (2nd video) and the Euclidean plane with an "oval" metric (3rd video).