This project branches off the multi-agent simulator to explore learning and control of swarms in lower dimensional space (hypospace). Specifically, we stabilize an arbitrary number of agents in 3D indirectly through a 2D embedding space. This is possible through the construction of homeomorphic polar curves defined in the article "Emergent homeomorphic curves in swarms" published in the journal Automatica (2025). Homeomorphic polar curves are continuous, closed, and differentiable curves produced by deforming a circle. Examples are provided in the twisted circle repository. We focus on the lemniscate of Gerono as studied previously in "Flocks, Mobs, and Figure Eights: Swarming as a Lemniscatic Arc" published in IEEE Transactions on Network Science and Engineering (2023).
The benefit of this embedding space is that it permits the application of linear control policies in reduced dimensions while preserving all of the functional properties of the swarm.
We extend previous work by applying reinforcement learning (RL) to control the orientation of the swarm. This is accomplished using Continuous Action Learning Automata to learn the optimal azimuth and altitude angle of the embedding plane. In this implementation, collective learning is coordinated by a randomly-selected leader agent. This is meant as a proof-of-concept for future work that will explore distributed learning strategies.
Below are initial results showing the swarm successfully learns the orientation of the embedding plane in order align the center of mass with a target.
The code is opensource but, if you reference this work in your own research, please cite me. I have provided an example bibtex citation below:
@techreport{Jardine-2025, title={Learning and Control of Swarms in Reduced Dimensions}, author={Jardine, P.T.}, year={2025}, institution={Queen's University, Kingston, Ontario}, type={GitHub Repository}, }
Alternatively, you can cite any of my related papers, which are listed in Google Scholar.