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1. Density-Driven Multi-Agent Swarm Control with Potential Field Based Collision Avoidance

   https://doi.org/10.1109/UEMCON59035.2023.10316140  

   Seo, Sungjun; Lee, Kooktae (October 2023, IEEE)

   In this paper, a density-driven multi-agent swarm control problem is investigated. Robot swarms can provide a great benefit, especially for applications where a single robot cannot effectively achieve a given task. For large spatial-scale applications such as search and rescue, environmental monitoring, and surveillance, a new multi-agent swarm control strategy is necessary because of physical constraints including a robot number and operation time. This paper provides a novel density-driven swarm control strategy for multi-agent systems based on the Optimal Transport theory, to cover a spacious domain with limited resources. In such a scenario, \textit{efficiency} will likely be a key point in achieving an efficient robot swarm behavior rather than uniform coverage that might be infeasible. With the given reference density, pre-constructed from available information, the proposed swarm control method will drive the multi-agent system such that their time-averaged behavior becomes similar to the reference density. In this way, density-driven swarm control will enable the multiple agents to spend most of their time on high-priority regions that are reflected in the reference density, leading to efficiency. To protect the agents from collisions, the Artificial Potential Field method is employed and combined with the proposed density-driven swarm control scheme. Simulations are conducted to validate density-driven swarm control as well as to test collision avoidance. Also, the swarm performance is analyzed by varying the agent number in the simulation. 

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2. Inferring bifurcation diagrams with transformers

   https://doi.org/10.1063/5.0204714  

   Zhornyak, Lyra; Hsieh, M Ani; Forgoston, Eric (May 2024, Chaos: An Interdisciplinary Journal of Nonlinear Science)

   The construction of bifurcation diagrams is an essential component of understanding nonlinear dynamical systems. The task can be challenging when one knows the equations of the dynamical system and becomes much more difficult if only the underlying data associated with the system are available. In this work, we present a transformer-based method to directly estimate the bifurcation diagram using only noisy data associated with an arbitrary dynamical system. By splitting a bifurcation diagram into segments at bifurcation points, the transformer is trained to simultaneously predict how many segments are present and to minimize the loss with respect to the predicted position, shape, and asymptotic stability of each predicted segment. The trained model is shown, both quantitatively and qualitatively, to reliably estimate the structure of the bifurcation diagram for arbitrarily generated one- and two-dimensional systems experiencing a codimension-one bifurcation with as few as 30 trajectories. We show that the method is robust to noise in both the state variable and the system parameter. 

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3. Constructing continuous multi-behavioral planar systems through motivation dynamics and bifurcations

   https://doi.org/10.1109/CDC45484.2021.9683759  

   Baxevani, Kleio; Tanner, Herbert G. (January 2021, 60th IEEE Conference on Decision and Control)

   This paper offers new analytical conditions on the system parameters of a particular class of planar dynamical systems which would allow them to undergo a Hopf bifurcation. These systems are constructed as a means of generating multiple behaviors from the same single continuous dynamical system model, without resorting to switching between distinct component continuous dynamics associated to each behavioral mode. This work builds on recent advances which introduced motivation dynamics as an efficient way to design multi-behavioral systems. The contribution of this paper is that it expands the scope of the motivation dynamics approach, and offers explicit analytic conditions on the system parameters to guarantee the existence of bifurcations, which can then be utilized to better engineer the structure and location of the resulting equilibria. Numerical simulations confirm the theoretical predictions for the onset of the Hopf bifurcations. 

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4. CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems

   https://doi.org/10.1145/3580305.3599272  

   Jiang, Song; Huang, Zijie; Luo, Xiao; Sun, Yizhou (August 2023, KDD’23: Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining)

   Multi-agent dynamical systems refer to scenarios where multiple units (aka agents) interact with each other and evolve collectively over time. For instance, people’s health conditions are mutually influenced. Receiving vaccinations not only strengthens the longterm health status of one unit but also provides protection for those in their immediate surroundings. To make informed decisions in multi-agent dynamical systems, such as determining the optimal vaccine distribution plan, it is essential for decision-makers to estimate the continuous-time counterfactual outcomes. However, existing studies of causal inference over time rely on the assumption that units are mutually independent, which is not valid for multi-agent dynamical systems. In this paper, we aim to bridge this gap and study how to estimate counterfactual outcomes in multi-agent dynamical systems. Causal inference in a multi-agent dynamical system has unique challenges: 1) Confounders are timevarying and are present in both individual unit covariates and those of other units; 2) Units are affected by not only their own but also others’ treatments; 3) The treatments are naturally dynamic, such as receiving vaccines and boosters in a seasonal manner. To this end, we model a multi-agent dynamical system as a graph and propose a novel model called CF-GODE (CounterFactual Graph Ordinary Differential Equations). CF-GODE is a causal model that estimates continuous-time counterfactual outcomes in the presence of inter-dependencies between units. To facilitate continuous-time estimation,we propose Treatment-Induced GraphODE, a novel ordinary differential equation based on graph neural networks (GNNs), which can incorporate dynamical treatments as additional inputs to predict potential outcomes over time. To remove confounding bias, we propose two domain adversarial learning based objectives that learn balanced continuous representation trajectories, which are not predictive of treatments and interference. We further provide theoretical justification to prove their effectiveness. Experiments on two semi-synthetic datasets confirm that CF-GODE outperforms baselines on counterfactual estimation. We also provide extensive analyses to understand how our model works. 

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5. Decentralized swarm desynchronization via inter-agent variation for logistic resupply

   Giordano, Joseph P.; Wu, Annie S.; Pherwani, Arjun; Mathias, H. David (January 2021, Proceedings of the 34th Florida Artificial Intelligence Research Society Conference)

   null (Ed.)

   Decentralized computational swarms have been used to simulate the workings of insect colonies or hives, often utilizing a response threshold model which underlies agent interaction with dynamic environmental stimuli. Here, we propose a logistics resupply problem in which agents must select from multiple incoming scheduled tasks that generate competing resource demands for workers. This work diverges from previous attempts toward analyzing swarm behaviors by examining relative amounts of stress placed on a multi-agent system in conjunction with two mechanisms of response: variable threshold distribution, or duration level. Further, we demonstrate changes to the general swarm performance’s dependence on paired desynchronization type and schedule design, as the result of varied swarm conditions. 

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