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1. Heterogeneous response intensity ranges and response probability improve goal achievement in multi-agent systems

   Mathias, H. David; Wu, Annie S.; Ruetten, Laik (January 2020, Proceedings of the 12th International Conference on Swarm Intelligence)

   null (Ed.)

   Inter-agent variation is well-known in both the biology and computer science communities as a mechanism for improving task selection and swarm performance for multi-agent systems. Response threshold variation, the most commonly used form of inter-agent variation, desynchronizes agent actions allowing for more targeted agent activation. Recent research using a less common form of variation, termed dynamic response intensity, demonstrates that modeling levels of agent experience or varying physical attributes and using these to allow some agents to perform tasks more efficiently or vigorously, significantly improves swarm goal achievement when used in conjunction with response thresholds. Dynamic intensity values vary within a fixed range as agents activate for tasks. We extend previous work by demonstrating that adding another layer of variation to response intensity, in the form of heterogeneous ranges for response intensity values, provides significant performance improvements when response is probabilistic. Heterogeneous intensity ranges break the coupling that occurs between response thresh- olds and response intensities when the intensity range is homogeneous. The decoupling allows for increased diversity in agent behavior. 

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2. Analysis of Evolved Response Thresholds for Decentralized Dynamic Task Allocation

   https://doi.org/10.1145/3530821  

   Mathias, H. David; Wu, Annie S.; Dang, Daniel (June 2022, ACM Transactions on Evolutionary Learning and Optimization)

   In this work, we investigate the application of a multi-objective genetic algorithm to the problem of task allocation in a self-organizing, decentralized, threshold-based swarm. We use a multi-objective genetic algorithm to evolve response thresholds for a simulated swarm engaged in dynamic task allocation problems: two-dimensional and three-dimensional collective tracking. We show that evolved thresholds not only outperform uniformly distributed thresholds and dynamic thresholds but achieve nearly optimal performance on a variety of tracking problem instances (target paths). More importantly, we demonstrate that thresholds evolved for some problem instances generalize to all other problem instances, eliminating the need to evolve new thresholds for each problem instance to be solved. We analyze the properties that allow these paths to serve as universal training instances and show that they are quite natural. After a priori evolution, the response thresholds in our system are static. The problem instances solved by the swarms are highly dynamic, with schedules of task demands that change over time with significant differences in rate and magnitude of change. That the swarm is able to achieve nearly optimal results refutes the common assumption that a swarm must be dynamic to perform well in a dynamic environment. 

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3. Response thresholds generalize across problem instances for a deterministic response multiagent system

   Mathias, H. David; Wu, Annie S.; and Dang, Daniel (January 2021, Proceedings of the Genetic and Evolutionary Computation Conference)

   null (Ed.)

   In this work, we use a multiobjective genetic algorithm to evolve agent response thresholds for a decentralized swarm and demonstrate that swarms with evolved thresholds outperform swarms with thresholds set using other methods. In addition, we provide evidence that the effectiveness of evolved thresholds is due in part to the evolutionary process being able to find, not just good distributions of thresholds for a given task across all agents, but also good combinations of thresholds over all tasks for individual agents. Finally, we show that thresholds evolved for some problem instances can effectively generalize to other problem instances with very different task demands. 

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4. 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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5. Density Stabilization Strategies for Nonholonomic Agents on Compact Manifolds

   https://doi.org/10.1109/tac.2023.3326060  

   Elamvazhuthi, Karthik; Berman, Spring (March 2024, IEEE Transactions on Automatic Control)

   In this article, we consider the problem of stabilizing a class of degenerate stochastic processes, which are constrained to a bounded Euclidean domain or a compact smooth manifold, to a given target probability density. This stabilization problem arises in the field of swarm robotics, for example, in applications where a swarm of robots is required to cover an area according to a target probability density. Most existing works on modeling and control of robotic swarms that use partial differential equation (PDE) models assume that the robots' dynamics are holonomic and, hence, the associated stochastic processes have generators that are elliptic. We relax this assumption on the ellipticity of the generator of the stochastic processes, and consider the more practical case of the stabilization problem for a swarm of agents whose dynamics are given by a controllable driftless control-affine system. We construct state-feedback control laws that exponentially stabilize a swarm of nonholonomic agents to a target probability density that is sufficiently regular. State-feedback laws can stabilize a swarm only to target probability densities that are positive everywhere. To stabilize the swarm to probability densities that possibly have disconnected supports, we introduce a semilinear PDE model of a collection of interacting agents governed by a hybrid switching diffusion process. The interaction between the agents is modeled using a (mean-field) feedback law that is a function of the local density of the swarm, with the switching parameters as the control inputs. We show that under the action of this feedback law, the semilinear PDE system is globally asymptotically stable about the given target probability density. The stabilization strategies with and without agent interactions are verified numerically for agents that evolve according to the Brockett integrator; the strategy with interactions is additionally verified for agents that evolve according to an underactuated s... 

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