Density control of multi-agent swarms via bio-inspired leader-follower plasticity

TL;DR

This paper addresses density-based control of large swarms by modeling leaders and followers with plastic transitions via a convection-diffusion-reaction PDE system on a periodic domain. The authors design a feedback velocity law and a mass-action–like reacting term that together drive the swarm density toward a target profile $\bar{\rho}$ while controlling the steady-state leader-to-follower ratio $\hat{r}$ and the fraction of plastic agents $p$. They prove existence and global stability of the desired steady state in 1D and extend to higher dimensions with isotropic interaction kernels, supported by numerical validation and an agent-based model showing qualitative agreement. The approach offers a scalable, energy-aware mechanism for self-organization with potential applications in swarm robotics and synthetic biology; limitations include reliance on full model knowledge and continuum-to-discrete transfer, guiding future work on robustness and self-assembly tasks.

Abstract

The design of control systems for the spatial self-organization of mobile agents is an open challenge across several engineering domains, including swarm robotics and synthetic biology. Here, we propose a bio-inspired leader-follower solution, which is aware of energy constraints of mobile agents and is apt to deal with large swarms. Akin to many natural systems, control objectives are formulated for the entire collective, and leaders and followers are allowed to plastically switch their role in time. We frame a density control problem, modeling the agents' population via a system of nonlinear partial differential equations. This approach allows for a compact description that inherently avoids the curse of dimensionality and improves analytical tractability. We derive analytical guarantees for the existence of desired steady-state solutions and their local stability for one-dimensional and higher-dimensional problems. We numerically validate our control methodology, offering support to the effectiveness, robustness, and versatility of our proposed bio-inspired control strategy.

Figures (4)

• Figure 1: Bimodal regulation. (a,b) Initial/final (solid black) and desired (dashed black) density of the collective. In the inset, we report the initial/final densities of leaders (solid blue), plastic followers (solid orange), and non-plastic followers (solid purple) along with the density predictions at steady state from Theorem \ref{['thch6:feasibility']} for the three populations (dashed and same color coding). (c) Time evolution of the KL divergence (top panel) and leaders' and followers' mass (bottom panel). (d) Final distribution profile of the leaders' velocity $u$ (top panel) and reacting term $q$ (bottom panel).
• Figure 2: Robustness analysis to perturbations in (a) diffusion coefficients and (b) parameters of the interaction kernels. For different values of $p$, we show $\mathcal{D}_{KL}^{ss}$ (blue) and leaders' mass (orange) at steady-state (in solid gray the predicted minimum plasticity from Theorem \ref{['thch6:feasibility']}).
• Figure 3: Agent-based bimodal regulation. (a, b) Initial/final collective densities (solid black). In the inset, discrete displacement of agents: leaders (blue), plastic followers (orange), non-plastic followers (purple), plotted on concentric circles for visualization. (c) Steady-state densities of the three populations. (d) Time evolution of KL divergence (top) and leaders' and followers' mass (bottom).
• Figure 4: 2D Mono-modal regulation. Final densities of (a) leaders', (b) plastic followers', and (c) non-plastic followers. (d) Time evolution of the KL divergence between $\rho$ and $\bar{\rho}$ (truncated to 10 time units for visualization purposes).