Distributed Swarm Morphogenesis with Neural Cellular Automata

Ray Verma; Eliseo Ferrante; Anthony Tzes

cs.ROOct 22, 2026

Distributed Swarm Morphogenesis with Neural Cellular Automata

Authors: Ray Verma, Eliseo Ferrante, Anthony Tzes

Organizations: Department of Computer Science, New York University Abu Dhabi United Arab Emirates · Department of Electrical Engineering, New York University Abu Dhabi, United Arab Emirates

Abstract

Swarm morphogenesis requires robots to assemble desired shapes through local interactions. We present a modular framework integrating neural cellular automata (NCA) with existing site assignment and collision-aware control. Within this framework, we introduce a decentralized attachment-site discovery mechanism. Robots already in the formation update and share local NCA states to identify new attachment sites, enabling progressive growth without a predefined list of sites during deployment. To bridge the mismatch between conventional NCA growth and gradual physical assembly, we additionally propose offline sparse-retention fine-tuning that simulates partial attachment, together with a false-positive loss that penalizes invalid site activations. Simulations demonstrate formation of diverse lattice morphologies, scaling to several hundred robots, and substantial improvements in morphology accuracy from the proposed fine-tuning. Experiments with Crazyflie quadrotors validate the integrated execution pipeline using robot-relative observations reconstructed from external tracking.

Figures & tables

Fig. 1: Swarm Morphogenesis over time. At each step $t_{k}$ , Advertisers maintain local NCA state around their occupied symbolic cells, refresh a $5\times 5$ neighborhood patch from observed attached neighbors, apply an NCA update, and advertise neighbouring unoccupied foreground cells as candidate attachment sites. Joiners can then occupy these advertised cells and become Advertisers, so the set of attached cells grows progressively toward the desired morphology.

Fig. 2: Formation progression and scalability. Left: representative assembly sequences for four desired morphologies using $250$ robots at $0\%$ , $30\%$ , $60\%$ , and $100\%$ progression, with reference images and corresponding F1 accuracy trajectories over time. Right: saturation time and final F1 versus robot count for Tree morphology; shaded regions denote one standard deviation.

Parameter	Value
State channels $C$	$16$
Foreground threshold $\theta_{\alpha}$	$0.5$
Training Rollout horizon $H$	$[64,96)$ steps
False-activation threshold $\tau_{\mathrm{fp}}$	$0.2$
Loss weights $(\lambda_{\mathrm{FP}},\lambda_{\mathrm{RGBA}})$	$(2.0,4.0)$
Lattice spacing $\ell_{\mathrm{space}}$	$0.5$

TABLE I: Parameters for offline training and simulated deployment.

Fig. 3: Real-robot experiments with eight Crazyflie quadrotors. Top: overhead snapshots during formation of E and 4 . Bottom: corresponding lattice-state visualizations, with gray and red circles denoting Joiners and Advertisers respectively, and colored cells indicating foreground morphology sites.

Training configuration	$F_{1}(t_{\mathrm{sat}})\uparrow$	Std.
Standard Growing NCA	$0.583$	$0.107$
+ Sparse-retention fine-tuning	$0.764$	$0.141$
+ False-positive loss	$\mathbf{0.988}$	$\mathbf{0.004}$

TABLE II: Fine-tuning ablation.

Swarm Robotics

Swarm robotics studies how groups of robots coordinate through local sensing, communication, and interaction to accomplish shared tasks.

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BraiNCA: brain-inspired neural cellular automata and applications to morphogenesis and motor control

Léo Pio-Lopez, Benedikt Hartl, Michael Levin

Allen Discovery Center at Tufts University, Medford, MA, USA · Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA, USA

Neural Cellular Automata Neural Network Robustness

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Most of the Neural Cellular Automata (NCAs) defined in the literature have a common theme: they are based on regular grids with a Moore neighborhood (one-hop neighbour). They do not take into account long-range connections and more complex topologies as we can find in the brain. In this paper, we introduce BraiNCA, a brain-inspired NCA with an attention layer, long-range connections and complex topology. BraiNCAs shows better results in terms of robustness and speed of learning on the two tasks compared to Vanilla NCAs establishing that incorporating attention-based message selection together with explicit long-range edges can yield more sample-efficient and damage-tolerant self-organization than purely local, grid-based update rules. These results support the hypothesis that, for tasks requiring distributed coordination over extended spatial and temporal scales, the choice of interaction topology and the ability to dynamically route information will impact the robustness and speed of learning of an NCA. More broadly, BraiNCA provides brain-inspired NCA formulation that preserves the decentralized local update principle while better reflecting non-local connectivity patterns, making it a promising substrate for studying collective computation under biologically-realistic network structure and evolving cognitive substrates.

Abstract

Swarm Robotics

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