Research

Arboria studies decentralized coordination under real communication constraints — communication delay, finite bandwidth, energy per bit, packet loss, and replica reconciliation — at agent counts where centralized coordination is not an option. That constraint set is the thread through everything below, and it is not what mainstream swarm and multi-agent reinforcement learning work models: the standard assumption is that an agent can see its neighbours now.

Delay-coordination

Four measured results, each derived from committed experiment records and scoped, deliberately, as algorithmic claims about coordination primitives in a simplified three-dimensional kinematic simulator — not as validation of physical hardware. Read in order, they answer four successive questions: where does coordination break, can an agent see around the break, what exactly is breaking, and relative to what is the break measured.

Phase Diagram of Decentralized Coordination Under Communication Delay

maps coordination quality across a 900-cell grid of primitive × task × delay × swarm size. Quality collapses through a boundary near 10–20 steps of delay. Two things about that collapse are surprising: it is primitive-independent — gossip, flocking, and CRDT-intent propagation all fall together — and it is invariant in swarm size across N ∈ 2000. What distinguishes the curves is whether an agent communicates at all, not how. The simulator is anchored against the Vicsek  order–disorder transition before any coordination number is trusted.

Anticipatory Coordination via Peer-State Prediction Under Communication Delay

asks whether an agent can recover what delay took from it by predicting where its peers have gone. It can, and cheaply: constant-velocity extrapolation of the stale peer view restores coordination quality to 0.66 at a delay where the unaided swarm scores 0.00. The ranking — constant-velocity ≳ linear > Kalman  > none — is itself the result. Sophisticated filtering loses to the simplest possible model, because bounded actuation keeps trajectories nearly linear over the prediction horizon and the Kalman filter’s priors add variance it never earns back.

Freshness or Throughput? Coordination Under Lossy Communication Depends on Staleness, Not Delivered Rate

separates the two ways a real link degrades — messages arriving late and messages not arriving at all — and asks which one coordination actually tracks. Only one does. Sweeping packet loss from every link delivered down to roughly one in fifty surviving, against delay, coordination quality moves by less than 0.012 at fixed delay while the same quality falls fivefold along the delay axis. At zero delay and 99% loss, coordination is still perfect. The loss curves collapse onto a single staleness curve: delivered rate and coordination quality are causally decoupled. The engineering reading is that link capacity is the wrong thing to buy — for peer-derived-target tasks, coordination is bought with latency.

Delay Relative to What? The Coordination Cliff Scales with the Task Timescale

fixes the yardstick. A cliff at “10–20 steps” is not yet a physical statement: twenty steps is fatal to a task that changes every ten and irrelevant to one that changes every thousand. Imposing an external task timescale — a goal that jumps on a fixed clock, visible to only a 15% informed minority, so the rest must acquire it through the delayed peer graph — the collapse delay moves with that clock, holding a constant ratio of about 0.047 while the task is the binding timescale. Past that, it saturates: the swarm’s own convergence time becomes the shorter timescale and the intrinsic cliff of the phase diagram reappears. Together the two results pin the boundary to delay over the shorter of the two timescales. A fully-informed control is delay-insensitive, which is what shows the cliff to be a coordination effect rather than an artifact of tracking a moving target.

Market-based coordination

Energy-Aware Hierarchical Markets: Decentralized Auctions for Autonomous Lunar Construction

is our fifth measured result, and the bridge to the orbital work below. A decentralized energy-aware auction schedules macro–micro robotic fleets for lunar construction, measured against an OR-Tools  central planner and a first-come baseline over 20 seeds per cell.

The market’s advantage is real, large, and confined to scarcity — and outside scarcity it is a measurable liability. Where hauling capacity is genuinely scarce, the auction raises printed mass by 34% over first-come and matches the central planner. One rung up the capacity ladder the effect is a null. One rung further, with haulers over-provisioned, the market is 11% worse than the naive baseline — significantly so.

Orbital compute

A compute constellation lives past the coordination boundary — but on contact-wait, not light-lag. Its nodes are microseconds apart at the speed of light and minutes apart in practice, because a message waits for a link to exist before it can travel. Measured on a realistic Walker constellation, the mean end-to-end delay is 140 seconds, 99.95% of it waiting. That is squarely past the 10–20-step boundary we measure in simulation, which makes the delay-coordination result directly applicable to orbital compute — the emerging class of systems that put datacenter hardware in orbit to run on uninterrupted solar power and radiate heat to vacuum.

Our programme there builds a constellation digital twin and a decentralized, energy-aware scheduler for orbital workloads: real orbit propagation, inter- satellite link visibility and range, eclipse geometry, and time-expanded contact plans, with coordination running over the contact graph rather than over an assumed always-on network. The near-term work is decentralized energy-aware scheduling under eclipse and link loss; the durable contribution is the benchmark itself.

Other work

Two earlier papers, each documenting an implemented mechanism — one in delay-tolerant intent propagation, one in large-scale phase transitions. Both predate the measurement discipline described under Practice below, and we are explicit about what that costs them: their mechanisms are real and implemented, but their result tables are illustrative rather than measured against a committed batch. Cite them for what they build, not for what they report. Both are being folded into the constellation benchmark, which is where their numbers will be earned back.

ICCD: CRDT-Based Intent Propagation over Contact-Plan DTN for Million-Agent Swarms at Hour-Scale Light Delay

is the delay-tolerance mechanism the rest of the stack inherits. Where the delay papers ask what a stale peer view does to coordination, ICCD asks the prior question: how does an agent get a peer view at all when there is no standing network to carry one. Mission intent — goal, constraints, a compact summary — is encoded as a conflict-free replicated data type  and disseminated over a delay-tolerant  contact plan, so replicas that were partitioned for hours reconcile on contact without a central arbiter and without a consensus round. Bundles are prioritized by freshness bought per joule, and relay duty rotates on remaining energy, so the scheme degrades by slowing rather than by partitioning permanently. The paper scopes itself to intra-cluster coordination, with inter-cluster intent flow carried by sparse high-power relays inside the contact plan — a boundary worth noting, because it is exactly the boundary an inter-satellite-link constellation lives on. That is the direct line from this paper to our orbital routing work, and its composite CRDT is the one described under Shared machinery.

Density-Modulated Boids and Stigmergic Coverage: Phase Transitions in 500k-Agent Exploration Swarms

is where the criticality instrumentation came from, and it is the reason we trust a phase boundary when we see one. It studies the order–disorder transition in a flocking variant whose cohesion and separation weights respond to local density rather than being fixed, paired with a coverage layer that stores its pheromone field as a replicated counter — stigmergy with no shared map and no central tally. The transition is characterized with the full apparatus the question demands: polar order parameter, susceptibility, correlation length, Binder cumulant, and a finite-size-scaling fit of the critical exponents across system sizes, which places the model in the 3-D Vicsek  universality class within statistical error. That anchoring is not incidental — it is the external result every delay number we publish is checked against before it is trusted, and the learned-policy baseline run alongside it is what lets us say a structural prior is doing real work rather than merely being cheaper to run.

Shared machinery

Three separate parts of the stack need the same property: replicas that converge under partition without a central arbiter. ICCD’s intent payload, the stigmergic pheromone field, and the market’s depot inventory all get it from one abstraction — a composite CRDT assembled from primitives that each form a join-semilattice , so their finite product does too, and the composite inherits convergence for free.

The convergence argument is stated once, in ICCD Appendix A, and reused. This is the structural reason the stack needs no separate consensus protocol per paper. Symbols — ψ, Q, AoI, χ, ξ — mean the same thing everywhere, per the unified table.

Practice

We scope claims to the fidelity that backs them, and we say what a simulator cannot tell us. Every published result names the batch it came from; when a number does not survive re-examination, we correct it in public. What we pin, what we share, and what we cannot are set out in Reproducibility and Data Availability. The canonical citation list, with BibTeX, is on the publications page.