V2V Energy-Safe Swarm Explorer · network battery safety

Let bi be robot i's state of charge, pi its position, α the energy cost per unit distance, and d(·,·) a distance metric on the workspace (Euclidean in this simulator). Robot i is directly safe when its reachable disk contains the depot:

Robot i is V2V-safe via peer j when both clauses hold:

The first clause is a pure proximity condition: i can physically drive to j's position. The second is an energy-balance condition: once at the rendezvous, j's surplus sj = bj − α · d(pj, depot) covers i's deficit δi(j) = α · (d(pi, pj) + d(pj, depot)) − bi. The first gives the broad reachability graph (red edges in the visual); the conjunction gives the strict help-feasibility subgraph (blue edges). The gap between them is "wasted proximity" — peers i could reach but who can't save it.

The conditions are per-pair: there is no general "helper" property. A given j may save some is with small deficits while being unable to save others. Rather than counting "helper robots," we count the directed j → i edges that could feasibly provide help (the "Feasible" count) and the subset of them that are actually being acted on (the "Help (active)" count). That is, each feasible edge is a directed j → i edge representing a viable hand-off from a robot with enough surplus to one whose deficit is small enough to cover in the field. Then, each "Help (active)" edge is a feasible edge that has been committed to — i is en route to its pinned helper j, where the transfer completes.

The condition is the same whether j stays deployed after the in-place exchange (default) or accompanies i home (ferry toggle), since j reserves α · d(pj, depot) for itself either way. Operationally, when i commits to j, j is pinned: it stops wandering and waits in place until i arrives and the transfer completes. This keeps the rendezvous deterministic; without it, helpers can drift away mid-approach.

The pairwise test above is the one-hop condition, and it is exactly what the three reference implementations compute: a robot is safe if it is directly safe, or if some single peer j satisfies both clauses. (Their check bi − α·d(pi,pj) + sj ≥ α·d(pj,depot) rearranges to the surplus-sufficiency clause verbatim.) With V2V off it collapses to the direct condition alone, which is why conservative solo motion never strands a robot.

The widget itself runs the multi-hop generalization. Every frame it assigns each robot a safety depth by breadth-first search over the help graph: depth 0 is the direct-safe set; a robot is depth d if it can reach a depth-(d−1) peer, take that peer's surplus, and from there reach the depot or another already-safe peer — i.e. a whole chain i → j → k → … → depot. This is the recursive, fixed-point form of "helper" on the help graph, exactly where a network-CBF or graph-theoretic invariant would live.

One caveat is worth stating plainly, because it is the whole reason V2V trades safety for reach: that multi-hop set is an optimistic, instantaneous estimate. It is recomputed from a frozen snapshot each frame and assumes every peer holds its position and donates its full surplus — assumptions the wandering peers break the moment anyone moves or drains, which is what lets a robot over-commit to a chain that then dissolves beyond its solo reach. Only the direct-safe set (depth 0) is a true invariant; the one-hop set is nearly one when the helper is a station-holding refueler. Turning the multi-hop layer into a guaranteed charge-safety certificate — via reserved donors, stationary anchors, or a margin sized for worst-case peer drift — is the open problem, not something this simulator claims to have solved. Its job is to show that such chain strategies reach measurably more tasks, not to prove they are safe.

When free of return commitments, each robot does a Levy walk: alternating long ballistic transits (step lengths drawn from a heavy-tailed Pareto distribution, μ ≈ 1.8) with bouts of area-restricted local search. There is no global task sensing — robots only discover task sites by physically passing within contact range. The motion is filtered by the safety condition: the proposed step must keep the robot inside its safe set — just the direct-safe set when V2V is off, or the full multi-hop safe set (any robot that can chain home through a sequence of peers, per the breadth-first safety-depth pass described above) when V2V is on. The reference implementations use the simpler one-hop version of this set. When the desired step would leave the safe set, the desired direction is blended toward the depot until it lies inside.

When SoC drops below a threshold, the robot commits to a return: it heads straight for the depot if possible, otherwise toward the nearest helper that can feasibly cover its deficit. On reaching a helper, the helper transfers just enough charge to make the receiver directly safe (with a small margin), then heads home. Task engagement burns extra energy; if engaging would push the robot off the safe set, it abstains and the encounter counts as a missed opportunity. The robot then ignores that particular task until it recharges (so a single under-budget encounter is counted only once, not every frame the robot lingers nearby).

Refuelers are the deliberate exception to this forage-everywhere default. When the Refueler role is enabled, a designated fraction of the swarm is pulled out of the Levy walk and assigned to hold station at fixed shell radii (a single ring at 0.5× solo-reach, or inner and outer rings at 0.33× and 0.67×). Depending on the motion mode they hold position exactly, drift tangentially around their shell, or roam on a short leash and engage only the tasks that come within it. The point is to turn ad hoc, position-dependent peer help into a dependable spatial scaffold: a worker that runs low near a shell can count on a donor being parked there to dock with, instead of hoping another forager happens to be carrying surplus nearby.

With V2V off, the team is bounded by the smallest reachable disk that still contains the depot — a hard individual constraint. With V2V on, the coverage expands because peers near the depot have surplus to spend on saving others. Turn on the help-feasibility layer and watch a directional structure emerge: peers near the depot with high SoC accumulate outgoing edges (they can save many), while peripheral peers with low SoC accumulate incoming edges (they have many potential saviors). There's no fixed split into "donor" and "recipient" robots — the same robot may simultaneously show feasibility edges in both directions. The current SoC of a robot and its distance from the depot help decide which way it leans. That structure is also coupled and fragile: when a peer's surplus shrinks — it engaged a task, or drifted away — its outgoing feasibility edges silently vanish, potentially stranding dependents that were counting on it. The motion filter keeps each robot individually safe but does nothing to preserve those edges, so network-level V2V safety can't be taken for granted; guaranteeing it would mean filtering motion against the help graph as a whole — exactly where a network-CBF invariant would live.

Read the trade off the metric panels rather than the animation. Whether V2V actually bought range shows up in Peak reach and Mean reach — the all-time and time-averaged farthest distance any robot held, as a multiple of solo-reach — together with Time past solo and Time at outer 80%: a value above 1.0×, or any nonzero time past solo, means a robot held ground no individual could have sustained alone. The cost shows up opposite it, in Tasks done versus Tasks expired — charge spent ferrying and time spent pinned is throughput not spent closing tasks — and in Safety vetoes, the encounters a robot declined because engaging would have left it unsafe (the "missed opportunities" from the motion filter). Mean SoC and the SoC distribution panel show the energy state underneath all of it: the harder V2V is working, the more charge should spread apart — depleted robots out at the periphery on the low end, topped-up donors near the depot on the high end.

To compare regimes cleanly, let the cumulative metrics build up over a minute or so, then change one thing and rerun on a comparable task stream: toggle Worker-to-worker V2V to isolate what peer help adds, or enable the Refueler role to ask whether a dedicated, spatially-fixed donor class outperforms ad hoc worker-to-worker transfer.