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Emergent Cooperative Thermoregulation in Lunar Swarm Robotics

Anais Jeger, Harry Holt, Lennart Puck

arXiv:2610.31868v1cs.ROcs.MA

TL;DR

Small robots face a 354 h lunar night, and radioisotope heating used by individual rovers is difficult to scale to swarms. This paper trains a shared policy to use the swarm itself as thermal shielding, with aggregation and circulation emerging from a terminal-temperature objective. The learned behavior reaches a 155.6 ± 1.3 pcm-h survival threshold, 37% below a motionless huddle, but full-night mechanical durability remains unvalidated.

  • Problem

    Small-rover lunar-night survival is difficult, and radioisotope heaters that enable individual rovers are difficult to supply at swarm scale.

    Source: §I · p. 1

  • Method

    A shared decentralized policy is trained by reinforcement learning on the terminal mean temperature of the five coldest robots, without explicit geometric reward terms.

    Source: §I · p. 2, A. Circulation Emerges · p. 5

  • Results

    155.6 ± 1.3 pcm-h: the learned policy’s survival threshold is 37% below a motionless huddle and 12.7% above the equalization bound.

    Source: A. Circulation Emerges · p. 5, §VII · p. 6

  • Takeaways & Limitations

    The behavior needs no shared spatial reference or robot–robot contact and transfers from N = 20 to N = 40 without retraining.

    Source: §VII · p. 6

    Full-night wheel–regolith wear and resulting drift in contact or friction properties are not modeled, so long-duration mechanical durability has not been validated.

    Source: §VI · p. 6

Abstract

from arXiv · show

Swarms of small robots are an attractive way to survey lunar caves and lava tubes. Missions such as NASA's CADRE will fly cooperating rovers for distributed mapping, but only in daylight. The 354 h lunar night drops the surface towards 95 K, and the radioisotope heaters that let single rovers survive it cannot be supplied at swarm scale. In this study we investigate whether a swarm can instead use its own members as thermal shielding. We train one policy, shared by all twenty robots, by reinforcement learning with an evolution-strategies estimator. The policy receives a single reward, once, at the end of the night: the mean temperature of the five coldest robots. Nothing in that reward refers to position, spacing, exposure or motion. Two behaviors nonetheless emerge. The swarm aggregates, and robots circulate between the sheltered core and the exposed rim, the same pair of behaviors with which emperor penguins survive the Antarctic winter. We measure the survival threshold, the smallest stored energy per robot at which every robot is still alive at sunrise. Across ten runs it is 155.6 +/- 1.3 pcm-h, where one pcm-h is 7.2 kJ of stored heat. That is 37% below a motionless huddle and within 13% of a physics-based lower bound, and at a budget where the motionless huddle loses six robots, every robot survives. The behavior needs no shared spatial reference and no robot-robot contact, and transfers from twenty robots to forty without retraining.

I. INTRODUCTION

Lunar-night survival remains difficult for small rovers, while radioisotope heating is difficult to scale to swarms. This study asks whether robots can shield one another and learns a shared decentralized policy in which aggregation and circulation emerge without geometric reward terms.

I. INTRODUCTION

  • The lunar night lasts about 354 h and temperatures fall toward 95 K; NASA’s CADRE rovers are designed for daylight operation, not lunar-night survival.Distributed exploration of caves and lava pits can tolerate losing an individual robot without necessarily compromising the whole mission.Source: §I · p. 1
  • Radioisotope heaters help some rovers survive lunar nights, but their fuel is scarce and difficult to supply at swarm scale.A 2 W heater needs about 5 g of plutonium dioxide per robot; the stated US production target is roughly 1.5 kg per year.Source: §I · p. 1
  • After the swarm gathers, the figure shows a shielded blue interior and a warmer exposed rim, with all twenty robots alive at hour 73.Ring color encodes each robot’s sky exposure.Source: Figure 1 · p. 1
  • A swarm could reduce each robot’s thermal burden by shielding one another, following the emperor-penguin pattern of huddling and exchanging exposed and sheltered positions.The study investigates this approach as a way to reduce the stored energy each robot needs to survive the lunar night.Source: §I · pp. 1–2
  • A shared decentralized policy trained by reinforcement learning produces aggregation and sustained core–rim circulation, keeping every robot alive where a motionless huddle does not.The policy uses local observations, with one parameter set shared across the swarm.Source: §I · p. 2

II. RELATED WORK

Prior robot huddling and aggregation work uses environmental cues, energy sharing, or boundary movement, while earlier lunar-night shielding work used phase labels and a huddle primitive. This paper removes explicit geometric reward terms; its simulation models a full 354 h night for twenty robots.

II. RELATED WORK

  • Unlike environmental-field aggregation and self-assembly methods, this work has robots create a thermally favorable configuration by shielding one another.Prior approaches often moved toward favorable external light or temperature conditions.Source: §II · p. 2
  • Earlier lunar-night shielding work reached 55% survival over a compressed cycle using phase-conditioned reward and a discrete huddle primitive; this paper removes those elements and reaches 20/20 survival over the full night.Other penguin-inspired approaches used inductive energy sharing or boundary movement, rather than modeling robots’ bodies as lunar-night radiative shields.Source: §II · p. 2
  • The thermodynamic objective contains no explicit geometric term, so robots are not directly rewarded for huddling, circulation, or equalizing exposure.The paper states that circulation emerges because it helps the swarm survive.Source: §II · p. 2

III. SIMULATION AND THERMAL MODEL

  • The simulation models twenty robots across a full 354 h lunar night in 23,556 steps, with stored energy also reported in pcm-h at 7.2 kJ per pcm-h.Each thermal step corresponds to 54.1 s.Source: §III · p. 2

A. Thermal Dynamics

The thermal model ties radiative loss to sky exposure and temperature, then relates stored-energy needs to time-averaged exposure. Evaluating the resulting expression at densest packing gives a physics-based equalization bound.

A. Thermal Dynamics

  • Radiative loss is modeled as linear in temperature about the setpoint, with loss rate set by sky exposure χ; the model is exact while the heater holds Tset and overestimates loss during post-exhaustion cooling.χ ranges from 0 for a fully surrounded robot to 1 for an isolated robot; Tenv is 95 K and Tset is 273.15 K.Source: A. Thermal Dynamics · p. 2
  • A robot is considered dead below Tdeath = 233.15 K, and a fully isolated robot’s modeled 1.92 W loss remains below the 2.0 W heater capacity.The thermal mass is Cth = 2000 J K−1.Source: A. Thermal Dynamics · p. 2
  • Stored-energy need depends on time-averaged exposure because the loss coefficient is affine in ⟨χ⟩; after energy runs out, the robot coasts from Tset to Tdeath.The model gives stored energy credit for the final cooling period rather than requiring the store to cover it.Source: A. Thermal Dynamics · p. 2
  • 138.1 pcm-h is the N = 20 equalization bound obtained by evaluating the stored-energy expression at the mean exposure of densest packing.The paper uses this physics-based value to normalize survival thresholds.Source: A. Thermal Dynamics · p. 2

B. Body Geometry

The study avoids fixing a robot geometry by constraining emissivity times radiating area from the setpoint balance. Its simulated body and contact settings are selected as operating points bounded by observed behavior changes.

B. Body Geometry

  • The model constrains the product εA by inverting radiative balance at the setpoint, yielding a family of thermally consistent designs rather than one assumed geometry.ε is emissivity and A is radiating area.Source: B. Body Geometry · p. 3
  • The simulation uses a 2.0 kg body and 2000 J K−1 thermal mass; its chosen ε = 0.035 gives A = 0.177 m2, H = 0.246 m, and ρ = 377 kg m−3.The paper relates this density to indicative small-robot bulk densities and notes the emissivity also matches a flown blanket value.Source: B. Body Geometry · p. 3
  • Locomotion and contact parameters are constrained by measured failures: below about 50 mN, the swarm stops penetrating the pack; at 600 N m−1 stiffness, force transmits across the cluster and behavior collapses to a jammed huddle.Explicit integration is stable for SUBD > 2Kcon∆t/µ, which is 109 at these values.Source: B. Body Geometry · p. 3

C. Exposure

Sky exposure is estimated from angular occlusion by neighboring robots. The resulting exposure depends on swarm geometry and is the only coupling between locomotion and thermal state.

C. Exposure

  • Each robot’s horizon is divided into 36 parts, with a part shielded when a neighbor within 3R subtends it.Source: C. Exposure · p. 3
  • The fitted 1.6 factor gives the proxy its best affine fit to Monte Carlo view-factor calculations, with R2 = 0.97 and 3.7 % RMS error.Source: C. Exposure · p. 3
  • Sky exposure χ depends entirely on current swarm geometry and is the only coupling between locomotion and thermal state.A living robot fully shields; one cooled towards Tenv provides partial shielding.Source: C. Exposure · p. 3

IV. METHOD

The method trains one decentralized, shared recurrent policy from local observations, using a sparse thermodynamic objective and evolution strategies. Training-budget sensitivity matters: 1.10× and 1.18× the equalization bound yield similar survival thresholds, while 1.40× yields a higher threshold.

A. Policy

  • Each robot uses the same decentralized recurrent policy, with a 64-unit hidden state and fourteen local observation channels, to produce velocity commands.The trained parameters are deployed unchanged across the swarm.Source: A. Policy · p. 3, Figure 2 · p. 4
  • The reward is a single end-of-night mean terminal temperature for the coldest quintile, with no terms for position, spacing, exposure, circulation, huddling, or motion.The coldest quintile emphasizes robots closest to failure while being less sensitive to a single outlier.Source: A. Policy · p. 3

B. Training

  • Evolution strategies train the shared parameters from delayed scalar rewards; each candidate is evaluated over eight starts for 200 generations.The reward arrives only after the 354 h episode, with no intermediate signal for per-step advantages.Source: B. Training · pp. 3–4
  • Training uses 1.18× the equalization bound: a motionless huddle keeps 14/20 robots alive, while a dispersed swarm keeps 0/20 alive at that budget.Below roughly 1.05× the bound, no policy keeps all twenty alive, leaving the coldest-five temperature objective without a path toward survival.Source: B. Training · p. 4
  • 155.8 pcm-h at 1.10× the bound and 155.7 pcm-h at 1.18×; training at 1.40× yields 176.4 pcm-h.Source: B. Training · p. 4, Table II · p. 4

C. Evaluation

The survival threshold is the smallest initial stored-energy budget at which every robot survives. It is estimated across held-out starting configurations using bisection to 0.5% precision.

C. Evaluation

  • The survival threshold is the smallest initial stored-energy budget for which all robots survive across ten held-out evaluation seeds.Bisection continues until 0.5% precision; each seed uses a different initial configuration not seen during training.Source: C. Evaluation · p. 4

V. RESULTS

The learned swarm reaches a 155.6 ± 1.3 pcm-h survival threshold, well below a motionless huddle and close to the equalization bound. Aggregation and sustained circulation emerge under a reward based on the coldest robots’ terminal temperatures, while aggregation alone is insufficient.

A. Circulation Emerges

  • From a scattered start, the learned swarm gathers within five hours and circulates; gather-only aggregation leaves a core–rim exposure gradient and nine robots die.With zero command, the swarm remains scattered and all robots die by 225 h.Source: Figure 3 · p. 5, A. Circulation Emerges · p. 5
  • 155.6 ± 1.3 pcm-h is the pooled learned survival threshold, 37% below a motionless huddle and 12.7% above the equalization bound.The table reports pooled converged learned runs.Source: Table III · p. 5, A. Circulation Emerges · p. 5
  • At 150 pcm-h, coldest-five terminal temperature is 232 K for a circulating swarm, versus 147 K for a motionless huddle and 127 K for gather-only.All conditions are below their survival thresholds at this budget.Source: A. Circulation Emerges · p. 5
  • The hand-coded circulating rule reaches 154.5 pcm-h, nearly matching the learned policies; removing its burrowing term yields the gather-only baseline.The rule steers inward and sends the least-energized contacted robot inward until it reaches the core.Source: A. Circulation Emerges · p. 5

B. No Shared Reference Is Required

Removing the shared spatial reference leaves survival thresholds essentially unchanged, though robots move more. Recurrence is not required for the behavior, and similar circulation was observed in an earlier implementation with different contact and reward.

B. No Shared Reference Is Required

  • Removing the shared reference leaves no external frame or shared infrastructure, avoiding a global observation that could make aggregation resemble simple navigation.The policy commands motion from local observations with shared parameters across the swarm.Source: B. No Shared Reference Is Required · p. 5
  • Without a shared reference, packed-start and scattered-start thresholds are 154.3 ± 1.6 and 156.7 ± 1.1 pcm-h, versus 155.7 ± 1.3 and 155.4 ± 0.6 with one.The reference-free policy makes roughly 4,500 crossings, compared with 1,800 with the shared reference.Source: B. No Shared Reference Is Required · p. 5

C. The Role of Memory

  • Feed-forward policies reach 160.8 ± 2.8 pcm-h, about 3% higher than recurrent policies; recurrent policies include both memory-using and memoryless solutions.Five of ten converged recurrent policies retain their threshold when hidden state is zeroed; the other five rise to 190–316 pcm-h.Source: C. The Role of Memory · p. 5
  • Qualitatively similar circulation appeared in an earlier ARGoS implementation using frictional, non-interpenetrating contact and a different reward.Source: C. The Role of Memory · p. 6

D. Transfer to Other Swarm Sizes

Five policies tested without retraining needed less stored energy as swarm size increased. Observation-channel ablations also showed that information dependencies vary by policy, including when neighbor telemetry is removed.

D. Transfer to Other Swarm Sizes

  • 5.0% at N = 30 and 8.0% at N = 40 were the average reductions in survival requirement, versus bound reductions of 5.5% and 10.7%, respectively.The five evaluated policies were selected by seed index, without regard to their thresholds, and tested without retraining.Source: D. Transfer to Other Swarm Sizes · p. 6
  • Removing one observation channel at deployment had policy-specific effects; neighbor stored energy was consistently cheap to remove, while other channels varied in importance.The policies had been trained with all fourteen channels, so the ablation tests robustness to losing a channel at evaluation, not dependence during learning.Source: E. What the Behavior Depends On · p. 6
  • With both neighbor telemetry channels removed, the three policies were respectively indifferent (154.9), degraded (175.5), or failed (268.4).Robots still sensed contact, bearing, and range; purely self-centered observation sufficed for some policies but not others.Source: E. What the Behavior Depends On · p. 6

VI. LIMITATIONS

The swarm reaches a survival threshold close to the physics-based bound, but avoiding robot contact costs stored energy. Sustained wheel–regolith interaction also leaves long-duration mechanical durability unvalidated.

VI. LIMITATIONS

  • Maintaining a 25 mm keep-out distance allowed the policies to survive without retraining, but cost about 13% in stored energy because separation reduced shielding.The added cost was independent of the controller.Source: §VI · p. 6
  • Robots averaged 4.3 m h−1 of travel over the 354 h night, and the model does not capture wear or resulting drift in contact or friction properties.Long-duration mechanical durability has not yet been validated; hardware testing under realistic regolith and contact conditions remains future work.Source: §VI · p. 6

VII. CONCLUSIONS

  • 155.6 ± 1.3 pcm-h was the survival threshold, 37% below a motionless huddle and 12.7% above the equalization bound.The conclusion identifies physical validation, especially wheel–regolith wear over a full night, as remaining work.Source: §VII · p. 6
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