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Humanoid Locomotion with a Fly-Inspired Recurrent Controller

Isabel Guan, Yuntian Zhao, Dingyuan Zhang, Shipeng Lyu

arXiv:2609.27001v1cs.RO

TL;DR

The paper asks how a fly-inspired recurrent controller participates in humanoid locomotion and which pathways support its deployed behavior. It formalizes and examines an engineered neural–body control system, finding locomotion in 61/63 specified conditions and linking behavior to carried motor state and direct body input.

  • Problem

    The paper asks how a fly-inspired recurrent controller participates in humanoid locomotion and which computational pathways support its behavior.

    Source: §1 · p. 1

  • Method

    The study analyzes a deployed recurrent controller coupled to humanoid mechanics through engineered observation and action interfaces.

    Source: §3.2 · p. 3, §6 · p. 7

  • Results

    The deployed controller sustains locomotion in 61/63 specified conditions, with recurrent motor state consequential and the measured depth-to-descending branch inactive.

    Source: §6 · p. 8

  • Takeaways & Limitations

    The analysis links an insect-labelled artificial recurrent representation to humanoid mechanics through an engineered action map, without establishing biological homology between insect and humanoid joints.

    Source: §6 · p. 7

    Evidence is limited to a fixed checkpoint, seven fixed terrain instances, controlled initial yaw offsets, and synthetic zero depth; the success criterion allows lateral drift.

    Source: §6 · p. 7

Abstract

from arXiv · show

We investigate humanoid locomotion with a fly-inspired recurrent controller and identify the pathways supporting its deployed behavior. The controller couples 3,609 continuous neural states to a simulated Unitree G1 through body-observation projections, a motor-neuron-labelled readout, and joint servos. We formulate this neural-body feedback system and evaluate a fixed checkpoint across seven terrain instances, three speeds, and three initial yaw offsets. It completes 61/63 conditions under a survival-and-forward-progress criterion; a privileged reference completes 62/63. At nominal yaw, resetting the recurrent motor state before every policy call changes success from 19/21 to 0/21. Conversely, depth and upstream-state substitutions at 252 recorded states leave actions unchanged, with zero measured descending output throughout the intact rollouts. Recorded trajectories and state-matched images connect these findings to sustained movement, lateral drift, and termination events. The study characterizes an embodied recurrent control system whose tested locomotion is supported by direct body-and-command input and carried motor state, providing a concrete basis for subsequent comparisons of circuit structure and control resources.

1 Introduction

This study asks how a fly-inspired recurrent controller participates in humanoid locomotion and which pathways support its deployed behavior. It situates that question among work on embodied control and connectome-informed networks, emphasizing the engineered interface to humanoid mechanics.

1 Introduction

  • Locomotion combines neural computation with body mechanics and environmental contact, motivating questions about how neural resources relate to motor capability.Prior examples include passive-dynamic bipeds, reflex controllers, recurrent motor models, and embodied learning.Source: §1 · p. 1
  • Applying an insect-labelled recurrent core to a humanoid requires engineered mappings between body observations, neural readouts, and a different joint arrangement and contact geometry.The study examines a fixed T_graph checkpoint with 3,609 continuous states and a readout from 135 motor-neuron-labelled entries to 15 leg-and-waist targets.Source: §1 · p. 1
  • The study asks how the deployed fly-inspired recurrent controller participates in humanoid locomotion and which computational pathways support its behavior.It formalizes the neural–body loop and uses input and state interventions to distinguish nominal architecture from effective control pathways.Source: §1 · pp. 1–2

2 Related work

  • Related work spans compact locomotor controllers, humanoid policies at different resource scales, and connectome-informed embodied systems, while this study examines effective pathways in a fixed humanoid deployment.The cited examples include reflex and oscillator controllers, humanoid MLP and transformer policies, and fly-control or robot-navigation systems.Source: §2 · p. 2

3 Controller and neural–body coupling

The controller uses an annotated 3,609-state recurrent core with body observations as input and a motor-neuron-labelled readout for leg-and-waist targets. Engineered projections, joint servos, and the simulated body form a feedback loop in which body motion changes subsequent neural inputs.

3.1 Recurrent controller

  • The 3,609-state core receives projected body, command, joint, and previous-action inputs, while its readout selects 135 motor-neuron-labelled entries to produce 15 actions.The package attributes neuronal annotations to MaleCNS v1.0; the depth bottleneck is zero in the evaluated regime and distinct from the 1,286 descending-neuron-labelled recurrent entries.Source: §3.1 · p. 2, Figure 1 · p. 3
  • The recurrent update combines carried state with a rectified input-driven recurrence using elementwise update coefficients.The update coefficient α ranges from 0.1473 to 0.7136; the recurrent matrix has 101,263 nonzero entries, while the input matrix is dense.Source: §3.1 · p. 2

3.2 Coupling to the simulated body

  • The G1 has 29 actuated joints; the policy targets 12 leg and three waist joints, while 14 arm joints use fixed hold targets.Clipped and scaled actions are offset and mapped to actuator order before local position servos act on the body.Source: §3.2 · p. 3
  • At 50 Hz, each policy target is held for twenty 1 kHz physics steps, and body motion changes the observations used by subsequent neural updates.Neural outputs change subsequent body motion, so the core, projections, readout, servos, and body jointly implement the feedback loop.Source: §3.2 · p. 3

4 Evaluation

The evaluation tests fixed checkpoints across seven terrain instances, three command speeds, and three initial yaw offsets, with success defined by survival and forward progress. It also evaluates recurrent-state reset and counterfactual input substitutions at recorded states, alongside trajectory and image records.

4.1 Terrain conditions and measures

  • The intact controller is evaluated in 63 conditions formed by seven terrain instances, three forward commands, and three initial yaw offsets.The terrains include rough ground, slopes, stairs, and discrete steps; runs begin from the exported spawn pose with zero recurrent states and last up to 12 seconds.Source: §4.1 · p. 4
  • Success requires surviving 12 seconds and reaching forward displacement of at least 0.7vT; termination also occurs at specified low-height, excessive-tilt, or invalid-height conditions.Lateral deviation and termination type are reported separately, and velocity RMSE uses only non-terminated observations.Source: §4.1 · p. 4
  • The T_graph depth input is fixed at normalized zero, while the R1 reference receives 187 privileged terrain-height samples in addition to the shared body-and-command vector.The checkpoints are fixed inference policies, but their sensory access and undocumented training budgets differ.Source: §4.1 · p. 4

4.2 State and input interventions

  • The study resets recurrent state before each policy call in 21 nominal-yaw episodes and tests six independent substitutions at 252 recorded states.The substitutions include depth, upstream state, motor state, and body-and-command input; archived replays also provide recorded poses and terrain images, not independent trials.Source: §4.2 · p. 4

5 Results

The fixed checkpoint completes most evaluated terrain conditions, while the interventions identify carried motor state and direct body-and-command input as supports for its tested behavior. Trajectories also reveal lateral drift and a terrain-boundary termination.

5.1 Locomotion across the evaluated terrains

  • A 0.5 m/s rough-ground replay sustains movement through 12 s, while atlas sequences document poses and displacement across slope and stair episodes.The rough-ground sequence shows the same intact replay at 2, 4, 8, and 12 seconds.Source: §5.1 · pp. 4–5, Figure 3 · p. 5
  • 61/63 conditions are completed by T_graph versus 62/63 by R1; failures occur on rough terrain and ascending stairs.T_graph meets the criterion in all nine speed–yaw combinations on flat ground, both slopes, descending stairs, and discrete steps.Source: §5.1 · p. 4, Figure 2 · p. 5
  • 3.17 m lateral displacement accompanies a successful 0.8 m/s discrete-steps run, outside the nominal corridor.At 0.3 m/s on ascending stairs, the nominal-yaw run remains upright but advances 1.77 m, below the required 2.52 m; the rough-run termination at 11.70 s is a height-query boundary event, not established physical toppling.Source: §5.1 · p. 5

5.2 Carried motor state supports the deployed behavior

  • At nominal yaw, resetting motor state drops success from 19/21 to 0/21; one-step substitutions yield median action sensitivity 2.436 over noninitial probes and maximum 4.965.All reset runs terminate between 1.14 and 1.30 s; at 1.28 s the reset run reaches the pelvis-height threshold while the intact counterpart remains upright.Source: §5.2 · p. 6, Figure 4 · p. 6

5.3 The effective input pathway bypasses the depth branch

  • Across 37,785 intact calls, zt stays zero; tested depth and upstream-state substitutions change no actions, while body-and-command zeroing yields a 1.507 median maximum-coordinate difference.The interventions were evaluated at 252 recorded states.Source: §5.3 · p. 7, Figure 5 · p. 7
  • The effective tested pathway uses direct body-and-command input and recurrent motor state; DN-labelled core entries can remain active despite the separate upstream bottleneck.The origin of the inactive upstream branch remains a training-history question.Source: §5.3 · p. 7

6 Discussion and conclusion

The study characterizes a fly-inspired recurrent controller coupled to humanoid mechanics through an engineered interface, without establishing biological homology between insect and humanoid joints. Within the tested scope, locomotion depends on carried motor state, while the evidence does not establish a resource advantage for the connectome-derived architecture.

6 Discussion and conclusion

  • The MN-labelled linear readout is an engineered action map between an insect-labelled representation and humanoid mechanics, not evidence of biological homology between their joints.The interface translates body observations into core drive and selected core states into leg-and-waist targets.Source: §6 · p. 7
  • The 3,609-state count characterizes this recurrent core but does not demonstrate a resource advantage over conventional policies.Establishing an advantage or minimum sufficient network size requires separately trained, resource-matched controls and scale comparisons.Source: §6 · p. 7
  • Evidence is limited to a fixed checkpoint, seven fixed terrain instances, controlled initial yaw offsets, and synthetic zero depth; broader perturbation tests and supervised hardware validation remain subsequent steps.The success criterion allows lateral drift, and the reference uses privileged sensing; simulated contact settings and disabled self-collisions further define the test conditions.Source: §6 · pp. 7–8
  • 61/63 specified conditions sustained locomotion, while recurrent motor state was consequential and the measured depth-to-descending branch was inactive as direct body input remained effective.These observations link neural computation, terrain-dependent motion, and pathway intervention in one inspectable control system.Source: §6 · p. 8

Data availability and AI assistance

The supplement records the evaluation materials and assistance, then specifies the observation and upstream-state pathway and the action-target and physics interface. Together, these details describe how policy calls connect inputs and neural updates to robot motion.

Data availability and AI assistance

  • The author-held archive includes the protocol, 147 episode summaries, trajectories, intervention records, scripts, model hashes, and visualization records; full reruns require a separate permission-dependent inference bundle.A public archive identifier has not yet been established; OpenAI Codex assisted with software inspection, evaluation, analysis, figures, and writing, while human authors retain responsibility for verification and interpretation.Source: Data availability and AI assistance · p. 8

S1.1 Observation and upstream branch

  • The 82-component policy input combines projected gravity, angular velocity, command targets, joint positions and velocities, and the previous raw action; the upstream branch combines depth features with body input to update βt.The depth array is compressed to 32 features, and normalized-zero depth is synthetic; the recurrent update mixes prior core states with encoded body information across DN-, IN-, and MN-labelled entries.Source: S1.1 Observation and upstream branch · p. 10

S1.2 Action targets, servos, and physics

  • The simulated body has 29 actuated coordinates and approximately 34.341 kg mass after the pelvis adjustment; both evaluated controllers use the same inspected physics settings.The contract disables self-collisions and uses implicitfast with solref set to (0.005, 1).Source: S1.2 Action targets, servos, and physics · p. 11
  • Fifteen policy outputs set 12 leg and three waist targets, while the remaining 14 joints use fixed targets; the engineered interface maps these outputs to robot joints.Targets are held for twenty 1 ms physics substeps before the next observation and neural update, while servo forces respond to changing positions and velocities.Source: S1.2 Action targets, servos, and physics · p. 10, Figure S1 · p. 11, Figure S2 · p. 11

S2 Core organization and resource context

This section characterizes recurrent connectivity and presents component-level context for the controller’s surrounding resources.

S2 Core organization and resource context

  • 101,263 nonzero recurrent-matrix entries include two diagonal entries, and each presynaptic row’s outgoing weights share one sign.The 1,979 positive and 1,544 negative annotations agree with these signs; 86 entries have unspecified annotation sign and contribute 1,452 nonzero outgoing weights.Source: S2 Core organization and resource… · p. 12
  • Grouped connectivity counts tally nonzero Wij connections between supplied annotation groups; Figure S4 aggregates them by annotation class and 37 supplied groups.The nine source-target class counts sum to 101,263, and positive counts use logarithmic color scaling.Source: S2 Core organization and resource… · p. 12, Figure S4 · p. 13
  • Figure S3 shows soma coordinates by annotation class and component counts for recurrent states, weights, inputs, readout states, and actuators; the body has 29 actuators.Fifteen joints are policy-controlled and 14 have fixed targets.Source: Figure S3 · p. 12
  • Table S1 contextualizes component counts across studies, while noting that tasks, embodiments, training, and unit dynamics differ.The caption says these differences require component-level interpretation.Source: Table S1 · p. 13

S3 Complete condition summaries

The section reports complete terrain–speed outcome summaries and specifies how displacement and velocity error are aggregated.

S3 Complete condition summaries

  • The recorded runtime uses Node.js 24.19.0 and ONNX Runtime Web 1.30.0 on an Apple M2 with macOS 14.8.5.The protocol was archived before evaluation; wall-clock values include instrumentation and are execution diagnostics.Source: S3 Complete condition summaries · p. 14
  • Planar body-frame velocity RMSE is computed over non-terminated post-step observations.Source: S3 Complete condition summaries · p. 14
  • Displacement and velocity RMSE are medians for T_graph across three controlled initial-yaw offsets, including failed conditions.Because failed episodes have shorter windows, these values are interpreted alongside termination time.Source: S3 Complete condition summaries · p. 14
  • Table S2 summarizes terrain–speed outcomes as T_graph and R1 success counts over three initial-yaw offsets.The caption identifies the table’s scope but provides no cell values here.Source: Table S2 · p. 14

S4 State-matched visual evidence

State-matched replays document terrain interactions, forward-position traces, and distinct trajectory-deviation and termination cases.

S4 State-matched visual evidence

  • Eleven replayed episodes reproduce the original endpoints, termination flags, and step counts, with 115 archived states and 28 retained screenshots.The viewer renders recorded poses; camera, lighting, colors, arrows, and labels are presentation settings.Source: S4 State-matched visual evidence · p. 14
  • Figure S5 shows the same intact checkpoint at 0.5 m/s, zero initial yaw, and 4.00 s on seven terrain instances.The external views show terrain geometry and recorded robot pose.Source: Figure S5 · p. 15
  • Figure S6 contrasts uphill and downhill 10° episodes at the same 0.5 m/s command and elapsed times, with distinct posture and displacement.The episodes differ in contact and gravity conditions.Source: Figure S6 · p. 16
  • Figure S7 shows ascending and descending 10 cm stairs at 0.5 m/s, with recorded poses and coordinates at 2 and 6 s.The annotation marks riser geometry.Source: Figure S7 · p. 16
  • Nominal-yaw examples show an upright upstairs run missing progress at 12 s, a rough-ground termination at 11.70 s, and a discrete-steps run passing despite lateral escape.The figure also marks the forward-displacement threshold, lateral boundaries, and exact final endpoints.Source: Figure S8 · p. 17
  • Figure S9 plots recorded forward position against commanded distance vt for nominal-yaw 0.5 m/s runs on flat, rough, and ascending-stair terrain.Traces end at termination and complement the condition-level outcome table.Source: Figure S9 · p. 18

S5 Recorded core activity

Recorded activations show that DN-labelled core states can be active while the separate descending bottleneck remains zero.

S5 Recorded core activity

  • During the intact 0.5 m/s rough-ground episode, DN-labelled core states can be active while the separate descending bottleneck is zero.Figure S10 shows annotation-group mean activations at four screenshot times and class-mean activations sampled every 0.1 s.Source: S5 Recorded core activity · p. 18, Figure S10 · p. 18

S6 Provenance and reproducibility records

The provenance record distinguishes model properties reconstructed from the deployed export from biological and training details unavailable in the supplied materials. Archived diagnostic checks validate implementation at six inputs, while a separate inference bundle is required for full evaluation reruns.

S6 Provenance and reproducibility records

  • The original graph-extraction code, selected biological adjacency, teacher lineage, training objectives and schedules, and training/validation splits were unavailable.The filtering meaning of w5 is also undocumented; anatomical provenance is attributed to package metadata, while computation and model-level counts are reconstructed from the deployed export.Source: S6 Provenance and reproducibility… · p. 19
  • Full evaluation reruns require the separate, permission-dependent inference bundle, and public redistribution awaits confirmed terms for its code, robot assets, and weights.The author-held archive contains evaluation records and analysis scripts.Source: S6 Provenance and reproducibility… · p. 19
  • Six diagnostic calls show maximum core-state error of 1.69 × 10−6 and raw-action error of 1.22 × 10−6 against float32 ONNX outputs.Joint-target mappings were exact; these checks validate implemented equations at those inputs and are separate from the 147 study episodes.Source: S6 Provenance and reproducibility… · p. 19

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