cs.ROSep 22, 2026
SaveHumanoid Locomotion with a Fly-Inspired Recurrent Controller
Organizations: The Hong Kong University of Science and Technology, Hong Kong · Zenbot · Nanyang Technological University, Singapore · The Hong Kong Polytechnic University, Hong Kong
Abstract
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.
Figures & tables
Figure 1: Fly-inspired neural–body coupling. (a) Conceptual overview linking the biological source and supplied neuron locations to G1 simulation through engineered interfaces. The human motor-control panel denotes a prospective research direction. (b) The implemented control loop: robot observations pass through an input projection, the 3,609-state recurrent core, and an MN-restricted readout to generate 12 leg and three waist targets; 14 arm joints use fixed targets. Robot-state feedback runs at 50 Hz with 1 kHz physics. The 128-dimensional bottleneck is zero in the evaluated regime and is distinct from the 1,286 DN-labelled recurrent entries.
Figure 2: All planned condition outcomes, including every failed condition. Numbers are success counts divided by the number of initial-yaw conditions (three for intact checkpoints, one for the state-reset intervention).
Figure 3: One rough-ground rollout at a constant 0.5 m/s forward command and zero initial yaw, shown at 2, 4, 8, and 12 s. The arrow identifies uneven ground near the robot. All poses come from the same intact T_graph replay with synthetic zero depth, documenting the progression of body posture and position over the recorded episode.
Figure 4: Matched-time state-reset intervention on flat ground at 0.5 m/s. Left: intact state; right: before every policy evaluation. Rows show 0.40, 0.80, and 1.28 s. The final right panel reaches the fall rule while the intact counterpart remains upright. The intervention jointly removes carried state and recurrent interaction within the same fixed checkpoint. Panel letters identify each captured image; columns and rows specify the comparison.
Figure 5: What changes the deployed controller? (a) Raw-action differences under six one-step substitutions at all 252 sampled states, including the 21 initial states. Boxes show median and interquartile range; whiskers use 1.5 interquartile ranges; red vertical markers show maxima. All tested depth and upstream-state substitutions give exactly zero action difference. (b) All 21 closed-loop motor-state-reset episodes terminate between 1.14 and 1.30 s. Distributions summarize sampled states and specified conditions of one graph checkpoint.
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
Figure S1: What is connected across embodiments? (a) The six robot-side observation groups total 82 dimensions. (b) The deployed action selection and order map: 15 outputs set six left-leg, six right-leg, and three waist targets; the remaining 14 joints use fixed targets. Rows follow policy action order and columns follow actuator order. This engineered interface translates the neural readout into robot joint targets.
Figure S2: Temporal coupling of neural and body dynamics. A policy call generates one set of joint targets; MuJoCo advances twenty 1 ms substeps under those targets before the next observation and neural update. Joint targets remain fixed during the interval, while servo forces respond to changing positions and velocities.
Figure S3: The bounded core and its surrounding control resources. (a) Projection of supplied soma coordinates, colored by annotation class. (b) Component-level counts for recurrent states, nonzero recurrent weights, dense input weights, readout states, and actuators. The 15 policy-controlled joints and 14 fixed-target joints together form the 29-actuator body.
Figure S4: Connectivity computed from the deployed recurrent matrix. (a) Nonzero weights aggregated by source and target annotation class; the nine counts sum to 101,263. (b) The same support aggregated into 37 supplied groups. Positive counts use logarithmic color scaling; empty cells indicate zero. The plots describe weighted model-connection counts and their distribution across annotations.
| Study | Reported control scale | Body and validation | Relevance to the present study |
|---|---|---|---|
| Collins et al. (2005) [ 8 ] | Passive dynamics with simple active control | Physical bipeds; level-ground walking | Body mechanics contribute directly to coordinated locomotion. |
| Liu et al. (2008) [ 10 ] | Six Matsuoka oscillators | Five-link biped; simulation | Compact rhythmic control with oscillator-level state dynamics. |
| Manoonpong et al. (2007) [ 9 ] | Reflex network plus six additional adaptive neurons | Physical RunBot; boom-constrained walking and ramp adaptation | An adaptive neural layer works together with reflexes and body mechanics. |
| Y. Liu et al. (2024) [ 13 ] | Eight Stein-model neurons in the CPG | Go1 quadruped; physics simulation | Joint mappings, predefined foot paths, and fixed hip abduction/adduction define the control setting. |
| Steffen et al. (2026) [ 14 ] | Reference MLP: hidden units; spiking replacement uses ensembles | H1 humanoid; simulation; walking and arm-control selection | Distinguishes reference-network width from the neuronal ensembles used by the spiking implementation. |
| Radosavovic et al. (2023 version) [ 15 ] | History-conditioned transformer | Full-size humanoid; physical outdoor locomotion | Provides a hardware-validated example of history-dependent humanoid control. |
Table S1: Selected primary-source context for control scale. Counts refer to the stated components. Task, embodiment, training, and unit dynamics differ across studies, so comparisons require component-level interpretation. The 2024 eight-neuron and 2026 spiking studies are cited in their arXiv versions.
| Terrain | (m/s) | T_graph | (m) | (m/s) | R1 |
|---|---|---|---|---|---|
| Flat | 0.3 | 3/3 | 4.85 | 0.139 | 3/3 |
| Flat | 0.5 | 3/3 | 6.85 | 0.120 | 3/3 |
| Flat | 0.8 | 3/3 | 9.59 | 0.125 | 3/3 |
| Rough, 0–6 cm | 0.3 | 3/3 | 3.75 | 0.102 | 3/3 |
| Rough, 0–6 cm | 0.5 | 3/3 | 6.02 | 0.119 | 3/3 |
| Rough, 0–6 cm | 0.8 | 2/3 | 7.92 | 0.271 | 2/3 |
Table S2: Complete terrain–speed summary. T_graph and R1 entries are success counts over three yaw offsets.
Figure S5: Annotated terrain atlas from exact-state simulation replays. (a–g) The same intact checkpoint, 0.5 m/s command, zero initial yaw, and 4.00 s elapsed time on flat, rough, uphill, downhill, upstairs, downstairs, and discrete-step terrain. (h) Shared reading protocol. External-view renders show the terrain geometry and recorded robot pose in each test environment.
Figure S6: Slope interaction at a fixed 0.5 m/s command. Top: uphill at 2 and 6 s; bottom: downhill at the same elapsed times. Geometry, pose, and reported coordinates are recorded simulation quantities. The two separate episodes show distinct posture and displacement under a common command, with different contact and gravity conditions.
Figure S7: Stair interaction at a fixed 0.5 m/s command. Top: ascending 10 cm stairs at 2 and 6 s; bottom: descending 10 cm stairs at the same elapsed times. The annotation marks riser geometry. Recorded pose and coordinates show the movement attained in these two episodes under identical command settings.
Figure S8: Termination and trajectory-deviation cases, all at zero initial yaw. (a) Upstairs, 0.3 m/s: upright at 12 s but below the progress threshold. (b) Rough, 0.8 m/s: the episode terminates at 11.70 s after leaving the valid ground-height domain. (c) Discrete steps, 0.8 m/s: the 12 s progress criterion passes despite lateral escape. Right: sampled trajectories with exact final endpoints; dashed lines mark m, dotted lines mark required forward displacement, and red dots mark endpoints. Screenshot dashed lines project the actual m boundary.
Figure S9: Forward position for the fixed 0.5 m/s, nominal-yaw conditions on flat, rough, and ascending-stair terrains. Colored curves show recorded position; the gray line gives the commanded distance . Traces end at termination. These examples complement the complete condition-level outcome table.
Figure S10: Recorded artificial core activity during the same 0.5 m/s rough-ground episode as Figure 3 . (a) Mean activation within each supplied anatomical annotation group at the four screenshot times, on one shared linear color scale. (b) Class-mean core activations sampled every 0.1 s, contrasted with the zero descending bottleneck. The DN-labelled entries belong to the recurrent core and receive its engineered drive, whereas is the separate upstream branch output.
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