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Bridging Body and Brain: Gene-Driven Morphology--Control Co-Design

Fu Feng, Ruixiao Shi, Yucheng Xie, Jing Wang, Xin Geng

arXiv:2609.31329v1cs.LG

TL;DR

Existing co-design methods typically use separate morphology and control networks coupled indirectly through a shared task objective, leaving explicit high-level coordination limited. This paper introduces Morphogene to jointly condition body and controller generation, then uses GeCode to explore and update Morphogene design anchors. Across twelve 2D and 3D design spaces, GeCode reports faster convergence and higher task performance; its evaluation remains in simulation.

  • Problem

    Existing embodied co-design methods typically use separate morphology and control networks coupled through a shared objective rather than explicit coordination at the representation or decision level.

    Source: §1 · p. 2

  • Method

    Morphogene is a shared latent blueprint that conditions morphology generation and controller adaptation, while GeCode explores local designs around anchors and updates them toward promising regions.

    Source: §1 · p. 2, §6 · p. 10

  • Results

    Across twelve 2D and 3D design spaces, GeCode averages 2.5× faster convergence and 69.48% higher task performance with less than 4.0% additional wall-clock overhead.

    Source: §1 · p. 2

  • Takeaways & Limitations

    GeCode’s reported experiments show faster convergence and higher final performance for Morphogene-driven co-design across diverse 2D and 3D tasks.

    Source: §1 · p. 2, §6 · p. 10

    The evaluation demonstrates Morphogene-driven co-design in simulation rather than on physical hardware.

    Source: §F.2 · p. 32

Abstract

from arXiv · show

Morphology--control co-design jointly optimizes an agent's body structure and control policy as an integrated embodied system. However, existing methods typically model morphology design and control with separate networks coupled only indirectly through a shared task objective, limiting explicit high-level coordination. Inspired by natural genes that coordinate biological development, we introduce \textbf{Morphogene}, a compact latent blueprint that bridges an agent's body and brain. Through AdaConcat, Morphogene jointly conditions morphology and control generation at the limb level, allowing its variations to induce coordinated changes in both components. Building on this representation, we propose \textbf{GeCode}, which formulates co-design as exploration in the compact Morphogene space. Each Morphogene anchors a local design region in which nearby body--brain designs are explored, while performance-guided updates move these anchors toward promising regions for more efficient exploration of the broader design space. This process combines local refinement with global exploration while preserving body--brain compatibility. Extensive experiments across diverse 2D and 3D co-design tasks demonstrate that GeCode consistently outperforms existing state-of-the-art methods, achieving substantially faster convergence and higher final performance.

1 INTRODUCTION

Morphology and control co-design is motivated by the limits of treating an embodied agent’s body and controller as largely independent. Morphogene and GeCode address this gap with coordinated generation and latent-space exploration, and the reported experiments show faster convergence and higher performance.

1 INTRODUCTION

  • Separate morphology and control networks coupled mainly through a shared task objective leave body–brain coordination indirect and cross-component credit assignment obscured.The paper identifies the lack of explicit representation- or decision-level coordination as the central gap.Source: §1 · p. 2
  • Morphogene is a shared developmental blueprint that anchors related body designs and jointly conditions morphology generation and controller adaptation.AdaConcat transforms the agent-level representation into limb-specific conditions based on each limb’s structural and functional role, so Morphogene variations induce coordinated changes in both components.Source: §1 · p. 2
  • GeCode explores a compact, continuous Morphogene space using design anchors, local rollouts, and performance-guided anchor updates to move toward higher-performing designs.This combines local exploration around anchors with broader latent-space exploration without exhaustively evaluating discrete morphologies.Source: §1 · p. 2
  • Across twelve 2D and 3D design spaces, GeCode averages 2.5× faster convergence and 69.48% higher task performance with less than 4.0% additional wall-clock overhead.The experiments span diverse morphologies and report consistent outperformance of state-of-the-art methods.Source: §1 · p. 2

2 RELATED WORK

Prior co-design work ranges from costly population-based morphology search to reinforcement-learning methods with separate body and control networks. GeCode makes their representation-level coupling explicit through Morphogene.

2 RELATED WORK

  • Early evolutionary co-design repeatedly searches morphologies and adapts controllers, while later RL methods jointly optimize sequential morphology construction and control.The related-work discussion characterizes early evolutionary approaches as incurring substantial sampling and computational costs.Source: §2 · p. 2
  • StackelbergPPO (Dai et al., 2026) explicitly models morphology–control interdependence at the optimization level, but its representation-level coupling remains implicit.GeCode contrasts this with explicit coupling through Morphogene throughout co-design.Source: §2 · p. 2
  • Morphogene is more than a representative embedding: it can move through latent space to guide body design while bridging morphology generation and controller adaptation.The paper uses “developmental blueprint” to emphasize this adaptive role.Source: §2 · p. 2

3 PRELIMINARIES

The preliminaries represent morphology both as a limb-and-joint graph and as a vector, then describe co-design as sequential body design followed by control on a fixed morphology. They also introduce the shared-objective coupling that the paper later makes explicit through Morphogene.

3 PRELIMINARIES

  • Morphology is an undirected graph whose nodes represent limbs and edges represent joints, with limb and joint properties encoded in the body representation.The paper also constructs a vector representation from simulator-derived limb and joint geometry; the graph and vector describe the same morphology.Source: §3 · p. 3
  • The design stage sequentially updates the morphology graph through topology edits and then attribute edits, producing a final morphology.Actions can add or remove limbs during topology design and adjust physical attributes such as limb length during attribute design.Source: §3 · p. 3
  • During the control stage, the final morphology remains fixed while the controller interacts with the environment to maximize expected task return.The co-design objective jointly optimizes design and control policy parameters for expected discounted return.Source: §3 · p. 3
  • Existing methods couple separate morphology and control policies mainly through a shared objective, whereas the paper formulates both processes as Morphogene-conditioned under an augmented objective.The cited prior methods are Lu et al. (2025) and Yuan et al. (2022).Source: §3 · p. 3
  • The agent is represented as ordered limb-wise proprioceptive states, embedded as limb tokens and processed by a Transformer before an action head produces stage-specific action distributions.Design actions are categorical, whereas control actions are continuous and Gaussian; the embedding function is shared (Gupta et al., 2022).Source: §3 · pp. 3–4

4 METHOD

The method learns a compact morphology latent space whose Morphogenes serve as anchors for coordinated body–brain design. GeCode uses limb-specific conditioning and performance-guided updates to explore locally around those anchors and across the broader space.

4.1 MORPHOGENE: A LATENT BLUEPRINT FOR BODY–BRAIN COORDINATION

  • The RAE encodes morphology into a latent space where Morphogenes act as searchable anchors distinct from codes for specific realized morphologies.Its decoder reconstructs morphological attributes and predicts limb presence; topology-aware and tree-structured losses align latent geometry with morphological relationships.Source: §4.1 · p. 4

4.2 MORPHOGENE-CONDITIONED MORPHOLOGY DESIGN AND CONTROL

  • AdaConcat adapts a shared Morphogene into limb-specific conditions for morphology design and control, aligning generation with controller adaptation.The limb-wise adaptation reflects limbs’ distinct structural and functional roles, allowing Morphogene variations to induce coherent body–brain changes.Source: §4.2 · pp. 4–5, Figure 2 · p. 5

4.3 GECODE: MORPHOGENE-DRIVEN CO-DESIGN OPTIMIZATION

  • GeCode explores locally through stochastic Morphogene-conditioned rollouts and globally by updating anchors with the best local and overall morphology codes.A proximity reward keeps candidates near their conditioning anchors; local bests preserve anchor-specific characteristics while the global best propagates high-performing designs across anchors.Source: §4.2 · p. 5, §4.3 · p. 6
  • GeCode combines latent-anchor updates with local rollouts and reuses policy-training rollouts, requiring neither additional environment interactions nor gradient-based latent optimization.Its updates use lightweight vector operations in the low-dimensional Morphogene space.Source: §4.3 · pp. 5, 7
  • GeCode removes anchors with too few locally valid rollouts and adaptively samples retained anchors using their top-rollout mean returns.The active set can shrink until one Morphogene remains.Source: §4.3 · pp. 6–7

5 EXPERIMENTS

Experiments compare GeCode with co-design baselines and analyze its conditioning, latent-space, anchor-update, and computational-cost components. Across diverse morphology–control tasks, GeCode achieves higher final returns, while the ablations examine how its design choices contribute.

5 EXPERIMENTS

  • The evaluation spans twelve 2D and 3D co-design tasks and compares GeCode with BodyGen, StackelbergPPO, and Transform2Act.The tasks include locomotion and manipulation benchmarks.Source: §5 · p. 7, §5.1 · pp. 7–8

5.1 COMPARISON WITH BASELINES

  • GeCode’s average final return is approximately 69.48% higher than StackelbergPPO’s, with larger gains on tasks with larger morphology spaces and complex terrain.The evaluation covers diverse morphology–control co-design tasks.Source: §5.1 · p. 8

5.2 ABLATION AND ANALYSIS

  • Removing Morphogene conditioning from either the morphology or control network degrades performance, with the more influential component varying by task complexity.Morphology conditioning matters especially in CRAWLER and STEPPER, while controller conditioning is more influential in CHEETAH and WALKER-REGULAR.Source: §5.2 · p. 8
  • AdaConcat adapts the shared Morphogene to each limb, whereas direct concatenation supplies a uniform feature and limits limb-specific conditioning.This provides context-aware conditioning for finer-grained morphology–control coordination.Source: §5.2 · pp. 8–9
  • Without performance-guided updates, Morphogenes remain static; five anchors balance design-space coverage and learning efficiency better than one or ten during early convergence.The ten-anchor setting reaches comparable final performance but slows initial convergence.Source: §5.2 · p. 9
  • Joint latent-space structural constraints balance local topology consistency with global structural alignment, supporting smooth, structurally meaningful Morphogene variations.The reported trajectories span broad latent-space regions while remaining structurally coherent.Source: §5.2 · p. 9
  • GeCode reaches StackelbergPPO’s peak performance with 48.4% less wall-clock time and 28.8M fewer environment interactions.Offline RAE training takes 3.5% of total training time, and Morphogene updates reuse existing rollouts without extra simulations or optimization loops.Source: §5.2 · p. 10

6 CONCLUSION

GeCode uses Morphogene to jointly condition morphology generation and controller adaptation, then searches a compact Morphogene space with local rollouts and performance-guided anchor updates. Experiments show faster convergence and higher final performance.

6 CONCLUSION

  • GeCode explores a compact Morphogene space with stochastic local rollouts and performance-guided anchor updates, and experiments show faster convergence and higher final performance.Morphogene jointly conditions morphology generation and controller adaptation through AdaConcat.Source: §6 · p. 10

AI USE STATEMENT

The supplied material records AI assistance, ethics and reproducibility statements, related-work positioning, and benchmark design details.

AI USE STATEMENT

  • Generative AI tools assisted with writing, LaTeX and figure formatting, and code editing; the authors state they independently reviewed and verified the work.The authors take responsibility for the final submission.Source: AI USE STATEMENT · p. 10

ETHICS STATEMENT

  • The work uses simulated environments and open-source benchmarks, with no human or animal participants or personal or sensitive data.The authors identify no specific ethical risks in the presented experiments.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

  • The appendix provides environment and task specifications, implementation details, and additional efficiency analyses and ablations to support reproducibility.The main paper and appendix describe GeCode and the experimental protocol.Source: REPRODUCIBILITY STATEMENT · p. 10

A ADDITIONAL RELATED WORK

  • Morphogene is distinguished from search genotypes and transferable knowledge carriers as an agent-level blueprint for jointly guiding morphology and control generation.Related work also covers universal morphology-control methods using graph networks, morphology-aware Transformers, modulation, distillation, and modular controllers.Source: A ADDITIONAL RELATED WORK · p. 14

B.1 BENCHMARK SETUP

  • The twelve benchmark tasks span planar and 3D locomotion, uneven-terrain traversal, and object manipulation across diverse morphology spaces and task complexities.The task list includes CRAWLER, STEPPER, PUSHER, TERRAINCROSSER, CHEETAH, SWIMMER, GLIDER variants, and WALKER variants.Source: §B.1 · p. 14
  • Agents are morphology graphs whose limbs have geometric attributes and whose motor-actuated joints have mechanical attributes.Limb properties include length and size; joint properties include rotation limits and maximum motor torque.Source: §B.1 · p. 14
  • Sequential design starts from one of four task-specific morphologies, edits topology and physical attributes under structural bounds, then fixes the resulting body for control.The initial structures vary in limb and joint count and, for some, plane of connection.Source: Figure 8 · p. 14, §B.1 · p. 15
  • The task objective evaluates the body–controller pair; observations include position and velocities, and control produces continuous motor actions.The morphology is instantiated and its parameters remain fixed throughout the control stage.Source: §B.1 · p. 15

B.2 TASK-SPECIFIC SPECIFICATIONS

The appendix describes benchmarks spanning varied 2D and 3D co-design settings, then details GeCode’s latent-space construction, co-design procedure, and structural regularization.

B.2 TASK-SPECIFIC SPECIFICATIONS

  • The benchmarks include 3D CRAWLER, STEPPER, and PUSHER tasks while remaining environments are 2D in x–z or x–y planes, spanning diverse morphology depths, symmetries, limb configurations, terrains, and locomotion/manipulation objectives.STEPPER evaluates 3D locomotion over elevated steps; PUSHER evaluates 3D object manipulation by pushing a movable cube along the positive x-axis while minimizing lateral drift along the y-axis.Source: §B.2 · p. 15, Figure 9 · p. 16

C.1 ALGORITHM DETAILS

  • GeCode trains a structure-aware RAE offline, then uses Morphogene anchors to jointly condition design and control policies during co-design.Rollouts provide learning experience and performance statistics for iteratively updating, eliminating, and resampling anchors.Source: §C.1 · p. 18

STAGE I: MORPHOGENE-SPACE CONSTRUCTION

  • Offline RAE training constructs the Morphogene space, whose latent geometry is regularized to support morphology-related organization.The topology loss groups codes with matching topology graphs, while the tree-structured loss preserves finer structural relationships.Source: §C.1 · p. 18, §C.2 · p. 18

C.2 STRUCTURAL REGULARIZATION OF THE MORPHOGENE SPACE

  • Topology-aware contrastive and tree-structured metric losses organize morphology codes around topology classes and finer structural relationships.Codes for isomorphic topologies are drawn closer, while tree-edit-distance triplets impose relative-distance margins between structurally similar and dissimilar morphologies.Source: §C.2 · p. 18, STAGE I: MORPHOGENE-SPACE CONSTRUCTION · p. 19

C.3 OFFLINE AND RL-BASED TRAINING OF THE MORPHOLOGY DECODER

The paper uses offline reconstruction to learn a morphology decoder, while also describing an RL-based alternative. RL decoding costs more pretraining computation but yields a policy that can continue to be optimized during co-design.

C.3 OFFLINE AND RL-BASED TRAINING OF THE MORPHOLOGY DECODER

  • The paper’s offline decoder learns the morphology latent space with a reconstruction-based RAE.An alternative trains the morphology-design policy to decode target codes through sequential design actions.Source: §C.3 · p. 20
  • RL-based decoding requires simulator rollouts and policy optimization, making pretraining more computationally demanding than direct supervised reconstruction.Without additional structural regularizers, its proximity reward provides less direct control over latent-space organization; its pretrained design policy can continue to be optimized during co-design.Source: §C.3 · p. 20

D.1 TRAINING DETAILS

The experiments use distributed trajectory collection and five random seeds; the appendix also records GeCode and baseline implementation settings.

D.1 TRAINING DETAILS

  • Experiments use distributed trajectory collection across CPU threads and five random seeds on a machine with two NVIDIA GeForce RTX 4090 GPUs.The implementation uses PyTorch 2.0.1 and MuJoCo 2.1.0.Source: §D.1 · p. 20

D.2 HYPERPARAMETERS

  • GeCode’s morphology RAE is trained for 100 epochs on randomly generated valid morphologies, and its encoder stays frozen during co-design.Morphogenes are randomly initialized in the learned latent space and updated after each epoch using existing rollout statistics, without additional environment interactions.Source: §D.2 · p. 20
  • The appendix specifies implementation settings for StackelbergPPO, BodyGen, and Transform2Act, and identifies Table 2 as listing GeCode hyperparameters.StackelbergPPO uses a Fisher regularization coefficient of 5.0; BodyGen and Transform2Act settings include their network architectures and learning rates.Source: §D.2 · pp. 20–21, Table 2 · p. 21

E.1 QUANTITATIVE RESULTS

GeCode outperforms the evaluated RL and evolutionary co-design baselines, while additional analyses examine its latent-space exploration and limb-specific conditioning. The ablations report stable RAE training and show that AdaConcat produces distinct limb conditions and generally outperforms direct concatenation.

E.1 QUANTITATIVE RESULTS

  • GeCode achieves the highest final return in all twelve environments, improving 6.5% on SWIMMER to 104.6% on PUSHER over each task’s strongest baseline.Table 3 reports final-episode returns as means and standard errors over five random seeds.Source: §E.1 · p. 21, Table 3 · p. 22
  • Local rollouts around Morphogene anchors and performance-guided updates target promising regions, focusing exploration in structurally coherent neighborhoods as morphology spaces expand.The authors highlight gains on CRAWLER, GLIDER-HARD, and WALKER-HARD, which have large, highly branched morphology spaces.Source: §E.1 · p. 22
  • Shared Morphogene conditioning is associated with gains on PUSHER, STEPPER, and TERRAINCROSSER, while the SWIMMER gain is smaller when simple morphologies suffice.The authors connect shared conditioning to adapting actions for morphology-dependent contacts, terrain interactions, and stability requirements.Source: §E.1 · p. 22
  • GeCode outperforms NGE across all twelve tasks, achieving approximately 3.7× to 17.3× its returns.The authors attribute the contrast partly to the cost of evaluating many morphology candidates and limited knowledge transfer among structurally distinct designs.Source: §E.1 · p. 22

E.2 ADDITIONAL ABLATION AND ANALYSIS

  • Across twelve tasks, the overall RAE objective has consistently small standard errors, limb-presence loss is near zero, and attribute-reconstruction loss is generally higher on 3D tasks.Attribute-reconstruction loss also generally rises as branching constraints are relaxed across GLIDER and WALKER variants.Source: §E.2 · pp. 22–23, Table 4 · p. 23
  • Topology-aware contrastive and tree-metric losses respectively organize local neighborhoods by topology and preserve graded latent distances by structural similarity.The authors describe these objectives as complementary structures for coherent latent-space exploration.Source: §E.2 · p. 23
  • GeCode generally outperforms direct concatenation, with pronounced gains on PUSHER and WALKER-REGULAR; AdaConcat also gives limbs distinct conditions from a shared Morphogene.Figure 10 depicts limb-specific conditions, and Figure 11 compares learning curves across twelve tasks.Source: §E.2 · pp. 23, 25, Figure 10 · p. 24, Figure 11 · p. 25
  • 16.5%–41.0% of total condition energy is between-limb variation under AdaConcat, while all three limb-specificity measures are zero under direct concatenation.The measures are Limb Diversity, Relative Modulation, and Between-Limb Energy Ratio.Source: Table 5 · p. 23, §E.2 · p. 25

E.3 SAMPLE AND TRAINING EFFICIENCY

GeCode reaches baseline performance thresholds with fewer environment interactions and keeps training and inference costs comparatively modest. Visual analyses describe diverse task-specific morphologies, structured Morphogene neighborhoods and trajectories, and the broader design scope of the benchmark.

E.3 SAMPLE AND TRAINING EFFICIENCY

  • GeCode reaches both baseline thresholds with the fewest interactions in all twelve tasks, requiring 48.06% and 57.69% fewer interactions than the fastest task-specific baseline in total.It reaches the BodyGen threshold on GLIDER-REGULAR in 8.65M interactions versus 28.00M for the fastest baseline, and reaches every StackelbergPPO threshold within 50M interactions.Source: §E.3 · p. 26, Table 6 · p. 26
  • Offline RAE training takes 0.77–1.03 hours, less than 4% of GeCode’s overall training time; Morphogene updates reuse policy-training trajectories without additional environment interactions.Table 7 reports training-time costs across design spaces.Source: §E.3 · p. 26, Table 7 · p. 27
  • GeCode has higher wall-clock costs on some 3D tasks, while on 2D planar tasks such as WALKER it incurs lower cost than StackelbergPPO.The authors attribute the higher 3D cost primarily to more complex morphologies, which increase simulation and policy-processing time, rather than to Morphogene updates.Source: §E.3 · pp. 26–27
  • GeCode’s parameter count is approximately 0.552M across tasks, and its per-limb inference cost remains within 0.303M–0.323M FLOPs.Total computation ranges from 1.514M to 9.354M FLOPs per control decision, primarily reflecting the number of limbs processed.Source: §E.3 · p. 27, Table 8 · p. 27

E.4 VISUALIZATION

  • Discovered agents vary in topology, limb arrangement, and body proportions, from compact locomotor structures to highly branched designs for complex terrain and object manipulation.The authors describe the designs as task-appropriate and structurally diverse.Source: §E.4 · p. 28, Figure 12 · p. 29
  • Morphogene distances form blocks and graded patterns aligned with morphology complexity, topology, limb configuration, and finer geometric and connectivity differences.Morphologies with similar structures are nearby, while increasingly different designs are farther apart in latent space.Source: §E.4 · p. 28, Figure 13 · p. 30
  • In broad design spaces, different Morphogenes traverse complementary regions, while elimination of underperforming anchors concentrates rollout budget on promising regions and retains diversity among survivors.Rollouts refine designs locally; performance-guided updates move anchors across broader regions.Source: §E.4 · p. 28, Figure 14 · p. 31

F.1 COMPARISON WITH UNIMAL

  • The BodyGen-based benchmark allows up to 29 limbs for CRAWLER, compared with UNIMAL’s limit of 10, and tests co-design across task-specific environments.GeCode uses a small set of Morphogene anchors with conditioned rollouts and updates rather than candidate-specific controller training or a separate global-search evaluation loop.Source: §F.1 · pp. 28, 32

F.2 LIMITATIONS AND FUTURE WORK

The discussion identifies three boundaries: uneven adaptation by the shared controller across diverse morphologies, untested transfer of Morphogene spaces across tasks, and evaluation in simulation rather than on hardware.

F.2 LIMITATIONS AND FUTURE WORK

  • When early morphologies differ substantially, a shared controller with limited capacity may learn some bodies more readily, biasing returns and performance-guided updates; the proposed mitigation does not fully remove this bias.The authors suggest investigating Morphogene-guided knowledge routing or modular policy selection.Source: §F.2 · p. 32
  • Morphogene spaces and policies are constructed separately for each environment, so transfer to new objectives or terrains remains an open question.The authors propose investigating shared spaces across compatible design domains with task-adaptive conditioning.Source: §F.2 · p. 32
  • GeCode is evaluated in MuJoCo simulation, not on hardware; diverse body structures, fabrication constraints, actuator limits, and sim-to-real contact differences complicate physical deployment.The authors state that the results demonstrate co-design in simulation rather than on hardware.Source: §F.2 · p. 32
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