Robot Morphology-Control Co-Design

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Overview

Robot morphology-control co-design studies how a robot’s shape, materials, actuators, and control policy can be designed together, since each constrains what the others can achieve. Common approaches include evolutionary and Bayesian search, bilevel reinforcement learning, and differentiable simulation or learned latent spaces that make design exploration more efficient. These methods are used across soft and legged robots, hands and tools, and aerial systems, with evaluations ranging from simulated locomotion benchmarks to fabricated robots and real-world tasks. A central challenge is finding designs that remain robust and manufacturable beyond their training conditions, while making comparisons fair across different controllers, search budgets, and benchmarks.

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60 papers11 papers in the last four weeks, up 10% on the four weeks before. 0.1% of all new papers.

Jul 8, 2026

Communicative Efficiency of Single vs. Multi-Axis Robot Neck Motion

Nonverbal communication through head and neck movement is fundamental to human social signalling, yet how robotic neck morphology translates motion into communicative information remains poorly understood. We present an information-theoretic framework characterising robot neck movement as a communication channel, quantifying information transmitted and energy expended across varied configurations. Using a robotic neck platform, we recorded 84 video stimuli spanning three rotational degrees of freedom (DoF), varying amplitude, acceleration, and frequency, measuring Shannon entropy of pixel-change signals alongside energy consumption. A perceptual study validated communicative interpretations of each motion. While humans typically engage one axis per gesture, robots are unconstrained by biological architecture, motivating tests up to 3 DoF. Yet communicative information peaks at two DoF and decreases at three despite rising energy cost, a phenomenon we term the morphological information bottleneck. Motion parameter effects were parameter-dependent, some additive, others non-linear. We introduce the Motor Information Space, a framework mapping entropy against energy to expose communicative efficiency across morphologies, in which the optimal configuration achieves 5.26 bits at competitive energy cost. Perception data further confirm multi-axis movements reduce clarity. These findings challenge the assumption that anatomical completeness improves robotic expressiveness, establishing a quantitative basis for morphological design in robots, especially humanoids.

Chapa Sirithunge, Haewon Jeong, Qinghua Guan +2

University of Bristol School of Engineering Mathematics and Technology, Tankard’s Close, Bristol BS8 1TW, UK · EPFL Institute of Mechanical Engineering, CH-1015 Lausanne, Switzerland · University of Tokyo Department of Precision Engineering, Tokyo 113-8656, Japan

Robot Morphology-Control Co-DesignRoboticsHuman-Robot InteractionHumanoid Robotics
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Jun 5, 2026

Rapid co-design of Buoyancy-assisted robots for Challenging Locomotion using Gaussian Evolutionary Specialists

Designing high-performance legged robots requires jointly optimizing morphology and control. Model-free Reinforcement Learning (RL) offers an alternative to model-predictive control for developing robust controllers without explicitly specifying robot dynamics. Thus, we have seen theuse of RL to train controllers and evaluate designs for robot morphology optimization. While RL has shown success inlocomotion, using it in the co-design inner loop is expensive due to repeated policy training. Universal policies conditioned on morphology offer a promising alternative, but suffer from behavioral diversity collapse, converging to a single strategy that performs sub-optimally across designs. On the other hand, end-to-end Mixture-of-Experts (MoE) architectures fail due to a collapse in its representation. We propose Gaussian Evolutionary Specialists (GES), a framework that decouples design-space partitioning from policy learning to capture diverse behaviors explicitly. GES assigns specialist policies to evolving Gaussian regions and iteratively refines them via training, probing, and territory expansion. The resulting specialists are integrated into a design sampling loop, replacing costly re-training with direct evaluation. When tested on the Buoyancy-Assisted Light Legged Unit (BALLU), GES discovers designs with 5 - 25% higher performance than naive universal policies. On hardware, a GES optimized design overcomes a 24 cm tall obstacle - 3x improvement over the baseline BALLU design. Moreover, GES curtails design optimization time by 37%.

Ankit Sinha, Nitish Sontakke, Dennis Hong +2

School of Interactive Computing, Georgia Institute of Technology, TSRB 85 5th St NW, Atlanta, GA - 30332, USA · Dept. of Mechanical and Aerospace Engineering, University of California, Los Angeles, 420 Westwood Plaza, CA 90095, USA · Robotic Systems Lab, ETH Zurich, Leonhardstrasse 21, 8092 Zurich, Switzerland

Legged RoboticsRobot Morphology-Control Co-DesignEvolutionary OptimizationRoboticsRL for Legged Locomotion
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May 28, 2026

Extreme dynamic symmetry enables omnidirectional and multifunctional robots

Symmetry is a central organizing principle in natural systems, yet its use as a unifying design strategy in robotics has largely remained limited to geometric form. We show that symmetry can instead be leveraged at the level of dynamic actuation capability. We introduce dynamic symmetry, the uniformity of a robot's attainable center-of-mass accelerations, and formalize it through a measure coined as dynamic isotropy. Across more than 1000 simulated morphologies, we found that higher dynamic symmetry consistently improved trajectory tracking, task success, robustness, resiliency, and energy efficiency, with the benefits becoming most pronounced as dynamic isotropy approached its theoretical limit. To study this regime systematically, we developed Argus, a family of spherical robots designed to explore the effects of increasing dynamic symmetry. Members of the Argus family vary in their actuation geometry and dynamic symmetry level while sharing a common architectural principle: radially oriented linear actuators that directly shape the robot's center-of-mass dynamics. Among them, we built a physical 20-leg Argus variant that achieved near-extreme dynamic isotropy and demonstrated orientation-invariant locomotion, agile traversal of cluttered and deformable terrain, rapid self-stabilization, and resilience to partial actuator failures. Its distributed sensing further enabled omnidirectional perception and object interaction during continuous motion. These results show that designing robots for symmetry not only in morphology but also in their attainable dynamics provides a powerful and general pathway toward agility, robustness, and multifunctionality in uncertain terrestrial and extraterrestrial environments.

Jiaxun Liu, Boxi Xia, Boyuan Chen

Department of Mechanical Engineering and Materials Science, Duke University · Department of Electrical and Computer Engineering, Duke University · Department of Computer Science, Duke University

Robot Morphology-Control Co-DesignRoboticsRobot Locomotion
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May 22, 2026

ECo-MoE: Embodiment-Conditioned Mixture of Experts Increases the Evolvability of Robots

In this paper, we introduce a model of evolution and learning in robots that co-optimizes a distribution of latent design vectors (genotypes) and a mixture of control experts (neural modules), which are gated by the latent coordinates of each decoded design (phenotype). This provides a scalable alternative to co-design algorithms that either train an individual policy for every robot, which is inefficient, or a monolithic universal controller for all robots, which results in overly conservative structures and behaviors. Our approach lies somewhere between these two extremes, preserving ancestral knowledge in a unified yet modular framework in which different body plans activate and deactivate different combinations of learned sensorimotor circuits for goal-directed behavior. This allows one part of the controller to be overhauled to better suit new species of designs as they emerge without disrupting the hard-earned knowledge contained within other expert modules. It also allows pretrained expert policies to be directly plugged into the mixture, which can steer evolution into otherwise unexplored areas of latent space containing desired morphological traits. We refer to this process as "evo by demo" and explore how it may be used to guide freeform evolution toward canonical structures defined by the pretrained model. Videos and code can be found at: https://eco-moe.github.io.

Yibin Wang, Muhan Li, Zihan Guo +1

Northwestern University, Evanston, IL, USA.

Robot Morphology-Control Co-DesignMixture of ExpertsCross-Embodiment Robot LearningRoboticsEvolutionary Robotics
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May 12, 2026

COSMIC: Concurrent Optimization of Structure, Material, and Integrated Control for robotic systems

Replicating and surpassing the autonomy of natural organisms remains a long-standing goal in robotics. Yet most robotic systems have their structure, materials, and control designed separately, in sharp contrast to the co-evolution in nature. This separation often leads to suboptimal designs, and we still have a limited understanding of the individual and collective contributions of these design entities. In this work, we propose a gradient-based co-design framework that simultaneously optimizes the topology, material distribution, and control policy of a truss-lattice robot. The framework embeds mixed-type topological and material variables into a continuous design space and integrates a neural network controller within a differentiable simulator, capturing their interactions and enabling efficient gradient calculation via automatic differentiation. Furthermore, we develop a constrained optimization to navigate the highly non-convex design landscape and jointly optimize all design entities. Case studies demonstrate that the proposed framework consistently discovers diverse locomotion strategies that outperform baselines obtained through separated design. The framework is also flexible to accommodate different functional requirements and boundary conditions. Using this framework, we further extract design insights that reveal the individual and collective effects of different entities on robotic performance. The proposed framework provides a computational foundation for the autonomous co-design of robotic systems, capable of reconfiguration, locomotion, and other complex autonomous behaviors.

Qinsong Guo, Liwei Wang

Dept. of Mechanical Engineering Carnegie Mellon University Pittsburgh, PA 15213

Topology OptimizationRobot Morphology-Control Co-DesignRoboticsRobot LocomotionHardware-Software Co-Design
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Apr 14, 2026

Evolving the Complete Muscle: Efficient Morphology-Control Co-design for Musculoskeletal Locomotion

Musculoskeletal robots offer intrinsic compliance and flexibility, providing a promising paradigm for versatile locomotion. However, existing research typically relies on models with fixed muscle physiological parameters. This static physical setting fails to accommodate the diverse dynamic demands of complex tasks, inherently limiting the robot's performance upper bound. In this work, we focus on the morphology and control co-design of musculoskeletal systems. Unlike previous studies that optimize single physiological attributes such as stiffness, we introduce a Complete Musculoskeletal Morphological Evolution Space that simultaneously evolves muscle strength, velocity, and stiffness. To overcome the exponential expansion of the exploration space caused by this comprehensive evolution, we propose Spectral Design Evolution (SDE), a high-efficiency co-optimization framework. By integrating a bilateral symmetry prior with Principal Component Analysis (PCA), SDE projects complex muscle parameters onto a low-dimensional spectral manifold, enabling efficient morphological exploration. Evaluated on the MyoSuite framework across four tasks (Walk, Stair, Hilly, and Rough terrains), our method demonstrates superior learning efficiency and locomotion stability compared to fixed-morphology and standard evolutionary baselines.

Lidong Sun, Wentao Zhao, Ye Wang +2

Naval University of Engineering, Wuhan 430033, China · Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China · Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

Robot Morphology-Control Co-DesignRoboticsRobot LocomotionEvolutionary Robotics
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Apr 14, 2026

Social Learning Strategies for Evolved Virtual Soft Robots

Optimizing the body and brain of a robot is a coupled challenge: the morphology determines what control strategies are effective, while the control parameters influence how well the morphology performs. This joint optimization can be done through nested loops of evolutionary and learning processes, where the control parameters of each robot are learned independently. However, the control parameters learned by one robot may contain valuable information for others. Thus, we introduce a social learning approach in which robots can exploit optimized parameters from their peers to accelerate their own brain optimization. Within this framework, we systematically investigate how the selection of teachers, deciding which and how many robots to learn from, affects performance, experimenting with virtual soft robots in four tasks and environments. In particular, we study the effect of inheriting experience from morphologically similar robots due to the tightly coupled body and brain in robot optimization. Our results confirm the effectiveness of building on others' experience, as social learning clearly outperforms learning from scratch under equivalent computational budgets. In addition, while the optimal teacher selection strategy remains open, our findings suggest that incorporating knowledge from multiple teachers can yield more consistent and robust improvements.

K. Ege de Bruin, Kyrre Glette, Kai Olav Ellefsen +2

Department of Informatics, University of Oslo, Oslo, Norway · Also with RITMO, University of Oslo. · University Toulouse Capitole, IRIT - CNRS UMR5505, Toulouse, France +1

Evolutionary RoboticsRobot Morphology-Control Co-Design
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Apr 13, 2026

A Foot Resistive Force Model for Legged Locomotion on Muddy Terrains

Legged robots face significant challenges in moving and navigating on deformable and highly yielding terrain such as mud. We present a resistive force model for legged foot-mud interactions. The model captures rheological behaviors such as visco-elasticity, thixotropy of the mud suspension and retractive suction. One attractive property of this new model lies in its effective, uniform formulation to provide underlying physical interpretation and accurate resistive force predictions. We further take advantage of the resistive force model to design a new morphing robotic foot for effective and efficient legged locomotion. We conduct extensive experiments to validate the force model, and the results demonstrate that the morphing foot enhances not only the locomotion mobility but also energy-efficiency of walking in mud. The new resistive force model can be further used to develop data-driven simulation and locomotion control of legged robots on muddy terrains.

Xunjie Chen, Liuyin Wang, Xinyan Huang +3

Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854 USA · Department of Electrical and Biomedical Engineering, University of Nevada, Reno, NV 89557 USA

Robot LocomotionTerrain-Aware Robot LocomotionEnergy-Efficient Robot LocomotionRobot Morphology-Control Co-Design
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Apr 13, 2026

Identifying and Exploiting Structure in Robot Co-Design

Co-design is a high-dimensional search problem in the robot morphology and control design space. Efficient search requires exploiting the structure shaped by their interaction. To understand this structure, we analyze the landscapes of soft locomotion and manipulation tasks. We identify three patterns consistent across regions of their co-design spaces: 1) Within a region, quality varies along a low-dimensional manifold, with minimal variation orthogonal to it, reducing the effective search space dimensionality. 2) In higher-quality regions, the variance in quality is spread across more dimensions, necessitating search to expand dimensionality as quality improves. 3) In higher-quality regions, quality varies along joint morphology-control dimensions, requiring search along them. Using these insights, we devise an efficient co-design algorithm that yields 36% better co-designs than state-of-the-art baselines. We examine their exploration patterns and show that these baselines required an order of magnitude more function evaluations to find co-designs of comparable quality. Finally, we ablate our algorithm to verify that exploiting the identified structure was the key to efficient co-design.

Apoorv Vaish, Oliver Brock

Robotics and Biology Laboratory, Technische Universität Berlin · Science of Intelligence (SCIoI), Cluster of Excellence, Berlin · Robotics Institute Germany (RIG)

Robot Morphology-Control Co-DesignRobotic ManipulationRobot LocomotionHardware-Software Co-Design
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Apr 9, 2026

LEGO: Latent-space Exploration for Geometry-aware Optimization of Humanoid Kinematic Design

Designing robot morphologies and kinematics has traditionally relied on human intuition, with little systematic foundation. Motion-design co-optimization offers a promising path toward automation, but two major challenges remain: (i) the vast, unstructured design space and (ii) the difficulty of constructing task-specific loss functions. We propose a new paradigm that minimizes human involvement by (i) learning the design search space from existing mechanical designs, rather than hand-crafting it, and (ii) defining the loss directly from human motion data via motion retargeting and Procrustes analysis. Using screw-theory-based joint axis representation and isometric manifold learning, we construct a compact, geometry-preserving latent space of humanoid upper body designs in which optimization is tractable. We then solve design optimization in this latent space using gradient-free optimization. Our approach establishes a principled framework for data-driven robot design and demonstrates that leveraging existing designs and human motion can effectively guide the automated discovery of novel robot design.

Jihwan Yoon, Taemoon Jeong, Jeongeun Park +5

Department of Artificial Intelligence, Korea University, Seoul 02841, Republic of Korea · Contoro Robotics, Austin, TX 78758, USA · Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA +1

Robot Morphology-Control Co-DesignHumanoid RoboticsLatent Space Optimization
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Apr 9, 2026

EvoGymCM: Harnessing Continuous Material Stiffness for Soft Robot Co-Design

In the automated co-design of soft robots, precisely adapting the material stiffness field to task environments is crucial for unlocking their full physical potential. However, mainstream platforms (e.g., EvoGym) strictly discretize the material dimension, artificially restricting the design space and performance of soft robots. To address this, we propose EvoGymCM (EvoGym with Continuous Materials), a benchmark suite formally establishing continuous material stiffness as a first-class design variable alongside morphology and control. Aligning with real-world material mechanisms, EvoGymCM introduces two settings: (i) EvoGymCM-R (Reactive), motivated by programmable materials with dynamically tunable stiffness; and (ii) EvoGymCM-I (Invariant), motivated by traditional materials with invariant stiffness fields. To tackle the resulting high-dimensional coupling, we formulate two Morphology-Material-Control co-design paradigms: (i) Reactive-Material Co-Design, which learns real-time stiffness tuning policies to guide programmable materials; and (ii) Invariant-Material Co-Design, which jointly optimizes morphology and fixed material fields to guide traditional material fabrication. Systematic experiments across diverse tasks demonstrate that continuous material optimization boosts performance and unlocks synergy across morphology, material, and control.

Le Shen, Kangyao Huang, Wentao Zhao +1

College of Control Science and Engineering, Zhejiang University. · Department of Computer Science and Technology, Tsinghua University.

Soft RoboticsRobot Morphology-Control Co-Design
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Apr 1, 2026

Physical Imitation Learning: Distilling Control Policies into Passive Elasticity

Due to brain-body co-evolution, animals' intrinsic body dynamics play a crucial role in their energy-efficient locomotion. Specifically, the control effort is shared between active muscles and passive body dynamics--a principle often referred to as Physical Intelligence. As a result, the body dynamics are part of the solution. In contrast, robot bodies are typically designed to be as simple as possible, but the active control often fights the intrinsic body dynamics, resulting in low energy-efficiency. We introduce Physical Imitation Learning (PIL), a novel approach that brings current robotics control closer to animals. PIL takes learned control policies obtained with Reinforcement Learning (RL) and systematically splits them up into an active and passive control contribution. The passive part can be then directly offloaded to passive Parallel Elastic Joints (PEJs). As a result, the active control contribution is significantly reduced, lowering the overall energy consumption. Furthermore, the policy can be trained via RL to leverage the PEJ assistance by generating gaits that are more readily emulated by the PEJs. This enables co-design of the active and passive control components, shifting a greater share of actuation effort to the PEJs. Here we demonstrate the potential of this approach in simulated quadrupeds. Our results show that the proposed approach can offload up to 95% of mechanical power to passive body dynamics on flat terrain and 13% on rough terrain. PIL thereby provides a generalisable route to task-specific Physical Intelligence applicable to a wide range of joint-based robot morphologies.

Huyue Ma, Yurui Jin, Helmut Hauser +1

School of Engineering Mathematics and Technology, University of Bristol, and the Bristol Robotics Laboratory, BS8 1QU, United Kingdom

Energy-Efficient Robot LocomotionRobot Morphology-Control Co-DesignImitation Learning
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Mar 27, 2026

SwarmCoDe: A Scalable Co-Design Framework for Heterogeneous Robot Swarms via Dynamic Speciation

Robot swarms offer inherent robustness and the capacity to execute complex, collaborative tasks surpassing the capabilities of single-agent systems. Co-designing these systems is critical, as marginal improvements in individual performance or unit cost compound significantly at scale. However, under traditional frameworks, this scale renders co-design intractable due to exponentially large, non-intuitive design spaces. To address this, we propose SwarmCoDe, a novel Collaborative Co-Evolutionary Algorithm (CCEA) that utilizes dynamic speciation to automatically scale swarm heterogeneity to match task complexity. Inspired by biological signaling mechanisms for inter-species cooperation, the algorithm uses evolved genetic tags and a selectivity gene to facilitate the emergent identification of symbiotically beneficial partners without predefined species boundaries. Additionally, an evolved dominance gene dictates the relative swarm composition, decoupling the physical swarm size from the evolutionary population. We apply SwarmCoDe to simultaneously optimize task planning and hardware morphology under fabrication budgets, successfully evolving specialized swarms of up to 200 agents -- four times the size of the evolutionary population. This framework provides a scalable, computationally viable pathway for the holistic co-design of large-scale, heterogeneous robot swarms.

Andrew Wilhelm, Josie Hughes

Department of Mechanical Engineering, École Polytechnique Fédérale de Lausanne

Swarm RoboticsEvolutionary RoboticsRobot Morphology-Control Co-DesignEvolutionary Optimization
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Mar 20, 2026

Generalized Task-Driven Design of Soft Robots via Reduced-Order FEM-based Surrogate Modeling

Task-driven design of soft robots requires models that are physically accurate and computationally efficient, while remaining transferable across actuator designs and task scenarios. However, existing modeling approaches typically face a fundamental trade-off between physical fidelity and computational efficiency, which limits model reuse across design and task variations and constrains scalable task-driven optimization. This paper presents a unified reduced-order finite element method (FEM)-based surrogate modeling pipeline for generalized task-driven soft robot design. High-fidelity FEM simulations characterize actuator behavior at the modular level, from which compact surrogate joint models are constructed for evaluation within a pseudo-rigid body model (PRBM). A meta-model maps actuator design parameters to surrogate representations, enabling rapid instantiation across a parameterized actuator family. The resulting models are embedded into a PRBM-based simulation environment, supporting task-level simulation and optimization under realistic physical constraints. The proposed pipeline is validated through sim-to-real transfer across multiple actuator types, including bellow-type pneumatic actuators and a tendon-driven soft finger, as well as two task-driven design studies: soft gripper co-design via Reinforcement Learning (RL) and 3D actuator shape matching via evolutionary optimization. The results demonstrate high accuracy, efficiency, and reliable reuse, providing a scalable foundation for autonomous task-driven soft robot design.

Yao Yao, David Howard, Perla Maiolino

Oxford Robotics Institute, University of Oxford, UK · CSIRO Robotics, CSIRO, Australia

Soft RoboticsSurrogate ModelingReduced-Order ModelingRobot Morphology-Control Co-Design
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Mar 20, 2026

Evolving Embodied Intelligence: Graph Neural Network--Driven Co-Design of Morphology and Control in Soft Robotics

The intelligent behavior of robots does not emerge solely from control systems, but from the tight coupling between body and brain, a principle known as embodied intelligence. Designing soft robots that leverage this interaction remains a significant challenge, particularly when morphology and control require simultaneous optimization. A significant obstacle in this co-design process is that morphological evolution can disrupt learned control strategies, making it difficult to reuse or adapt existing knowledge. We address this by develop a Graph Neural Network-based approach for the co-design of morphology and controller. Each robot is represented as a graph, with a graph attention network (GAT) encoding node features and a pooled representation passed through a multilayer perceptron (MLP) head to produce actuator commands or value estimates. During evolution, inheritance follows a topology-consistent mapping: shared GAT layers are reused, MLP hidden layers are transferred intact, matched actuator outputs are copied, and unmatched ones are randomly initialized and fine-tuned. This morphology-aware policy class lets the controller adapt when the body mutates. On the benchmark, our GAT-based approach achieves higher final fitness and stronger adaptability to morphological variations compared to traditional MLP-only co-design methods. These results indicate that graph-structured policies provide a more effective interface between evolving morphologies and control for embodied intelligence.

Jianqiang Wang, Shuaiqun Pan, Alvaro Serra-Gomez +2

LIACS, Leiden University · School of Mechanical Engineering, Xi’an Jiaotong University · Department of Computer Science, Loughborough University

Robot Morphology-Control Co-DesignRobot Policy AdaptationEvolutionary RoboticsSoft Robotics
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Mar 19, 2026

Efficient and Versatile Quadrupedal Skating: Optimal Co-design via Reinforcement Learning and Bayesian Optimization

In this paper, we present a hardware-control co-design approach that enables efficient and versatile roller skating on quadrupedal robots equipped with passive wheels. Passive-wheel skating reduces leg inertia and improves energy efficiency, particularly at high speeds. However, the absence of direct wheel actuation tightly couples mechanical design and control. To unlock the full potential of this modality, we formulate a bilevel optimization framework: an upper-level Bayesian Optimization searches the mechanical design space, while a lower-level Reinforcement Learning trains a motor control policy for each candidate design. The resulting design-policy pairs not only outperform human-engineered baselines, but also exhibit versatile behaviors such as hockey stop (rapid braking by turning sideways to maximize friction) and self-aligning motion (automatic reorientation to improve energy efficiency in the direction of travel), offering the first system-level study of dynamic skating motion on quadrupedal robots.

Hanwen Wang, Zhenlong Fang, Josiah Hanna +1

Hanwen Wang, Zhenlong Fang, and Josiah Hanna are with the University of Wisconsin - Madison. · Xiaobin Xiong was with the University of Wisconsin - Madison, and now with the Shanghai Innovation Institute (SII).

Robot Morphology-Control Co-DesignQuadruped LocomotionEnergy-Efficient Robot Locomotion
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Mar 17, 2026

Reconciling distributed compliance with high-performance control in continuum soft robotics

High-performance closed-loop control of truly soft continuum manipulators has remained elusive. Experimental demonstrations have largely relied on sufficiently stiff, piecewise architectures in which each actuated segment behaves as a distributed yet effectively rigid element, while deformation modes beyond simple bending are suppressed. This strategy simplifies modeling and control, but sidesteps the intrinsic complexity of a fully compliant body and makes the system behave as a serial kinematic chain, much like a conventional articulated robot. An implicit conclusion has consequently emerged within the community: distributed softness and dynamic precision are incompatible. Here we show this trade-off is not fundamental. We present a highly compliant, fully continuum robotic arm - without hardware discretization or stiffness-based mode suppression - that achieves fast, precise task-space convergence under dynamic conditions. The platform integrates direct-drive actuation, a tendon routing scheme enabling coupled bending and twisting, and a structured nonlinear control architecture grounded in reduced-order strain modeling of underactuated systems. Modeling, actuation, and control are co-designed to preserve essential mechanical complexity while enabling high-bandwidth loop closure. Experiments demonstrate accurate, repeatable execution of dynamic Cartesian tasks, including fast positioning and interaction. The proposed system achieves the fastest reported task-execution speed among soft robots. At millimetric precision, execution speed increases nearly fourfold compared with prior approaches, while operating on a fully compliant continuum body. These results show that distributed compliance and high-performance dynamic control can coexist, opening a path toward truly soft manipulators approaching the operational capabilities of rigid robots without sacrificing morphological richness.

Vito Daniele Perfetta, Daniel Feliu-Talegon, Ebrahim Shahabi +1

Cognitive Robotics Department, Faculty of Mechanical Engineering, Delft University of Technology, Delft 2628 CD, The Netherlands.

Continuum Robot ControlSoft RoboticsRobotic ControlRobot Morphology-Control Co-Design
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Mar 16, 2026

Efficient Morphology-Control Co-Design via Stackelberg Proximal Policy Optimization

Morphology-control co-design concerns the coupled optimization of an agent's body structure and control policy. This problem exhibits a bi-level structure, where the control dynamically adapts to the morphology to maximize performance. Existing methods typically neglect the control's adaptation dynamics by adopting a single-level formulation that treats the control policy as fixed when optimizing morphology. This can lead to inefficient optimization, as morphology updates may be misaligned with control adaptation. In this paper, we revisit the co-design problem from a game-theoretic perspective, modeling the intrinsic coupling between morphology and control as a novel variant of a Stackelberg game. We propose Stackelberg Proximal Policy Optimization (Stackelberg PPO), which explicitly incorporates the control's adaptation dynamics into morphology optimization. By modeling this intrinsic coupling, our method aligns morphology updates with control adaptation, thereby stabilizing training and improving learning efficiency. Experiments across diverse co-design tasks demonstrate that Stackelberg PPO outperforms standard PPO in both stability and final performance, opening the way for dramatically more efficient robotics designs.

Yanning Dai, Yuhui Wang, Dylan R. Ashley +1

Center of Excellence for Generative AI, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia. · Dalle Molle Institute for Artificial Intelligence Research (IDSIA), Lugano, Switzerland. · Università della Svizzera italiana (USI), Lugano, Switzerland. +1

Robot Morphology-Control Co-DesignBilevel OptimizationProximal Policy Optimization
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Mar 12, 2026

Robots that redesign themselves through kinematic self-destruction

Every robot built to date was predesigned by an external process, prior to deployment. Here we show a robot that actively participates in its own design during its lifetime. Starting from a randomly assembled body, and using only proprioceptive feedback, the robot dynamically ``sculpts'' itself into a new design through kinematic self-destruction: identifying redundant links within its body that inhibit its locomotion, and then thrashing those links against the surface until they break at the joint and fall off the body. It does so using a single autoregressive sequence model, a universal controller that learns in simulation when and how to simplify a robot's body through self-destruction and then adaptively controls the reduced morphology. The optimized policy successfully transfers to reality and generalizes to previously unseen kinematic trees, generating forward locomotion that is more effective than otherwise equivalent policies that randomly remove links or cannot remove any. This suggests that self-designing robots may be more successful than predesigned robots in some cases, and that kinematic self-destruction, though reductive and irreversible, could provide a general adaptive strategy for a wide range of robots.

Chen Yu, Sam Kriegman

Northwestern University

RoboticsRobot Morphology-Control Co-DesignRobot LearningRobot Locomotion
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Mar 11, 2026

Robust Co-design Optimisation for Agile Fixed-Wing UAVs

Co-design optimisation of autonomous systems has emerged as a powerful alternative to sequential approaches by jointly optimising physical design and control strategies. However, existing frameworks often neglect the robustness required for autonomous systems navigating unstructured, real-world environments. For agile Unmanned Aerial Vehicles (UAVs) operating at the edge of the flight envelope, this lack of robustness yields designs that are sensitive to perturbations and model mismatch. To address this, we propose a robust co-design framework for agile fixed-wing UAVs that integrates parametric uncertainty and wind disturbances directly into the concurrent optimisation process. Our bi-level approach optimises physical design in a high-level loop while discovering nominal solutions via a constrained trajectory planner and evaluating performance across a stochastic Monte Carlo ensemble using feedback LQR control. Validated across three agile flight missions, our strategy consistently outperforms deterministic baselines. The results demonstrate that our robust co-design strategy inherently tailors aerodynamic features, such as wing placement and aspect ratio, to achieve an optimal trade-off between mission performance and disturbance rejection.

Adrian Andrei Buda, Xavier Chen, Nicolò Botteghi +1

Department of Aeronautics, Imperial College London, United Kingdom · Department of Mathematics, Politecnico di Milano, Italy

Robot Morphology-Control Co-DesignAerial RoboticsRobust ControlUAV Trajectory Optimization
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Mar 10, 2026

Embodied Human Simulation for Quantitative Design and Analysis of Interactive Robotics

Physical interactive robotics, ranging from wearable devices to collaborative humanoid robots, require close coordination between mechanical design and control. However, evaluating interactive dynamics is challenging due to complex human biomechanics and motor responses. Traditional experiments rely on indirect metrics without measuring human internal states, such as muscle forces or joint loads. To address this issue, we develop a scalable simulation-based framework for the quantitative analysis of physical human-robot interaction. At its core is a full-body musculoskeletal model serving as a predictive surrogate for the human dynamical system. Driven by a reinforcement learning controller, it generates adaptive, physiologically grounded motor behaviors. We employ a sequential training pipeline where the pre-trained human motion control policy acts as a consistent evaluator, making large-scale design space exploration computationally tractable. By simulating the coupled human-robot system, the framework provides access to internal biomechanical metrics, offering a systematic way to concurrently co-optimize a robot's structural parameters and control policy. We demonstrate its capability in optimizing human-exoskeleton interactions, showing improved joint alignment and reduced contact forces. This work establishes embodied human simulation as a scalable paradigm for interactive robotics design.

Chenhui Zuo, Jinhao Xu, Michael Qian Vergnolle +1

The authors are with the School of Aerospace Engineering, Tsinghua University, Beijing, China 100084.

Musculoskeletal ModelingRoboticsHuman-Robot InteractionRobotics SimulationRobot Morphology-Control Co-Design
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Mar 8, 2026

Unifying Sidewinding and Rolling: A Wave-Based Framework for Self-Righting in Elongated Limbless and Multi-Legged Robots

Centipede-like robots offer unique locomotion advantages due to their small cross-sectional area for accessing confined spaces, and their redundant legs enhance robustness in cluttered environments such as search-and-rescue and pipe inspection. However, elongated robots are particularly vulnerable to tipping over when climbing large obstacles, making reliable self-righting essential for field deployment. Self-righting strategies for elongate, multi-legged systems remain poorly understood. In this study, we conduct a comparative biomechanics and robophysical investigation to address three key questions: (1) What self-righting strategies are effective for elongate, many-legged systems? (2) How should these strategies depend on morphological parameters such as leg length and leg number? (3) Is there a morphological limit beyond which reliable self-righting becomes infeasible? We compare two biological exemplars: Scolopendra subspinipes (short legs) and Scutigera coleoptrata (house centipedes with long legs). Scolopendra subspinipes reliably self-rights both during aerial phases and through ground-assisted self-righting, whereas house centipedes rely predominantly on aerial reorientation and struggle to generate effective self-righting torques during ground contact. Motivated by these observations, we construct a parameterized space of bio-inspired self-righting strategies and develop an elongate robot with adjustable leg lengths. Systematic experiments reveal that increasing leg length necessitates a shift in control strategy to prevent torque over-concentration in mid-body actuators, and we identify a critical limb-length threshold above which robust self-righting becomes challenging. These results establish morphology-strategy coupling principles for self-righting in elongate robots and provide design guidelines for centipede-like systems operating in uncertain terrain.

Hangjun Liu, Jiarui Geng, Jinxuan Ding +7

Legged RoboticsRobot LocomotionRobot Morphology-Control Co-Design
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Mar 6, 2026

A Unified Low-Dimensional Design Embedding for Joint Optimization of Shape, Material, and Actuation in Soft Robots

Soft robots achieve functionality through tight coupling among geometry, material composition, and actuation. As a result, effective design optimization requires these three aspects to be considered jointly rather than in isolation. This coupling is computationally challenging: nonlinear large-deformation mechanics increase simulation cost, while contact, collision handling, and non-smooth state transitions limit the applicability of standard gradient-based approaches. We introduce a smooth, low-dimensional design embedding for soft robots that unifies shape morphing, multi-material distribution, and actuation within a single structured parameter space. Shape variation is modeled through continuous deformation maps of a reference geometry, while material properties are encoded as spatial fields. Both are constructed from shared basis functions. This representation enables expressive co-design while drastically reducing the dimensionality of the search space. In our experiments, we show that design expressiveness increases with the number of basis functions, unlike comparable neural network encodings whose representational capacity does not scale predictably with parameter count. We further show that joint co-optimization of shape, material, and actuation using our unified embedding consistently outperforms sequential strategies. All experiments are performed independently of the underlying simulator, confirming compatibility with black-box simulation pipelines. Across multiple dynamic tasks, the proposed embedding surpasses neural network and voxel-based baseline parameterizations while using significantly fewer design parameters. Together, these findings demonstrate that structuring the design space itself enables efficient co-design of soft robots.

Vittorio Candiello, Manuel Mekkattu, Mike Y. Michelis +1

Soft Robotics Lab, D-MAVT, ETH Zurich, Switzerland. · ETH AI Center, ETH Zurich, Switzerland.

Soft RoboticsRobot Morphology-Control Co-Design
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Mar 6, 2026

Neural-Surrogate Co-Design of Aerodynamic Shape and Control

Control co-design jointly optimizes a robot's physical design and its controller. Existing techniques are limited in the number of model parameters and the complexity of the physical models they can handle. In this paper, we propose a gradient-based bilevel formulation that replaces the dynamics models of earlier techniques with a differentiable neural surrogate and differentiates through the trajectory optimizer using a structure-exploiting approach. We validate the framework on fixed-wing gliders, using NeuralFoil as the aerodynamic surrogate. The tasks are maximum-distance gliding, minimum-distance landing, and perching. Experiments on 2D airfoils and 3D wings show that our method runs about five times faster than a state-of-the-art evolutionary baseline. It also outperforms pipelines that optimize aerodynamic proxy metrics.

Daniele Affinita, Mingda Xu, Benoît Valentin Gherardi +1

École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

Robot Morphology-Control Co-DesignAerial RoboticsUAV Trajectory Optimization
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Feb 25, 2026

System Design of the Ultra Mobility Vehicle: A Driving, Balancing, and Jumping Bicycle Robot

Trials cyclists and mountain bike riders can hop, jump, balance, and drive on one or both wheels. This versatility allows them to achieve speed and energy-efficiency on smooth terrain and agility over rough terrain. Inspired by these athletes, we present the design and control of a robotic platform, Ultra Mobility Vehicle (UMV), which combines a bicycle and a reaction mass to move dynamically with minimal actuated degrees of freedom. We employ a simulation-driven design optimization process to synthesize a spatial linkage topology with a focus on vertical jump height and momentum-based balancing on a single wheel contact. Using a constrained Reinforcement Learning (RL) framework, we demonstrate zero-shot transfer of diverse athletic behaviors, including track-stands, jumps, wheelies, rear wheel hopping, and front flips. This 23.5 kg robot is capable of high speeds (8 m/s) and jumping on and over large obstacles (1 m tall, or 130% of the robot's nominal height).

Benjamin Bokser, Daniel Gonzalez, Aaron Preston +39

Robot LocomotionRobot Morphology-Control Co-DesignRobotic Control
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Feb 21, 2026

Bumper Drone: Elastic Morphology Design for Aerial Physical Interaction

Aerial robots are evolving from avoiding obstacles to exploiting the environmental contact interactions for navigation, exploration and manipulation. A key challenge in such aerial physical interactions lies in handling uncertain contact forces on unknown targets, which typically demand accurate sensing and active control. We present a drone platform with elastic horns that enables touch-and-go manoeuvres - a self-regulated, consecutive bumping motion that allows the drone to maintain proximity to a wall without relying on active obstacle avoidance. It leverages environmental interaction as a form of embodied control, where low-level stabilisation and near-obstacle navigation emerge from the passive dynamic responses of the drone-obstacle system that resembles a mass-spring-damper system. Experiments show that the elastic horn can absorb impact energy while maintaining vehicle stability, reducing pitch oscillations by 38% compared to the rigid horn configuration. The lower horn arrangement was found to reduce pitch oscillations by approximately 54%. In addition to intermittent contact, the platform equipped with elastic horns also demonstrates stable, sustained contact with static objects, relying on a standard attitude PID controller.

Pongporn Supa, Alex Dunnett, Feng Xiao +3

School of Engineering Mathematics and Technology, University of Bristol. · School of Civil, Aerospace and Design Engineering, University of Bristol. · Department of Aeronautics, Imperial College London, London, UK. +1

Aerial RoboticsRobot Morphology-Control Co-Design
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Feb 20, 2026

Latent Diffeomorphic Co-Design of End-Effectors for Deformable and Fragile Object Manipulation

Manipulating deformable and fragile objects remains a fundamental challenge in robotics due to complex contact dynamics and strict requirements on object integrity. Existing approaches typically optimize either end-effector design or control strategies in isolation, limiting achievable performance. In this work, we present the first co-design framework that jointly optimizes end-effector morphology and manipulation control for deformable and fragile object manipulation. We introduce (1) a latent diffeomorphic shape parameterization enabling expressive yet tractable end-effector geometry optimization, (2) a stress-aware bi-level co-design pipeline coupling morphology and control optimization, and (3) a privileged-to-pointcloud policy distillation scheme for zero-shot real-world deployment. We evaluate our approach on challenging food manipulation tasks, including grasping and pushing jelly and scooping fillets. Simulation and real-world experiments demonstrate the effectiveness of the proposed method.

Kei Ikemura, Yifei Dong, Florian T. Pokorny

Robot Morphology-Control Co-DesignDeformable Object ManipulationRobotic GraspingDexterous Manipulation
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Dec 3, 2025

House of Dextra: Cross-embodied Co-design for Dexterous Hands

Dexterous manipulation is limited by both control and design, without consensus as to what makes manipulators best for performing dexterous tasks. This raises a fundamental challenge: how should we design and control robot manipulators that are optimized for dexterity? We present a co-design framework that learns task-specific hand morphology and complementary dexterous control policies. The framework supports 1) an expansive morphology search space including joint, finger, and palm generation, 2) scalable evaluation across the wide design space via morphology-conditioned cross-embodied control, and 3) real-world fabrication with accessible components. We evaluate the approach across multiple dexterous tasks, including in-hand rotation with simulation and real deployment. Our framework enables an end-to-end pipeline that can design, train, fabricate, and deploy a new robotic hand in under 24 hours. The full framework and generated robot hands are open-sourced and available on our website.

Kehlani Fay, Darin Anthony Djapri, Anya Zorin +6

University of California, San Diego · University of California, Santa Barbara

Robotic Hand DesignDexterous ManipulationRobot Morphology-Control Co-DesignCross-Embodiment Robot LearningRobotics
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Oct 29, 2025

Debate2Create: Robot Co-design via Multi-Agent LLM Debate

We introduce Debate2Create (D2C), a multi-agent LLM framework that formulates robot co-design as structured, iterative debate grounded in physics-based evaluation. A design agent and control agent engage in a thesis-antithesis-synthesis loop, while criterion-specific LLM judges provide multi-objective feedback to steer exploration. Across five MuJoCo locomotion benchmarks, D2C achieves the highest default-normalized score among the evaluated LLM-based and black-box baselines, with gains up to 3.2x on Ant and nearly 9x on Swimmer. Iterative debate yields 18-35% gains over compute-matched zero-shot generation, and D2C-generated rewards transfer to default morphologies in 4/5 tasks. These results suggest that structured, simulator-grounded multi-agent interaction is a useful mechanism for joint morphology-reward optimization under a fixed-topology, per-candidate-RL protocol. Project page: debate2create.github.io.

Kevin Qiu, Marek Cygan

University of Warsaw · 2IDEAS NCBR · 3Nomagic

Robot Morphology-Control Co-DesignMulti-Agent DebateRobot LocomotionMulti-Agent LLMsAgentic AI for RoboticsMulti-Agent Deliberation
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Oct 3, 2025

Toward Physical Recursive Self-Improvement: A Call for Body-Control Co-Design for Humanoid Robot

Humanoid robots, as general-purpose physical agents, must integrate both intelligent control and adaptive morphology to operate effectively in diverse real-world environments. While recent research primarily optimizes control policies for fixed bodies, we advocate body-control co-design as a path toward physical Recursive Self-Improvement (RSI): using experience from a humanoid's current body and policy to guide successive improvements to both. Inspired by biological evolution, this approach enables robots to recursively adapt both their form and behavior to optimize performance within task-specific and resource-constrained contexts. Despite its promise, co-design in humanoid robotics remains a relatively underexplored domain, raising fundamental questions about its feasibility and necessity in achieving true embodied intelligence. To address these challenges, we discuss potential co-design methodologies grounded in strategic exploration, Sim2Real transfer, and meta-policy learning. We further argue for the essential role of co-design by analyzing it from methodological, application-driven, and community-oriented perspectives. Striving to guide and inspire future studies, we present open research questions, spanning from short-term innovations to long-term goals. Ultimately, co-design offers a path toward physical RSI in humanoids that improves their bodies and policies while learning to make this improvement process more effective.

Guiliang Liu, Bo Yue, Yi Jin Kim +1

The Chinese University of Hong Kong (Shenzhen) · DexForce Technology

Robot Morphology-Control Co-DesignHumanoid Robotics
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