Over the past few decades, biomimetic robotic experiments have significantly advanced our understanding of undulatory swimming. Compared to animal experiments, robotic experiments offer repeatability and controlled parameter variations, but the robots operate under constraints that differ from those experienced by their natural counterparts. Freely swimming robots often remain on the surface, whereas most undulatory fish, including eels, are typically fully submerged during locomotion. Studies focusing on submerged swimming commonly rely on tethered robots to maintain depth control. 
This study examines the performance implications for free versus tethered swimming at the surface, and for tethered swimming at the surface to tethered fully submerged swimming, using the robotic undulatory swimmer 1-guilla.
The robot was tested in two configurations: free swimming in a pool and tethered swimming in a water channel at the surface and at varying depths down to three body heights. We varied kinematic input parameters and quantified performance in terms of swimming speed, cost of transport, and body kinematics. Our results reveal that at the surface, tethered swimming achieves speeds comparable to free swimming but at a lower energetic cost. 
This reduction in cost of transport is attributed to the mechanical stabilisation imposed by tethering, including the suppression of body roll and lateral head motion.
Increasing submergence depth improved both the maximum speed and energy efficiency by more than 10\% relative to the surface swimming performance. As the body kinematics remained unchanged when submerged, the performance deficit near the surface is attributed to increased wave drag. Overall, our findings provide explanations and insights into discrepancies in results obtained for tethered and free-swimming robotic studies, they highlight the hydrodynamic challenges of surface locomotion, and can help explain why natural undulatory swimmers predominantly favour submerged propulsion.

Computational models are critical to advance our understanding of how neural, biomechanical, and physical systems interact to orchestrate animal behaviors. Despite the availability of near-complete reconstructions of the Drosophila melanogaster central nervous system, musculature, and exoskeleton, anatomically and physically grounded models of fly leg muscles are still missing. These models provide an indispensable bridge between motor neuron activity and joint movements. Here, we introduce the first 3D, data-driven musculoskeletal model of Drosophila legs, implemented in both OpenSim and MuJoCo simulation environments. Our model incorporates a Hill-type muscle representation based on high-resolution X-ray scans from multiple fixed specimens. We present a pipeline for constructing muscle models using morphological imaging data and for optimizing unknown muscle parameters specific to the fly. We then combine our musculoskeletal models with detailed 3D pose estimation data from behaving flies to achieve muscle-actuated behavioral replay in OpenSim. Simulations of muscle activity across diverse walking and grooming behaviors predict coordinated muscle synergies that can be tested experimentally. Furthermore, by training imitation learning policies in MuJoCo, we test the effect of different passive joint properties on learning speed and find that damping and stiffness facilitate learning. Overall, our model enables the investigation of motor control in an experimentally tractable model organism, providing insights into how biomechanics contribute to generation of complex limb movements. Moreover, our model can be used to control embodied artificial agents to generate naturalistic and compliant locomotion in simulated environments.

A cervical spinal cord injury disrupts the signals between the brain and the region of the spinal cord that coordinates arm and hand movements, causing paralysis. Here, we engineered a chronically implanted and durable Digital Bridge that reestablishes communication between the brain and cervical spinal cord. This technology consists of a brain implant to record electrocorticography from the sensorimotor cortex, and a neurostimulation platform to deliver epidural electrical stimulation over the entire cervical spinal cord unilaterally. We implanted this Digital Bridge in three individuals with chronic incomplete tetraplegia. We configured a library of stimulation patterns that supported gradual control over various elementary movements of the arm and hand. A decoding pipeline incorporating a foundation model of human brain activity predicted up to 8 motor states with high accuracy. In turn, linking decoding predictions to the modulation of stimulation patterns targeting the preprogrammed elementary movements enabled the three participants to perform functional tasks with their otherwise paralyzed arm and hand. The Digital Bridge has remained stable for more than one year, and has been compatible with long-term stability and safety. While additional technological developments and clinical validations in a diverse patient population are required, these results establish essential concepts to enable arm and hand movements in humans living with chronic tetraplegia.

Large-scale neuroscience is generating rich datasets across animals, brain areas and behavioral contexts, yet our modeling efforts remains fragmented across isolated experiments. We argue that understanding behavior requires integrative neurocybernetic models: understandable dynamical models that capture the closed-loop coupling of brain, body and environment, treat the brain as a controller pursuing latent objectives, represent structured variation across scales, and scale to heterogeneous datasets. Such models shift the goal from predicting neural recordings in isolation to inferring the organizing principles that govern neural and behavioral dynamics. We outline a practical route toward this goal by combining nonlinear state-space models and meta-dynamical extensions with scalable inference, knowledge distillation, mixed open- and closed-loop training, and connectomics-informed architectures. By pooling complementary constraints from recordings, behavior, perturbations and anatomy, integrative neurocybernetic models can provide statistical amplification, few-shot generalization, and mechanistic insight into shared dynamical structure, individual variation, and the control objectives that govern behavior. This agenda offers a model-centric path from fragmented data to a mechanistic science of how brains produce behavior.

Modular reconfigurable robot (MRR) systems have attracted growing attention because of their versatility and ability to operate across diverse domains. Research on MRR systems has made notable progress, evolving from laboratory settings to real-world applications. However, a gap remains in aligning MRR technologies with specific needs, and a comprehensive review of challenges in practical applications is still lacking. To address these issues, this Review adopts an application-oriented perspective. Focusing on locomotion, manipulation, and construction, it proposes a previously unreported perspective centered on real-world demands. The Review outlines these needs and identifies major challenges facing MRR systems, categorized into three areas: general hardware challenges, general software challenges, and application-specific challenges. This Review aims to inform the development of MRR systems from theory to practice through a demand-technology-application approach. By working backward from practical applications to technical requirements, it identifies technological gaps in specific use cases. It also surveys current research, highlighting strengths, limitations, and potential directions while emphasizing key challenges for future progress.

Amphibious legged robots inspired by salamanders are promising in applications in complex amphibious environments. However, despite the significant success of training controllers that achieve diverse locomotion behaviors in conventional quadrupedal robots, most salamander robots relied on central-pattern-generator (CPG)-based and model-based coordination strategies for locomotion control. Learning unified joint-level whole-body control that reliably transfers from simulation to highly articulated physical salamander robots remains relatively underexplored. In addition, few legged robots have tried learning-based controllers in amphibious environments. In this work, we employ Reinforcement Learning to map proprioceptive observations and commanded velocities to joint-level actions, allowing coordinated locomotor behaviors to emerge. To deploy these policies on hardware, we adopt a system-level real-to-sim matching and sim-to-real transfer strategy. The learned controller achieves stable and coordinated walking on both flat and uneven terrains in the real world. Beyond terrestrial locomotion, the framework enables transitions between walking and swimming in simulation, highlighting a phenomenon of interest for understanding locomotion across distinct physical modes.

Modern imitation-learning policies for robot manipulation often represent actions as fixed-resolution action chunks, which are simple and effective but expose limited geometric and temporal structure before execution. This paper studies Spline Policy (SP), a structured representation that replaces action chunks with spline parameters while keeping the policy backbone unchanged. The predicted spline can be decoded as a compact continuous trajectory, queried at different temporal resolutions, constrained or edited in parameter space, and passed to downstream controllers. For quadratic spline outputs, the same representation can also be converted into a state-dependent vector field through an analytical distance-field construction. Under the regularity and projection assumptions of this construction, the induced dynamics do not increase the distance to the generated spline, yielding a principled local corrective mechanism around the predicted motion. The spline output further supports uncertainty propagation from observations to spline parameters, trajectories, and flow fields, and can be combined with classical control mechanisms such as null-space collision avoidance without retraining the policy backbone. We instantiate SP with diffusion, flow-matching, transformer-based, and vision-language-action backbones. Experiments in low-dimensional motion learning, simulated manipulation under matched backbones, dexterous manipulation, and real-robot case studies show that SP remains compatible with modern policy learners while exposing useful motion-structure properties, including compact decoding, temporal resampling, local correction around predicted motions, uncertainty evaluation, and controller compatibility.

The coordinated movement of animal groups is one of the most widespread social behaviors, which are generally attributed to high-order cognitive processing in the brain. Yet, collective coordination can seemingly emerge from rapid, local interactions between individuals, suggesting the existence of decentralized mechanisms of online coordination that remain to be identified. Here, we show that a low-order spinal sensorimotor circuit is required for real-time social coordination during schooling in zebrafish. Central to this circuit are intraspinal proprioceptive neurons that detect local body bending and deliver direct, curvature-based inhibition to precisely time the locomotor network. Combining electrophysiology, calcium imaging, optogenetics, and behavioral analysis, we show that this circuit encodes both self-generated (egocentric) and neighbor-induced (allocentric) body bending signals, enabling fish to match the phase of their swimming to the wakes of their neighbors (vortex phase matching). In a neuromechanical model and physical robot, this single feedback loop is sufficient to generate vortex phase matching and to lower the energetic cost of swimming. Disrupting this circuit uncouples neighboring fish and abolishes schooling behavior. These results show that a spinal circuit dynamically synchronizes individuals through simple, local interactions, revealing how low-order mechanisms can drive the emergence of coordinated group behavior.

This study introduces a novel neuromechanical model employing a detailed spiking neural network to explore the role of axial proprioceptive sensory feedback, namely stretch feedback, in salamander locomotion. Unlike previous studies that often oversimplified the dynamics of the locomotor networks, our model includes detailed simulations of the classes of neurons that are considered responsible for generating movement patterns. The locomotor circuits, modeled as a spiking neural network of adaptive leaky integrate-and-fire neurons, are coupled to a three-dimensional mechanical model of a salamander with realistic physical parameters and simulated muscles. In open-loop simulations (i.e., without sensory feedback), the model replicates locomotor patterns observed in-vitro and in-vivo for swimming and trotting gaits. Additionally, a modular descending reticulospinal drive to the central pattern generation network allows to accurately control the activation, frequency and phase relationship of the different sections of the limb and axial circuits. In closed-loop swimming simulations (i.e. including axial stretch feedback), systematic evaluations reveal that intermediate values of feedback strength increase the tail beat frequency and reduce the intersegmental phase lag, contributing to a more coordinated, faster and energy-efficient locomotion. Interestingly, the result is conserved across different feedback topologies (ascending or descending, excitatory or inhibitory), suggesting that it may be an inherent property of axial proprioception. Moreover, intermediate feedback strengths expand the stability region of the network, enhancing its tolerance to a wider range of descending drives, internal parameters’ modifications and noise levels. Conversely, high values of feedback strength lead to a loss of controllability of the network and a degradation of its locomotor performance. Overall, this study highlights the beneficial role of proprioception in generating, modulating and stabilizing locomotion patterns, provided that it does not excessively override centrally-generated locomotor rhythms. This work also underscores the critical role of detailed, biologically-realistic neural networks to improve our understanding of vertebrate locomotion.

Simulation is a core component of robotics workflows that can shed light on the complex interplay between a physical body, the environment and sensory feedback mechanisms in silico. To this goal several simulation methods, originating in rigid body dynamics and in continuum mechanics have been employed, enabling the simulation of a plethora of phenomena such as rigid/soft body dynamics, fluid dynamics, muscle simulation as well as sensor and actuator dynamics. The physics engines commonly employed in robotics simulation focus on rigid body dynamics, whereas continuum mechanics methods excel on the simulation of phenomena where deformation plays a crucial role, keeping the two fields relatively separate. Here, we propose a shift of paradigm that allows for the accurate simulation of fluids in interaction with rigid bodies within the same robotics simulation framework, based on the continuum mechanics-based Smoothed Particle Hydrodynamics method. The proposed framework is useful for simulations such as swimming robots with complex geometries, robots manipulating fluids and even robots emitting highly viscous materials such as the ones used for 3D printing. Scenarios like swimming on the surface, air-water transitions, locomotion on granular media can be natively simulated within the proposed framework. Firstly, we present the overall architecture of our framework and give examples of a concrete software implementation. We then verify our approach by presenting one of the first of its kind simulation of self-propelled swimming robots with a smooth particle hydrodynamics method and compare our simulations with real experiments. Finally, we propose a new category of simulations that would benefit from this approach and discuss ways that the sim-to-real gap could be further reduced. One Sentence Summary: We present a framework for the interaction of rigid body dynamics with SPH-based fluid simulation in robotics, showcase its application on self-propelled swimming robots and validate the method by comparing simulations with physical experiments.

We present a framework for learning a single policy capable of producing all quadruped gaits and transitions. The framework consists of a policy trained with deep reinforcement learning (DRL) to modulate the parameters of a system of abstract oscillators (i.e. Central Pattern Generator), whose output is mapped to joint commands through a pattern formation layer that sets the gait style, i.e. body height, swing foot ground clearance height, and foot offset. Different gaits are formed by changing the coupling between different oscillators, which can be instantaneously selected at any velocity by a user. With this framework, we systematically investigate which gait should be used at which velocity, and when gait transitions should occur from a Cost of Transport (COT), i.e. energy-efficiency, point of view. Additionally, we note how gait style changes as a function of locomotion speed for each gait to keep the most energy-efficient locomotion. While the currently most popular gait (trot) does not result in the lowest COT, we find that considering different co-dependent metrics such as mean base angular velocity and joint acceleration result in different 'optimal' gaits than those that minimize COT. We deploy our controller in various hardware experiments, focusing on 9 quadruped animal gaits, and demonstrate generalizability to novel and unseen gaits during training, and robustness to leg failures.

Gait phase (GP) estimation is a critical component in control of exoskeletons and prostheses, enabling seamless user interaction in various controllers. In recent years, methods based on machine learning and sensor fusion have offered advances in GP estimation, but their high computational costs and reliance on training and numerous sensors present practical challenges. Estimation methods using phase variables, such as phase-portrait-based methods, can circumvent these drawbacks. However, their lower accuracy has limited their application. To address this limitation, we introduce a novel human-in-the-loop (HIL) optimization approach for improving the accuracy of GP estimation in phase-portrait-based methods. The approach is based on geometric manipulation of the phase portraits with linear transformations, which are adapted online by employing Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The performance of this adaptive method (termed AM) is compared against using a fixed transformation (FM) at different walking speeds on level and inclined treadmill. The results demonstrate the superior performance of AM in all tested conditions in terms of accuracy and linearity, with an average RMS error of $1.97 \pm 0.20\%$ . Convergence times for one round of optimization on a low-end single-board computer were less than 11 s on average. This study confirms the potential of leveraging HIL optimization for enhancing the performance of phase-portrait-based methods to reach accuracy levels comparable to more complex state-of-the-art methods.

Robots have to adjust their motor behavior to changing environments and variable task requirements to successfully operate in the real world and physically interact with humans. Thus, robotics strives to enable a broad spectrum of adjustable motor behavior, aiming to mimic the human ability to function in unstructured scenarios. In humans, motor behavior arises from the integrative action of the central nervous system and body biomechanics; motion must be understood from a neuromechanics perspective. Nervous regions such as the cerebellum facilitate learning, adaptation, and coordination of our motor responses, ultimately driven by muscle activation. Muscles, in turn, self-stabilize motion through mechanical viscoelasticity. In addition, the agonist-antagonist arrangement of muscles surrounding joints enables cocontraction, which can be regulated to enhance motion accuracy and adapt joint stiffness, thereby providing impedance modulation and broadening the motor repertoire. Here, we propose a control solution that harnesses neuromechanics to enable adjustable robot motor behavior. Our solution integrates a muscle model that replicates mechanical viscoelasticity and cocontraction together with a cerebellar network providing motor adaptation. The resulting cerebello-muscular controller drives the robot through torque commands in a feedback control loop. Changes in cocontraction modify the muscle dynamics, and the cerebellum provides motor adaptation without relying on prior analytical solutions, driving the robot in different motor tasks, including payload perturbations and operation across unknown terrains. Experimental results show that cocontraction modulates robot stiffness, performance accuracy, and robustness against external perturbations. Through cocontraction modulation, our cerebello-muscular torque controller enables a broad spectrum of robot motor behavior.

Humans can perform movements in various physical environments and positions (corresponding to different experienced gravity), requiring the interaction of the musculoskeletal system, the neural system and the external environment. The neural system is itself comprised of several interactive components, from the brain mainly conducting motor planning, to the spinal cord (SC) implementing its own motor control centres through sensory reflexes. Nevertheless, it remains unclear whether similar movements in various environmental dynamics necessitate adapting modulation at the brain level, correcting modulation at the spinal level, or both. Here, we addressed this question by focusing on upper limb motor control in various gravity conditions (magnitudes and directions) and using neuromusculoskeletal simulation tools. We integrated supraspinal sinusoidal commands with a modular SC model controlling a musculoskeletal model to reproduce various recorded arm trajectories (kinematics and EMGs) in different contexts. We first studied the role of various spinal pathways (such as stretch reflexes) in movement smoothness and robustness against perturbation. Then, we optimised the supraspinal sinusoidal commands without and with a fixed SC model including stretch reflexes to reproduce a target trajectory in various gravity conditions. Inversely, we fixed the supraspinal commands and optimised the spinal synaptic strengths in the different environments. In the first optimisation context, the presence of SC resulted in easier optimisation of the supraspinal commands (faster convergence, better performance). The main supraspinal commands modulation was found in the flexor sinusoid’s amplitude, resp. frequency, to adapt to different gravity magnitudes, resp. directions. In the second optimisation context, the modulation of the spinal synaptic strengths also remarkably reproduced the target trajectory for the mild gravity changes. We highlighted that both strategies of modulation of the supraspinal commands or spinal stretch pathways can be used to control movements in different gravity environments. Our results thus support that the SC can assist gravity compensation.

The relationship between morphology and locomotion performance in amphibious fish remains poorly understood, particularly in axial-appendage-based and appendage-based movements. To address this, we introduce Polymander, a reconfigurable robot capable of mimickingPolypterus-like walking and mudskipper-like crutching, enabling systematic investigation of body length and limb movement. Using a CPG-driven controller, we optimize locomotion patterns via multi-objective optimization in simulation, comparing resulting Pareto fronts across different morphological configurations. Our results reveal that (1) mudskipper-like crutching is better suited for short bodies, whilePolypterus-like walking is better suited for longer bodies; (2) symmetric anterior-to-posterior motion of the limbs is optimal for crutching, while increased anterior limb movement benefitsPolypterus-like walking; and (3) sufficient limb strength is necessary for crutching but less so for walking, where axial bending mitigate its effects. Overall, our findings provide a potential explanation of whyPolypterusand mudskippers adopt their distinct gaits, emerging as optimal solutions for their morphology within the broader space of all possible gaits.

The study of animal locomotion and neuromechanical control offers valuable insights for advancing research in neuroscience, biomechanics, and robotics. We have developed FARMS (Framework for Animal and Robot Modeling and Simulation), an open-source, interdisciplinary framework, designed to facilitate access to neuromechanical simulations for modeling, simulation, and analysis of animal locomotion and bio-inspired robotic systems. By providing an accessible and user-friendly platform, FARMS aims to lower the barriers for researchers to explore the complex interactions between the nervous system, musculoskeletal structures, and their environment. Integrating the MuJoCo physics engine in a modular manner, FARMS enables realistic simulations and fosters collaboration among neuroscientists, biologists, and roboticists. FARMS has already been extensively used to study locomotion in animals such as mice, drosophila, fish, salamanders, and centipedes, serving as a platform to investigate the role of central pattern generators and sensory feedback. This article provides an overview of the FARMS framework, discusses its interdisciplinary approach, showcases its versatility through specific case studies, and highlights its effectiveness in advancing our understanding of locomotion. In particular, we show how we used FARMS to study amphibious locomotion by presenting experimental demonstrations across morphologies and environments based on neural controllers with central pattern generators and sensory feedback circuits models. Overall, the goal of FARMS is to contribute to a deeper understanding of animal locomotion, the development of innovative bio-inspired robotic systems, and promote accessibility in neuromechanical research.

Hip exoskeletons are known for their versatility in assisting users across varied scenarios. However, current assistive strategies often lack the flexibility to accommodate for individual walking patterns and adapt to diverse locomotion environments. In this work, we present a novel control strategy that adapts the mechanical impedance of the humanexoskeleton system. We design the hip assistive torques as an adaptive virtual negative damping, which is able to inject energy into the system while allowing the users to remain in control and contribute voluntarily to the movements. Experiments with five healthy subjects demonstrate that our controller reduces the metabolic cost of walking compared to free walking (average reduction of 7.2 %), and it preserves the lower-limbs kinematics. Additionally, our method achieves minimal power losses from the exoskeleton across the entire gait cycle (less than 2 % negative mechanical power out of the total power), ensuring synchronized action with the users' movements. Moreover, we use Bayesian Optimization to adapt the assistance strength and allow for seamless adaptation and transitions across multiterrain environments. Our strategy achieves efficient power transmission under all conditions. Our approach demonstrates an individualized, adaptable, and straightforward controller for hip exoskeletons, advancing the development of viable, adaptive, and user-dependent control laws.

Despite recent advances in learning-based controllers for legged robots, deployments in human-centric environments remain limited by safety concerns. Most of these approaches use position-based control, where policies output target joint angles that must be processed by a low-level controller (e.g., PD or impedance controllers) to compute joint torques. Although impressive results have been achieved in controlled real-world scenarios, these methods often struggle with compliance and adaptability when encountering environments or disturbances unseen during training, potentially resulting in extreme or unsafe behaviors. Inspired by how animals achieve smooth and adaptive movements by controlling muscle extension and contraction, torque-based policies offer a promising alternative by enabling precise and direct control of the actuators in torque space. In principle, this approach facilitates more effective interactions with the environment, resulting in safer and more adaptable behaviors. However, challenges such as a highly nonlinear state space and inefficient exploration during training have hindered their broader adoption. To address these limitations, we propose SATA, a bio-inspired framework that mimics key biomechanical principles and adaptive learning mechanisms observed in animal locomotion. Our approach effectively addresses the inherent challenges of learning torque-based policies by significantly improving early-stage exploration, leading to high-performance final policies. Remarkably, our method achieves zero-shot sim-to-real transfer. Our experimental results indicate that SATA demonstrates remarkable compliance and safety, even in challenging environments such as soft/slippery terrain or narrow passages, and under significant external disturbances, highlighting its potential for practical deployments in human-centric and safety-critical scenarios.

Assistive devices, such as exoskeletons and prostheses, have revolutionized the field of rehabilitation and mobility assistance. Efficiently detecting transitions between different activities, such as walking, stair ascending and descending, and sitting, is crucial for ensuring adaptive control and enhancing user experience. We present an approach for real-time transition detection, aimed at optimizing the processing-time performance. By establishing activity-specific threshold values through trained machine learning models, we effectively distinguish motion patterns and we identify transition moments between locomotion modes. This threshold-based method improves real-time embedded processing time performance by up to 11 times compared to machine learning approaches. The efficacy of the developed finite-state machine is validated using data collected from three different measurement systems. Moreover, experiments with healthy participants were conducted on an active pelvis orthosis to validate the robustness and reliability of our approach. The proposed algorithm achieved high accuracy in detecting transitions between activities. These promising results show the robustness and reliability of the method, reinforcing its potential for integration into practical applications.