arXiv subjects

Auke Ijspeert

Publications and source records attributed to Auke Ijspeert.

At least 19 recordsLinked to original sources

arXiv2026

Spline Policy: A Structured Representation for Robot Policies

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.

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arXiv2026

Integrative neurocybernetic modeling in the era of large-scale neuroscience

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.

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arXiv2026

Learning Whole-Body Control for a Salamander Robot

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.

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arXiv2025

Geometry-aware Policy Imitation

We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

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arXiv2025

Musculoskeletal simulation of limb movement biomechanics in Drosophila melanogaster

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.

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arXiv2025

Adaptive Negative Damping Control for User-Dependent Multi-Terrain Walking Assistance with a Hip Exoskeleton

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 human-exoskeleton 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 multi-terrain 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.

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arXiv2025

Rapid Online Learning of Hip Exoskeleton Assistance Preferences

Hip exoskeletons are increasing in popularity due to their effectiveness across various scenarios and their ability to adapt to different users. However, personalizing the assistance often requires lengthy tuning procedures and computationally intensive algorithms, and most existing methods do not incorporate user feedback. In this work, we propose a novel approach for rapidly learning users' preferences for hip exoskeleton assistance. We perform pairwise comparisons of distinct randomly generated assistive profiles, and collect participants preferences through active querying. Users' feedback is integrated into a preference-learning algorithm that updates its belief, learns a user-dependent reward function, and changes the assistive torque profiles accordingly. Results from eight healthy subjects display distinct preferred torque profiles, and users' choices remain consistent when compared to a perturbed profile. A comprehensive evaluation of users' preferences reveals a close relationship with individual walking strategies. The tested torque profiles do not disrupt kinematic joint synergies, and participants favor assistive torques that are synchronized with their movements, resulting in lower negative power from the device. This straightforward approach enables the rapid learning of users preferences and rewards, grounding future studies on reward-based human-exoskeleton interaction.

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arXiv2025

SATA: Safe and Adaptive Torque-Based Locomotion Policies Inspired by Animal Learning

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.

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arXiv2024

Locomotion Mode Transitions: Tackling System- and User-Specific Variability in Lower-Limb Exoskeletons

Accurate detection of locomotion transitions, such as walk to sit, walk to stair ascent, and descent, is crucial to effectively control robotic assistive devices, such as lower-limb exoskeletons, as each locomotion mode requires specific assistance. Variability in collected sensor data introduced by user- or system-specific characteristics makes it challenging to maintain high transition detection accuracy while avoiding latency using non-adaptive classification models. In this study, we identified key factors influencing transition detection performance, including variations in user behavior, and different mechanical designs of the exoskeletons. To boost the transition detection accuracy, we introduced two methods for adapting a finite-state machine classifier to system- and user-specific variability: a Statistics-Based approach and Bayesian Optimization. Our experimental results demonstrate that both methods remarkably improve transition detection accuracy across diverse users, achieving up to an 80% increase in certain scenarios compared to the non-personalized threshold method. These findings emphasize the importance of personalization in adaptive control systems, underscoring the potential for enhanced user experience and effectiveness in assistive devices. By incorporating subject- and system-specific data into the model training process, our approach offers a precise and reliable solution for detecting locomotion transitions, catering to individual user needs, and ultimately improving the performance of assistive devices.

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arXiv2024

AllGaits: Learning All Quadruped Gaits and Transitions

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 velocity and joint acceleration result in different `optimal' gaits than those that minimize COT. We deploy our controller in various hardware experiments, showing all 9 typical quadruped animal gaits, and demonstrate generalizability to unseen gaits during training, and robustness to leg failures. Video results can be found at https://youtu.be/OLoWSX_R868.

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arXiv2024

Online Optimization of Central Pattern Generators for Quadruped Locomotion

Typical legged locomotion controllers are designed or trained offline. This is in contrast to many animals, which are able to locomote at birth, and rapidly improve their locomotion skills with few real-world interactions. Such motor control is possible through oscillatory neural networks located in the spinal cord of vertebrates, known as Central Pattern Generators (CPGs). Models of the CPG have been widely used to generate locomotion skills in robotics, but can require extensive hand-tuning or offline optimization of inter-connected parameters with genetic algorithms. In this paper, we present a framework for the \textit{online} optimization of the CPG parameters through Bayesian Optimization. We show that our framework can rapidly optimize and adapt to varying velocity commands and changes in the terrain, for example to varying coefficients of friction, terrain slope angles, and added mass payloads placed on the robot. We study the effects of sensory feedback on the CPG, and find that both force feedback in the phase equations, as well as posture control (Virtual Model Control) are both beneficial for robot stability and energy efficiency. In hardware experiments on the Unitree Go1, we show rapid optimization (in under 3 minutes) and adaptation of energy-efficient gaits to varying target velocities in a variety of scenarios: varying coefficients of friction, added payloads up to 15 kg, and variable slopes up to 10 degrees. See demo at: https://youtu.be/4qq5leCI2AI

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arXiv2024

Dynamic Object Catching with Quadruped Robot Front Legs

This paper presents a framework for dynamic object catching using a quadruped robot's front legs while it stands on its rear legs. The system integrates computer vision, trajectory prediction, and leg control to enable the quadruped to visually detect, track, and successfully catch a thrown object using an onboard camera. Leveraging a fine-tuned YOLOv8 model for object detection and a regression-based trajectory prediction module, the quadruped adapts its front leg positions iteratively to anticipate and intercept the object. The catching maneuver involves identifying the optimal catching position, controlling the front legs with Cartesian PD control, and closing the legs together at the right moment. We propose and validate three different methods for selecting the optimal catching position: 1) intersecting the predicted trajectory with a vertical plane, 2) selecting the point on the predicted trajectory with the minimal distance to the center of the robot's legs in their nominal position, and 3) selecting the point on the predicted trajectory with the highest likelihood on a Gaussian Mixture Model (GMM) modelling the robot's reachable space. Experimental results demonstrate robust catching capabilities across various scenarios, with the GMM method achieving the best performance, leading to an 80% catching success rate. A video demonstration of the system in action can be found at https://youtu.be/sm7RdxRfIYg .

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arXiv2024

Learning Human-Robot Handshaking Preferences for Quadruped Robots

Quadruped robots are showing impressive abilities to navigate the real world. If they are to become more integrated into society, social trust in interactions with humans will become increasingly important. Additionally, robots will need to be adaptable to different humans based on individual preferences. In this work, we study the social interaction task of learning optimal handshakes for quadruped robots based on user preferences. While maintaining balance on three legs, we parameterize handshakes with a Central Pattern Generator consisting of an amplitude, frequency, stiffness, and duration. Through 10 binary choices between handshakes, we learn a belief model to fit individual preferences for 25 different subjects. Our results show that this is an effective strategy, with 76% of users feeling happy with their identified optimal handshake parameters, and 20% feeling neutral. Moreover, compared with random and test handshakes, the optimized handshakes have significantly decreased errors in amplitude and frequency, lower Dynamic Time Warping scores, and improved energy efficiency, all of which indicate robot synchronization to the user's preferences. Video results can be found at https://youtu.be/elvPv8mq1KM .

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arXiv2024

Learning-based Hierarchical Control: Emulating the Central Nervous System for Bio-Inspired Legged Robot Locomotion

Animals possess a remarkable ability to navigate challenging terrains, achieved through the interplay of various pathways between the brain, central pattern generators (CPGs) in the spinal cord, and musculoskeletal system. Traditional bioinspired control frameworks often rely on a singular control policy that models both higher (supraspinal) and spinal cord functions. In this work, we build upon our previous research by introducing two distinct neural networks: one tasked with modulating the frequency and amplitude of CPGs to generate the basic locomotor rhythm (referred to as the spinal policy, SCP), and the other responsible for receiving environmental perception data and directly modulating the rhythmic output from the SCP to execute precise movements on challenging terrains (referred to as the descending modulation policy). This division of labor more closely mimics the hierarchical locomotor control systems observed in legged animals, thereby enhancing the robot's ability to navigate various uneven surfaces, including steps, high obstacles, and terrains with gaps. Additionally, we investigate the impact of sensorimotor delays within our framework, validating several biological assumptions about animal locomotion systems. Specifically, we demonstrate that spinal circuits play a crucial role in generating the basic locomotor rhythm, while descending pathways are essential for enabling appropriate gait modifications to accommodate uneven terrain. Notably, our findings also reveal that the multi-layered control inherent in animals exhibits remarkable robustness against time delays. Through these investigations, this paper contributes to a deeper understanding of the fundamental principles of interplay between spinal and supraspinal mechanisms in biological locomotion. It also supports the development of locomotion controllers in parallel to biological structures which are ...

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arXiv2024

Quadruped-Frog: Rapid Online Optimization of Continuous Quadruped Jumping

Legged robots are becoming increasingly agile in exhibiting dynamic behaviors such as running and jumping. Usually, such behaviors are either optimized and engineered offline (i.e. the behavior is designed for before it is needed), either through model-based trajectory optimization, or through deep learning-based methods involving millions of timesteps of simulation interactions. Notably, such offline-designed locomotion controllers cannot perfectly model the true dynamics of the system, such as the motor dynamics. In contrast, in this paper, we consider a quadruped jumping task that we rapidly optimize online. We design foot force profiles parameterized by only a few parameters which we optimize for directly on hardware with Bayesian Optimization. The force profiles are tracked at the joint level, and added to Cartesian PD impedance control and Virtual Model Control to stabilize the jumping motions. After optimization, which takes only a handful of jumps, we show that this control architecture is capable of diverse and omnidirectional jumps including forward, lateral, and twist (turning) jumps, even on uneven terrain, enabling the Unitree Go1 quadruped to jump 0.5 m high, 0.5 m forward, and jump-turn over 2 rad. Video results can be found at https://youtu.be/SvfVNQ90k_w.

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arXiv2023

ExoRecovery: Push Recovery with a Lower-Limb Exoskeleton based on Stepping Strategy

Balance loss is a significant challenge in lower-limb exoskeleton applications, as it can lead to potential falls, thereby impacting user safety and confidence. We introduce a control framework for omnidirectional recovery step planning by online optimization of step duration and position in response to external forces. We map the step duration and position to a human-like foot trajectory, which is then translated into joint trajectories using inverse kinematics. These trajectories are executed via an impedance controller, promoting cooperation between the exoskeleton and the user. Moreover, our framework is based on the concept of the divergent component of motion, also known as the Extrapolated Center of Mass, which has been established as a consistent dynamic for describing human movement. This real-time online optimization framework enhances the adaptability of exoskeleton users under unforeseen forces thereby improving the overall user stability and safety. To validate the effectiveness of our approach, simulations, and experiments were conducted. Our push recovery experiments employing the exoskeleton in zero-torque mode (without assistance) exhibit an alignment with the exoskeleton's recovery assistance mode, that shows the consistency of the control framework with human intention. To the best of our knowledge, this is the first cooperative push recovery framework for the lower-limb human exoskeleton that relies on the simultaneous adaptation of intra-stride parameters in both frontal and sagittal directions. The proposed control scheme has been validated with human subject experiments.

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arXiv2023

ManyQuadrupeds: Learning a Single Locomotion Policy for Diverse Quadruped Robots

Learning a locomotion policy for quadruped robots has traditionally been constrained to a specific robot morphology, mass, and size. The learning process must usually be repeated for every new robot, where hyperparameters and reward function weights must be re-tuned to maximize performance for each new system. Alternatively, attempting to train a single policy to accommodate different robot sizes, while maintaining the same degrees of freedom (DoF) and morphology, requires either complex learning frameworks, or mass, inertia, and dimension randomization, which leads to prolonged training periods. In our study, we show that drawing inspiration from animal motor control allows us to effectively train a single locomotion policy capable of controlling a diverse range of quadruped robots. The robot differences encompass: a variable number of DoFs, (i.e. 12 or 16 joints), three distinct morphologies, a broad mass range spanning from 2 kg to 200 kg, and nominal standing heights ranging from 18 cm to 100 cm. Our policy modulates a representation of the Central Pattern Generator (CPG) in the spinal cord, effectively coordinating both frequencies and amplitudes of the CPG to produce rhythmic output (Rhythm Generation), which is then mapped to a Pattern Formation (PF) layer. Across different robots, the only varying component is the PF layer, which adjusts the scaling parameters for the stride height and length. Subsequently, we evaluate the sim-to-real transfer by testing the single policy on both the Unitree Go1 and A1 robots. Remarkably, we observe robust performance, even when adding a 15 kg load, equivalent to 125% of the A1 robot's nominal mass.

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arXiv2023

Maximizing Performance with Minimal Resources for Real-Time Transition Detection

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 here 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.

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