Overview

Robot locomotion concerns the mechanisms and control strategies that let robots walk, run, hop, roll, climb, swim, or combine these modes. Researchers use physics-based models, gait planning, model predictive control, and reinforcement learning, often combining perception or tactile sensing with proprioception to adapt to terrain and contact. Work is tested in simulation and on physical robots, with benchmarks for stability, speed, energy use, obstacle traversal, and transfer to unfamiliar settings. A central challenge is making versatile learned controllers reliable in the real world, where uncertain contacts, deformable terrain, sensor errors, and hardware limits can undermine performance.

Latest papers

233 papers31 papers in the last four weeks, down 16% on the four weeks before. 0.2% of all new papers.

May 10, 2026

Neuromorphic Reinforcement Learning for Quadruped Locomotion Control on Uneven Terrain

Reinforcement learning (RL) has enabled robust quadruped locomotion over complex terrain, but most learned controllers are trained offline with backpropagation in massively parallel simulation and deployed as fixed policies, limiting adaptation to terrain variation, payload changes, actuator wear, and other real-world conditions under onboard power constraints. Local learning provides a potential path toward energy-aware on-robot adaptation by replacing global backpropagation graphs with updates driven by local neural states, making the learning rule more compatible with neuromorphic and in-memory computing substrates. This work proposes an equilibrium-propagation (EP)-based proximal policy optimization (PPO) framework for uneven-terrain quadruped locomotion. The controller combines a bio-inspired central pattern generator (CPG) policy with a residual postural adjustment policy, while replacing conventional backpropagation-trained policy and value networks with EP-enabled local learning. To train stochastic continuous-control policies with EP, we derive an EP-compatible PPO output-nudging signal and introduce a two-sided ratio clipping mechanism that stabilizes policy updates during relaxation. Experiments on a 12-DoF A1 quadruped show that the proposed controller achieves stable policy convergence in a two-stage uneven terrain locomotion task. Its locomotion performance is comparable to a backpropagation-trained PPO baseline in success rate, velocity tracking, actuator power, and body stability, while improving GPU memory efficiency by 4.3×\times compared with backpropagation through time (BPTT). These results suggest that local equilibrium-based learning can support high-dimensional embodied locomotion and provide an algorithmic foundation for low-power on-robot adaptation and fine-tuning.
May 7, 2026

Cycle-resolved Cephalopod-Inspired Pulsed-Jet Robot With High-Volume Expulsion and Drag-Reduced Gliding

Cephalopod pulsed-jet locomotion is not a single isolated expulsion event, but a coordinated cycle involving jet expulsion, passive gliding, and mantle refilling. Inspired by this cycle-resolved biological strategy, this paper presents a cephalopod-inspired pulsed-jet robot with a rigid-soft hybrid origami mantle that enables large, actively driven, and geometry-guided body deformation. The proposed mantle integrates rigid folding panels with a compliant silicone framework, allowing a 75% effective cavity-volume reduction during expulsion and reducing the projected cross-sectional drag area by approximately 75.7% in the contracted gliding configuration. Using this platform, we formulate a cycle-resolved framework to separately investigate how expelled volume, glide duration, and refill pathway influence whole-cycle locomotion performance. Experiments show that the robot reaches a peak speed of approximately 0.5 m/s (3.8 BL/s) and an average speed exceeding 0.2 m/s (1.5 BL/s) within the first jetting cycle. The results further demonstrate the roles of high expelled-volume-ratio contraction in speed generation, reduced-drag-area gliding under different glide durations, and mantle-aperture-inspired passive inlet valves in assisting refill. This work provides both a robotic implementation of actively deformable cephalopod-like jet propulsion and a unified experimental platform for studying expulsion-gliding-refilling dynamics in pulsed-jet locomotion.
May 6, 2026

Right Model, Right Time: Real-Time Cascaded-Fidelity MPC for Bipedal Walking

This paper presents a multi-phase whole-body model predictive control (MPC) approach for bipedal walking, combining a detailed whole-body model in the near horizon with a simplified single-rigid-body model in the later prediction steps. This reduces computational complexity while retaining prediction capabilities. The resulting nonlinear optimal control problem is solved entirely within the general-purpose, off-the-shelf nonlinear MPC framework acados, using sequential quadratic programming (SQP). Given a contact schedule and a target walking speed, the controller optimizes joint torques without depending on preselected footstep locations. The controller is validated in MuJoCo simulation on the 18-DoF bipedal robot HyPer-2.
May 5, 2026

Height Control and Optimal Torque Planning for Jumping With Wheeled-Bipedal Robots

This paper mainly studies the accurate height jumping control of wheeled-bipedal robots based on torque planning and energy consumption optimization. Due to the characteristics of underactuated, nonlinear estimation, and instantaneous impact in the jumping process, accurate control of the wheeled-bipedal robot's jumping height is complicated. In reality, robots often jump at excessive height to ensure safety, causing additional motor loss, greater ground reaction force and more energy consumption. To solve this problem, a novel wheeled-bipedal jumping dynamical model(W-JBD) is proposed to achieve accurate height control. It performs well but not suitable for the real robot because the torque has a striking step. Therefore, the Bayesian optimization for torque planning method(BOTP) is proposed, which can obtain the optimal torque planning without accurate dynamic model and within few iterations. BOTP method can reduce 82.3% height error, 26.9% energy cost with continuous torque curve. This result is validated in the Webots simulation platform. Based on the torque curve obtained in the W-JBD model to narrow the searching space, BOTP can quickly converge (40 times on average). Cooperating W-JBD model and BOTP method, it is possible to achieve the height control of real robots with reasonable times of experiments.
May 4, 2026

Adaptive Gait Generation for Multi-Terrain Exoskeletons via Constrained Kernelized Movement Primitives

Lower limb exoskeletons (LLEs) present the potential to make motor-impaired individuals walk again. Their application in real-world environments is still limited by the lack of effective adaptive gait planning. Indeed, current exoskeletons are meant to walk only on a flat and even terrain. Generating environment-aware, physiologically consistent gait trajectories in real-time is an open challenge. To overcome this, we propose a novel Kernelized Movement Primitives (KMP)-based framework for adaptive gait generation (AGG) across multiple indoor terrains. The proposed approach learns a probabilistic representation of human gait in both the joint and task spaces from a limited number of human demonstrations, representing natural gait characteristics and ensuring kinematic feasibility. In addition, the learned trajectories are adapted using environmental information extracted from an onboard RGB-D camera by treating the AGG as a linearly constrained optimization problem with via-points. The proposed method has been thoroughly validated first in simulations for gait generation in different scenarios, such as flat-ground walking, slopes, stairs, and obstacles crossing. Finally, the effectiveness and robustness of the method have been demonstrated with experiments on a commercial LLE in real-world scenarios. The results obtained demonstrate the feasibility of an environment-aware gait planning system for a new generation of intelligent lower limb exoskeletons for assisting people with disabilities in their every-day life.
May 1, 2026

Learning to Race in Minutes: Infoprop Dyna on the Mini Wheelbot

Reinforcement Learning (RL) has the potential to enable robots with fast, nonlinear, and unstable dynamics to reach the limits of their performance. However, most recent advances rely on carefully designed physics-based simulators and domain randomization to achieve successful sim-to-real transfer within reasonable wall-clock time. In this work, we bypass the need for such simulators and demonstrate that Infoprop Dyna, a state-of-the-art uncertainty-aware model-based reinforcement learning (MBRL) framework, can enable robots to learn directly from real-world interactions. Using Infoprop Dyna, the Mini Wheelbot, an underactuated unicycle robot, learns to race around a track within 11 minutes of real-world experience.
Apr 30, 2026

Task-Conditioned Uncertainty Costmaps for Legged Locomotion

Legged robots maintain dynamic feasibility through multicontact interactions with terrain. Learned foothold prediction can provide feasibility-aware costs for motion planning and path selection, but accurately predicting future contacts from perceptual inputs such as height scans remains challenging on highly unstructured terrain, even with a repetitive gait cycle. In this work, we show that modeling epistemic uncertainty in predicted footholds, conditioned on terrain observations and commanded motion, distinguishes in-distribution from out-of-distribution operating regimes in simulation and real-world settings. This allows a single learned model, trained on limited data distributions, to express uncertainty caused by missing training coverage. We use this learned uncertainty to detect OOD regions and incorporate them into a unified costmap-generation framework for uncertainty-aware path planning. Using these uncertainty-aware costmaps, we evaluate feasibility error across in-distribution and OOD terrains in simulation and real-world settings. The results show improved OOD detection, up to a 37% reduction in simulation feasibility error, and more reliable planning behavior than geometry-only baselines.
Apr 29, 2026

Bi-Level Optimization for Contact and Motion Planning in Rope-Assisted Legged Robots

This paper presents a planning pipeline framework for locomotion in rope-assisted robots climbing vertical surfaces. The proposed framework is formulated as a bi-level optimization scheme that addresses a mixed-integer problem: selecting feasible terrain regions for landing while simultaneously optimizing the control inputs, namely rope tensions and leg forces, and landing location. The outer level of the optimization is solved using the Cross-Entropy Method, while the inner level relies on gradient-based nonlinear optimization to compute dynamically feasible motions. The approach is validated on a novel climbing robot platform, ALPINE, across a variety of challenging terrain configurations.
Apr 27, 2026

asRoBallet: Closing the Sim2Real Gap via Friction-Aware Reinforcement Learning for Underactuated Spherical Dynamics

We introduce asRoBallet, to the best of our knowledge, the first end-to-end reinforcement learning (RL) locomotion policy deployed on a humanoid ballbot hardware platform. Historically, ballbots have served as a canonical benchmark for underactuated and nonholonomic control, which are characterized by a reality gap in complex friction models for wheel-ball-floor interactions. While current literature demonstrates successful handling of 3D balancing with LQR and MPC, transitioning to actual hardware for a humanoid ballbot using RL is currently hindered by critical gaps in contact modeling, actuator latency & jitter, and safe hardware exploration. This study proposes a high-fidelity MuJoCo simulation that explicitly models the discrete roller mechanics of ETH-type omni-wheels, thereby capturing parasitic vibrations and contact discontinuities that have previously been ignored. We also developed a Friction-Aware Reinforcement Learning framework that achieves zero-shot Sim2Real transfer by mastering the coupled rolling, lateral, and torsional friction channels at the wheel-ball and ball-floor interfaces. We designed asRoBallet through subtractive reconfiguration, repurposing key components from an overconstrained quadruped and integrating them into a newly designed structural frame to achieve a robust research platform at low cost. We also developed a generalized iOS ecosystem that transforms consumer electronics into a low-latency interface, enabling a single operator to orchestrate expressive humanoid maneuvers via intuitive natural motion.
Apr 26, 2026

Unleashing the Agility of Wheeled-Legged Robots for High-Dynamic Reflexive Obstacle Evasion

Wheeled-legged robots combine the efficiency of rolling with the adaptability of legged locomotion, offering unique agility for dynamic environments. However, enabling rapid reflexive evasion remains challenging due to the coexistence of heterogeneous wheel-leg dynamics, hybrid locomotion modes, and non-holonomic constraints. In this work, we investigate how wheeled-legged robots can exploit their hybrid morphology for high-dynamic obstacle avoidance. We propose AWARE, a hierarchical reinforcement learning framework that decomposes avoidance into navigation-avoidance and reflexive-evasion regimes coordinated by a threat-conditioned high-level policy. By learning specialized low-level experts, AWARE autonomously discovers distinct rolling-, stepping-, and hybrid-dominated evasive behaviors, including forward lunges and lateral dodges. Simulation experiments across different reaction times and approach directions, together with real-robot evaluations on the M20 platform, demonstrate improved evasion capability and effective online transition between locomotion regimes. These results highlight the potential of exploiting hybrid wheel-leg actuation for agile and reactive mobility in dynamic environments. Paper homepage: https://aware-ral-2026.github.io/.
Apr 26, 2026

QuietWalk: Physics-Informed Reinforcement Learning for Ground Reaction Force-Aware Humanoid Locomotion Under Diverse Footwear

Humanoid robots operating in human-centered environments (e.g., homes, hospitals, and offices) must mitigate foot--ground impact transients, as impact-induced vibration and noise degrade user experience and repeated impacts accelerate hardware wear. However, existing low-noise locomotion training often relies on kinematic proxy objectives or fragile force sensors, and footwear-induced changes in contact dynamics introduce distribution shifts that hinder policy generalization.We present QuietWalk, a physics-informed reinforcement learning framework for ground-reaction-force-aware humanoid locomotion under diverse footwear conditions. QuietWalk employs an inverse-dynamics-constrained physics-informed neural network (PINN) to estimate per-foot vertical ground reaction forces (GRFs) from proprioceptive signals, and integrates the frozen predictor into the RL training loop to penalize predicted impact forces without requiring force sensors at deployment.On a held-out real-robot dataset, enforcing inverse-dynamics consistency reduces vertical GRF prediction errors by 82%-86% compared with a purely supervised predictor and improves the coefficient of determination from 0.39/0.67 to 0.99/0.99 for the left/right feet. On hardware at 1.2 m/s (barefoot; averaged over four floor materials), QuietWalk reduces mean A-weighted noise level by 7.17 dB and peak noise level by 4.98 dB under a consistent recording setup. Cross-footwear experiments (barefoot, skate shoes, athletic sneakers, and high heels) across multiple surfaces further demonstrate robust adaptation to footwear-induced contact variations.
Apr 24, 2026

False Feasibility in Variable Impedance MPC for Legged Locomotion

Variable impedance model predictive control (MPC) formulations often treat joint stiffness as an instantaneous decision variable. The resulting feasible set strictly contains the physically realizable set under first-order actuator dynamics. We identify this as a formulation error rather than a modeling approximation, formalize the distinction between the parameter-based feasible set F_param and the realizable set F_real, and characterize the regime of mismatch via the dimensionless parameter α = ωsT (actuator bandwidth times task timescale). For the 1D hopping monoped, we prove that below an analytical threshold α_crit derived in closed form from task physics, no admissible stiffness command realizes the parameter-based prediction. Numerical validation in 1D shows monotonic deviation growth as α decreases, with the predicted scaling holding across ten parameter combinations (log-log R2 = 0.986). Mechanism transfer to planar spring-loaded inverted pendulum dynamics confirms center-of-mass and stance-timing deviation as the primary consequence, with regime-dependent friction effects as a tertiary observable. A second threshold α_infeas < α_crit establishes a floor below which restricting the admissible stiffness range cannot repair realizability, closing the conservative-tuning objection. Augmenting the prediction state with stiffness closes the mismatch by construction.
Apr 23, 2026

Dynamic Coupling and Indirect Control of Jointed Robots Rolling Atop A Moving Platform

An asymmetric two-link robot supported atop a flat platform by wheels that roll and pivot freely, but do not slip laterally, will develop forward momentum if the joint between the links is actuated internally. In particular, oscillations in the joint angle will generate undulatory locomotion suggesting fishlike swimming. If two such robots surmount a common platform that's free to translate with its own inertial dynamics, then the individual robots' dynamics will be coupled so that the locomotion of either robot is affected by that of the other. We develop a mathematical model for this system and present simulations demonstrating its behavior. We then consider a single robot with an unactuated joint rolling atop a platform that moves under control, and show that actuation of the platform is sufficient to dictate the robot's behavior. In particular, with the acceleration of the platform as an input, the robot's heading can be made to track a chosen function of time. This is sufficient to guarantee that the robot can be induced to orbit a fixed point on the platform or to locomote persistently in a desired direction.
Apr 23, 2026

X2-N: A Transformable Wheel-legged Humanoid Robot with Dual-mode Locomotion and Manipulation

Wheel-legged robots combine the efficiency of wheeled locomotion with the versatility of legged systems, enabling rapid traversal over both continuous and discrete terrains. However, conventional designs typically employ fixed wheels as feet and limited degrees of freedom (DoFs) at the hips, resulting in reduced stability and mobility during legged locomotion compared to humanoids with flat feet. In addition, most existing platforms lack a full upper body with arms, which limits their ability to perform dexterous manipulation tasks. In this letter, we present X2-N, a high-DoF transformable robot with dual-mode locomotion and manipulation. X2-N can operate in both humanoid and wheel-legged forms and transform seamlessly between them through joint reconfiguration. We further propose a reinforcement learning (RL)-based whole-body control framework tailored to this morphology, enabling unified control across hybrid locomotion, transformation, and manipulation. We validate X2-N in a range of challenging locomotion and manipulation tasks, including dynamic skating-like motion, stair climbing and package delivery. Results demonstrate high locomotion efficiency, strong terrain adaptability, and stable loco-manipulation performance of X2-N, highlighting its potential for real-world deployment.
Apr 21, 2026

Quadruped Parkour Learning: Sparsely Gated Mixture of Experts with Visual Input

Robotic parkour provides a compelling benchmark for advancing locomotion over highly challenging terrain, including large discontinuities such as elevated steps. Recent approaches have demonstrated impressive capabilities, including dynamic climbing and jumping, but typically rely on sequential multilayer perceptron (MLP) architectures with densely activated layers. In contrast, sparsely gated mixture-of-experts (MoE) architectures have emerged in the large language model domain as an effective paradigm for improving scalability and performance by activating only a subset of parameters at inference time. In this work, we investigate the application of sparsely gated MoE architectures to vision-based robotic parkour. We compare control policies based on standard MLPs and MoE architectures under a controlled setting where the number of active parameters at inference time is matched. Experimental results on a real Unitree Go2 quadruped robot demonstrate clear performance gains, with the MoE policy achieving double the number of successful trials in traversing large obstacles compared to a standard MLP baseline. We further show that achieving comparable performance with a standard MLP requires scaling its parameter count to match that of the total MoE model, resulting in a 14.3% increase in computation time. These results highlight that sparsely gated MoE architectures provide a favorable trade-off between performance and computational efficiency, enabling improved scaling of control policies for vision-based robotic parkour. An anonymized link to the codebase is https://osf.io/v2kqj/files/github?view_only=7977dee10c0a44769184498eaba72e44.
Apr 21, 2026

Multi-Gait Learning for Humanoid Robots Using Reinforcement Learning with Selective Adversarial Motion Prior

Learning diverse locomotion skills for humanoid robots in a unified reinforcement learning framework remains challenging due to the conflicting requirements of stability and dynamic expressiveness across different gaits. We present a multi-gait learning approach that enables a humanoid robot to master five distinct gaits -- walking, goose-stepping, running, stair climbing, and jumping -- using a consistent policy structure, action space, and reward formulation. The key contribution is a selective Adversarial Motion Prior (AMP) strategy: AMP is applied to periodic, stability-critical gaits (walking, goose-stepping, stair climbing) where it accelerates convergence and suppresses erratic behavior, while being deliberately omitted for highly dynamic gaits (running, jumping) where its regularization would over-constrain the motion. Policies are trained via PPO with domain randomization in simulation and deployed on a physical 12-DOF humanoid robot through zero-shot sim-to-real transfer. Quantitative comparisons demonstrate that selective AMP outperforms a uniform AMP policy across all five gaits, achieving faster convergence, lower tracking error, and higher success rates on stability-focused gaits without sacrificing the agility required for dynamic ones.
Apr 20, 2026

Locomotion of an Elastic Snake Robot via Natural Dynamics

Nature suggests that exploiting the elasticities and natural dynamics of robotic systems could increase their locomotion efficiency. Prior work on elastic snake robots supports this hypothesis, but has not fully exploited the nonlinear dynamic behavior of the systems. Recent advances in eigenmanifold theory enable a better characterization of the natural dynamics in complex nonlinear systems. This letter investigates if and how the nonlinear natural dynamics of a kinematic elastic snake robot can be used to design efficient gaits. Two types of gaits based on natural dynamics are presented and compared to a state-of-the-art approach using dynamics simulations. The results reveal that a gait generated by switching between two nonlinear normal modes does not improve the locomotion efficiency of the robot. In contrast, gaits based on non-brake periodic trajectories (non-brake orbits) are perfectly efficient in the energy-conservative case. Further simulations with friction reveal that, in a more realistic scenario, non-brake orbit gaits achieve higher efficiency compared to the baseline gait on the rigid system. Overall, the investigation offers promising insights into the design of gaits based on natural dynamics, fostering further research.
Apr 19, 2026

Learning Whole-Body Humanoid Locomotion via Motion Generation and Motion Tracking

Whole-body humanoid locomotion is challenging due to high-dimensional control, morphological instability, and the need for real-time adaptation to various terrains using onboard perception. Directly applying reinforcement learning (RL) with reward shaping to humanoid locomotion often leads to lower-body-dominated behaviors, whereas imitation-based RL can learn more coordinated whole-body skills but is typically limited to replaying reference motions without a mechanism to adapt them online from perception for terrain-aware locomotion. To address this gap, we propose a whole-body humanoid locomotion framework that combines skills learned from reference motions with terrain-aware adaptation. We first train a diffusion model on retargeted human motions for real-time prediction of terrain-aware reference motions. Concurrently, we train a whole-body reference tracker with RL using this motion data. To improve robustness under imperfectly generated references, we further fine-tune the tracker with a frozen motion generator in a closed-loop setting. The resulting system supports directional goal-reaching control with terrain-aware whole-body adaptation, and can be deployed on a Unitree G1 humanoid robot with onboard perception and computation. The hardware experiments demonstrate successful traversal over boxes, hurdles, stairs, and mixed terrain combinations. Quantitative results further show the benefits of incorporating online motion generation and fine-tuning the motion tracker for improved generalization and robustness.
Apr 16, 2026

Model-Based Reinforcement Learning Exploits Passive Body Dynamics for High-Performance Biped Robot Locomotion

Embodiment is a significant keyword in recent machine learning fields. This study focused on the passive nature of the body of a biped robot to generate walking and running locomotion using model-based deep reinforcement learning. We constructed two models in a simulator, one with passive elements (e.g., springs) and the other, which is similar to general humanoids, without passive elements. The training of the model with passive elements was highly affected by the attractor of the system. This lead that although the trajectories quickly converged to limit cycles, it took a long time to obtain large rewards. However, thanks to the attractor-driven learning, the acquired locomotion was robust and energy-efficient. The results revealed that robots with passive elements could efficiently acquire high-performance locomotion by utilizing stable limit cycles generated through dynamic interaction between the body and ground. This study demonstrates the importance of implementing passive properties in the body for future embodied AI.
Apr 15, 2026

CART: Context-Aware Terrain Adaptation using Temporal Sequence Selection for Legged Robots

Animals in nature combine multiple modalities, such as sight and feel, to perceive terrain and develop an understanding of how to walk on uneven terrain in an efficient manner. Similarly, legged robots need to develop their ability to stably walk on complex terrains by developing an understanding of the relationship between vision and proprioception. Most current terrain-adaptation methods remain susceptible to failure on complex off-road terrain because they do not explicitly model the context between exteroceptive terrain appearance and proprioceptive physical interaction. This experience-based learning often creates a Visual-Texture Paradox between what has been seen and how it actually feels. In this work, we introduce CART, a high-level controller built on a context-aware terrain adaptation approach that integrates proprioception and exteroception from onboard sensing to achieve a robust understanding of terrain. We evaluate our method on multiple terrains using the Unitree Go2 and ANYmal-C robot on the IsaacSim simulator and a Boston Dynamics SPOT robot for our real-world experiments. To evaluate whether the learned context improves locomotion behavior under the various paradox circumstances, we measure the robot s stability, traversal success, and task completion time in both simulation and real-world experiments. We compare CART against state-of-the-art locomotion and terrain- adaptation baselines across diverse terrain conditions. CART improves the average success rate by 5% over the baselines in simulation, while improving context-conditioned locomotion behavior, including up to 41% lower base oscillation in simulation and 22% in the real world, without increasing the time required to complete the locomotion tasks.
Apr 15, 2026

Stability Principle Underlying Passive Dynamic Walking of Rimless Wheel

Rimless wheels are known as the simplest model for passive dynamic walking. It is known that the passive gait generated only by gravity effect always becomes asymptotically stable and 1-period because a rimless wheel automatically achieves the two necessary conditions for guaranteeing the asymptotic stability; one is the constraint on impact posture and the other is the constraint on restored mechanical energy. The asymptotic stability is then easily shown by the recurrence formula of kinetic energy. There is room, however, for further research into the inherent stability principle. In this paper, we reconsider the stability of the stance phase based on the linearization of the equation of motion, and investigate the relation between the stability and energy conservation law. Through the mathematical analysis, we provide a greater understanding of the inherent stability principle.
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.
Apr 14, 2026

Asymptotically Stable Gait Generation and Instantaneous Walkability Determination for Planar Almost Linear Biped with Knees

A class of planar bipedal robots with unique mechanical properties has been proposed, where all links are balanced around the hip joint, preventing natural swinging motion due to gravity. A common property of their equations of motion is that the inertia matrix is a constant matrix, there are no nonlinear velocity terms, and the gravity term contains simple nonlinear terms. By performing a Taylor expansion of the gravity term and making a linear approximation, it is easy to derive a linearized model, and calculations for future states or walkability determination can be performed instantaneously without the need for numerical integration. This paper extends the method to a planar biped robot model with knees. First, we derive the equations of motion, constraint conditions, and inelastic collisions for a planar 6-DOF biped robot, design its control system, and numerically generate a stable bipedal gait on a horizontal plane. Next, we reduce the equations of motion to a 3-DOF model, and derive a linearized model by approximating the gravity term as linear around the expansion point for the thigh frame angle. Through numerical simulations, we demonstrate that calculations for future states and walkability determination can be completed in negligible time. By applying control inputs to the obtained model, performing state-space realization, and then discretizing it, instantaneous walkability determination through iterative calculation becomes possible. Through detailed gait analysis, we discuss how the knee joint flexion angle and the expansion point affect the accuracy of the linear approximation, and the issues that arise when descending a small step.
Apr 13, 2026

Dynamic Modeling and Robust Gait Optimization of a Compliant Worm Robot

Worm-inspired robots provide an effective locomotion strategy for constrained environments by combining cyclic body deformation with alternating anchoring. For compliant robots, however, the interaction between deformable anchoring structures and the environment makes predictive modeling and deployable gait optimization challenging. This paper presents an experimentally grounded modeling and optimization framework for a compliant worm robot capable of traversing corrugated pipes. First, a hybrid dynamic locomotion model is derived, in which the robot motion is represented by continuous dynamics within a corrugation groove and discrete switching of anchoring positions between adjacent grooves. A slack-aware actuation model is further introduced to map the commanded gait input to the realized body-length change, and an energy model is developed based on physics and calibrated with empirical power measurement. Based on these models, a multi-objective gait optimization problem is formulated to maximize average speed while minimizing average power. To reduce the fragility of nominal boundary-seeking solutions, a kinematic robustness margin is introduced into the anchoring-transition conditions, leading to a margin-based robust gait optimization framework. Experimental results show that the proposed framework captures the dominant locomotion and energy-consumption behavior of the robot over the tested conditions, and enables robust gait optimization for achieving speed-power trade-off.
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.
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.
Apr 13, 2026

Modeling, Analysis and Activation of Planar Viscoelastically-combined Rimless Wheels

This paper proposes novel passive-dynamic walkers formed by two cross-shaped frames and eight viscoelastic elements. Since it is a combination of two four-legged rimless wheels via viscoelastic elements, we call it viscoelastically-combined rimless wheel (VCRW). Two types of VCRWs consisting of different cross-shaped frames are introduced; one is formed by combining two Greek-cross-shaped frames (VCRW1), and the other is formed by combining two-link cross-shaped frames that can rotate freely around the central axis (VCRW2). First, we describe the model assumptions and equations of motion and collision. Second, we numerically analyze the basic gait properties of passive dynamic walking. Furthermore, we consider an activation of VCRW2 for generating a stable level gait, and discuss the significance of the study as a novel walking support device.
Apr 11, 2026

GPU-Accelerated Continuous-Time Successive Convexification for Contact-Implicit Legged Locomotion

Contact-implicit trajectory optimization (CITO) enables the automatic discovery of contact sequences, but most methods rely on fine time discretization to capture all contact events accurately, which increases problem size and runtime while tying solution quality to grid resolution. We extend the recently proposed sequential convex programming (SCP) approach for trajectory optimization, continuous-time successive convexification (ct-SCvx), to CITO by introducing integral cross-complementarity constraints, which eliminate the risk of missing contact events between discretization nodes while preserving the flexibility of contact mode changes. The resulting framework, contact-implicit successive convexification (ci-SCvx), models full multibody dynamics in maximal coordinates, including stick-slip friction and partially elastic impacts. To handle complementarity constraints, we embed a backtracking homotopy scheme within SCP for reliable convergence. We implement this framework in a stand-alone Python software, leveraging JAX for GPU acceleration and a custom canonical-form parser for the convex subproblems of SCP to avoid the overhead of general-purpose modeling tools such as CVXPY. We demonstrate ci-SCvx on diverse legged-locomotion tasks. In particular, we validate the approach in MuJoCo with the Gymnasium HalfCheetah model against the MuJoCo MPC baseline, showing that a tracking simulation with the optimized torque profiles from ci-SCvx produces physically consistent trajectories with lesser energy consumption. We also show that the resulting software achieves faster solve times than existing state-of-the-art SCP implementations by over an order of magnitude, thereby demonstrating a practically important contribution to scalable real-time trajectory optimization.
Mar 31, 2026

CReF: Cross-modal and Recurrent Fusion for Depth-conditioned Humanoid Locomotion

Stable traversal over geometrically complex terrain increasingly requires exteroceptive perception, yet prior perceptive humanoid locomotion methods often remain tied to explicit geometric abstractions, either by mediating control through robot-centric 2.5D terrain representations or by shaping depth learning with auxiliary geometry-related targets. While effective, these approaches introduce additional map-construction procedures or multi-stage skill-transfer processes beyond direct depth-to-control learning. We propose CReF (Cross-modal and Recurrent Fusion), a single-stage depth-conditioned humanoid locomotion framework that learns locomotion-relevant features directly from raw forward-facing depth without explicit geometric intermediates. CReF couples proprioception and depth tokens through proprioception-queried cross-modal attention, fuses the resulting representation with a gated residual fusion block, and performs temporal integration with a Gated Recurrent Unit (GRU) regulated by a highway-style output gate for state-dependent blending of recurrent and feedforward features. To further improve terrain interaction, we introduce a terrain-aware foothold placement reward that extracts supportable foothold candidates from foot-end point-cloud samples and rewards touchdown locations that lie close to the nearest supportable candidate. Experiments in simulation and on a physical humanoid demonstrate robust traversal over diverse terrains and effective zero-shot transfer to real-world scenes containing handrails, hollow pallet assemblies, severe reflective interference, and visually cluttered outdoor surroundings.
Mar 30, 2026

A Foldable and Agile Soft Electromagnetic Robot for Multimodal Navigation in Confined and Unstructured Environments

Multimodal locomotion is crucial for an animal's adaptability in unstructured wild environments. Similarly, in the human gastrointestinal tract, characterized by viscoelastic mucus, complex rugae, and narrow sphincters like the cardia, multimodal locomotion is also essential for a small-scale soft robot to conduct tasks. Here, we introduce a small-scale compact, foldable, and robust soft electromagnetic robot (M-SEMR) with more than nine locomotion modes designed for such a scenario. Featuring a six-spoke elastomer body embedded with liquid metal channels and driven by Laplace forces under a static magnetic field, the M-SEMR is capable of rapid transitions (< 0.35 s) among different locomotion modes. It achieves exceptional agility, including high-speed rolling (818 mm/s, 26 BL/s), omnidirectional crawling, jumping, and swimming. Notably, the robot can fold to reduce its volume by 79%, enabling it to traverse confined spaces. We further validate its navigation capabilities on complex terrains, including discrete obstacles, viscoelastic gelatin surfaces, viscous fluids, and simulated biological tissues. This system offers a versatile strategy for developing high-mobility soft robots for future biomedical applications.