Inverted Pendulum

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Sep 28, 2026cs.RO

Model-Informed Safe Reinforcement Learning for Bipedal Locomotion via Step-to-Step Prediction

Humanoid robots promise versatile mobility in cluttered, human-centric environments, but real deployment demands principled safety. Classical model-based gait generators yield interpretable motions but often lack the robustness and adaptability of modern reinforcement learning (RL) based approaches. We propose a model-informed reinforcement learning framework anchored to the analytical Angular Momentum Linear Inverted Pendulum (ALIP) template. We provide a step-to-step safety certificate for ALIP stepping via a discrete exponential control barrier function (DECBF) and use it as (i) a training-time shaping signal and (ii) a runtime action filter that minimally adjusts swing-foot placement to satisfy template-level constraints. Full-order safety is evaluated empirically on the Digit humanoid in MuJoCo with a whole-body controller stack. Compared to an unconstrained baseline, our approach reduces safety-violation events in the reported external-disturbance trial, while larger lateral-velocity transients reveal a safety-tracking tradeoff.

Victor Paredes, Ayonga Hereid

Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH, USA.

Scalable Robot Learning Gait Dynamics Offline Reinforcement Learning Inverted Pendulum

Aug 10, 2026cs.LG

A matched-integrator evaluation of Hamiltonian neural networks on pendulum and Kepler dynamics

Hamiltonian Neural Networks (HNNs) parameterize conservative dynamics through a learned scalar Hamiltonian, providing an architectural prior that is absent from generic vector-field neural networks. We evaluate this prior under a controlled protocol in which an HNN and a parameter-matched feedforward baseline are trained on the same RK4-generated trajectories, use the same central-difference derivative targets and optimization settings, and are integrated at inference with the same RK4 scheme. Results are reported over five independent training seeds. On the nonlinear pendulum, the HNN reduces mean energy drift by 42-fold and mean trajectory MSE by 15.8-fold at T = 100, approximately 16 pendulum periods. Its energy drift also remains bounded and exhibits substantially lower seed-to-seed variability than the standard-network baseline. An energy-stratified analysis shows that the difference becomes more pronounced as trajectories explore more nonlinear regions of phase space. As an additional diagnostic, we examine an explicit Störmer--Verlet-style rollout of the learned HNN. Because the learned Hamiltonian is not constrained to the separable form H(q,p) = T(p) + V(q), the standard symplecticity guarantee of velocity Verlet does not directly apply. We further apply the same matched-integrator protocol to the three-dimensional Kepler two-body problem. The HNN again exhibits lower trajectory, energy, and angular-momentum drift than the parameter-matched baseline. These experiments provide a controlled study of how Hamiltonian parameterization affects long-horizon prediction and physical consistency across two conservative dynamical systems.

Lenick Kemunto Nyabuto, Yae Ulrich Gaba, Birahim Tewe

African Institute for Mathematical Sciences (AIMS) Senegal

Hamiltonian Inverted Pendulum Parametric Physics-Informed Neural Network Time Discretization

Aug 10, 2026eess.SY

Real-Time Nonlinear MPC via Sequential Quadratic Programming with Structure-Exploiting ADMM and Interior-Point Methods for Underactuated Double-Pendulum Swing-Up

The 4th "AI Olympics with RealAIGym" competition, to be held at IJCAI-ECAI 2026 in Bremen, challenges participants to develop a global control policy for swinging up and stabilizing an underactuated two-link system in its upright position. In contrast to previous editions, participants develop and evaluate their control strategies directly on remotely accessible CloudPendulum hardware, with limited interaction time and without prior knowledge of the system's model parameters. This paper presents an optimal-control-based approach employing real-time nonlinear model predictive control implemented using sequential quadratic programming. The results demonstrate that the proposed SQP-based MPC controller achieves reliable swing-up and stabilization performance, while maintaining robustness against disturbances.

Nick Karydakis, Konstantinos Chatzilygeroudis

Laboratory of Automation and Robotics (LAR) in the Department of Electrical & Computer Engineering, University of Patras, GR-26504 Patras, Greece

Underactuated Dynamics Inverted Pendulum Model Predictive Control Quadratic Programs Alternating Direction Method Of Multiplier Primal-Dual Methods+1

Jul 26, 2026eess.SY

Observer-Assisted Relative-Velocity Compensation with LPV- $H_\infty$ Robust Correction for 3D Trajectory Tracking of Underactuated Non-Minimum-Phase AUVs under Ocean Currents

This paper develops an observer-assisted control architecture for 3D trajectory tracking of torpedo-type underactuated AUVs with non-minimum-phase sway/heave dynamics under unknown ocean currents. A three-stage state-current observer provides relative-velocity estimates to a nonlinear feedforward term for dominant current rejection and to an LMI-certified LPV-

\mathcal{H}_\infty

correction layer. Feedback-linearising cancellation yields a constant input matrix, enabling convex synthesis without pairwise cross terms. A residual-level break-even law shows that the effective surge disturbance depends on current-estimation error, while a singular-perturbation analysis proves local practical uniform ultimate boundedness on the embedded LPV model. REMUS simulations over three trajectories and four current scenarios show 89-96% current-estimation reduction, about 99% translational residual reduction, and RMS tracking-error reduction from 4.04 m to 0.24 m.

Mohammad Sabouri

Department of Informatics, Bioengineering, Robotics and Systems Engineering (DIBRIS), University of Genoa, Via all’Opera Pia 13, Genoa, 16145, Italy

Autonomous Underwater Vehicles Conditional Velocity Inverted Pendulum

Jul 15, 2026cs.LG

Lyapunov Exponent as Physics-Informed Dense Reward: RL Discovery of Stabilization Beyond the Kapitza Pendulum

We suggest using the Lyapunov characteristic exponent (LCE) as a dense reward signal for the reinforcement learning problem of stabilizing the inverted pendulum with vertical motion. With LCE, the agent not only successfully found the oscillatory motion known as the Kapitza pendulum but also damped the pendulum's pivoting, leaving it in a strictly upright position.

Slava Andrejev

Inverted Pendulum Lyapunov Function Offline Reinforcement Learning Oscillatory Dynamics

Jul 7, 2026cs.RO

CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts

Physics-informed learning promises data-efficient and stable dynamics prediction, yet its strongest geometric guarantees have largely remained confined to closed conservative systems. This excludes robotic systems of interest, where actuation, dissipation, and constraints exchange energy and momentum with the environment. We introduce CaLiSym, a lightweight framework that extends symplectic learning to such systems by changing where the geometric prior is imposed. Rather than enforcing symplecticity on the measured state, CaLiSym embeds the state and its ports into a lifted phase space, where the dynamics evolve through a symplectic map. The lift is explicit and algebraic, requiring neither recurrent latent states, transformer decoders, implicit optimization, nor inference-time numerical integration. We instantiate the framework with SympNet predictors and introduce GRB-SympNet, a B-spline variant combining approximation with exact symplectic structure. Experiments on a controlled dissipative double pendulum, a real-world quadrotor, and a contact-constrained real-world quadruped demonstrate the lowest out-of-distribution autoregressive rollout error across systems, improving by up to 69.5% while using fewer parameters and up to 85x fewer floating-point operations per step than sequence-model baselines. The lifted dynamics preserve the symplectic form to numerical precision, extending symplectic learning beyond conservative mechanics toward real-world robotics.

Aristotelis Papatheodorou, Pranav Vaidhyanathan, Natalia Ares +2

Department of Engineering Science, University of Oxford, Oxford, UK · School of Mathematics and Physics, University of Sussex, Brighton, BN1 9RH, UK. National Centre for Quantum Computing, Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxfordshire, OX11 0QX UK

Inverted Pendulum Scalable Robot Learning Quadrotor

Jul 3, 2026cs.LG

CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systems

Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification. For linearly damped Hamiltonian systems, the exact flow is generally not symplectic but conformally symplectic, contracting the canonical symplectic form by a scalar factor that reflects the net dissipation. We propose Conformal Symplectic Networks with damping identification (CSympNet-ID), a discrete-time map-learning framework that learns the one-step flow map directly from snapshot pairs while enforcing exact discrete conformal symplecticity by construction, without penalty terms or projection. The architecture composes an exact symplectic neural core with explicit diagonal scaling layers whose factors are parameterized exponentially by a scalar damping-rate parameter, thereby guaranteeing positivity and interpretability of the learned dissipation factor. We establish a scaling-conjugacy factorization for conformal symplectic maps and derive a pointwise-in-step density result for CSympNet-ID. We evaluate an irregular-step damped oscillator, a damped spring-mass chain, a damped nonlinear cubic oscillator, and additional high-dimensional extensions. CSympNet-ID gives the most favorable overall results among the compared models in the reported experiments, particularly in data-scarce regimes, target contraction-law recovery, and high-dimensional tests where unstructured baselines degrade rapidly.

Jiale Gong, Pengzhan Jin, Dongyang Kuang +2

School of Mathematics · School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai 519082, China · National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, China +3

Hamiltonian Chaos Oscillatory Dynamics Inverted Pendulum Flow Map

Jun 27, 2026physics.med-ph

An Optimal Contact-Mechanically Consistent and Flow-Separation Adapted Modeling of Vocal Fold Dynamics

Single mass-spring-damper models of vocal folds have been effective in simulating vocal fold vibrations without added complexity. However, single-degree-of-freedom models cannot sustain oscillation in the presence of structural damping unless source-tract interaction is considered. Moreover, existing lumped models struggle to accurately simulate vocal fold closure during phonation. This study aims to develop a reliable and simplified single-degree-of-freedom model of phonation that can simulate sustained oscillation in a damped system without incorporating a vocal tract model. Additionally, the proposed model maintains vocal fold closure in a manner consistent with the physics of phonation, addressing a longstanding challenge in existing lumped models. High-speed videoendoscopy (HSV) data from four normophonic subjects producing sustained vowel /i/ were used to extract glottal area waveforms (GAWs) via deep learning-based image segmentation for particle swarm optimization of the model parameters. An additional resistance force was incorporated to compensate for flow separation and generate the force imbalance required for sustained oscillation. An external structural force was also added during closure to sustain the closed phase. The 4th-order Runge-Kutta method was used to solve the governing equations with enhanced numerical stability and accuracy. The model parameters were optimized for individual subjects, resulting in normalized errors below 3% between experimental and simulated GAWs. The proposed model accurately reproduced subject-specific vocal fold vibrations and vocal fold closure in agreement with experimental data. Overall, the proposed model provides a computationally efficient framework for simulating sustained phonation without requiring complex source-tract coupling while capturing the key biomechanical and aerodynamic mechanisms of phonation.

Sardar Nafis Bin Ali, Maryam Naghibolhosseini, Mohsen Zayernouri

Department of Mechanical Engineering, Michigan State University, 428 S. Shaw Lane, East Lansing, 48824, MI, USA. · Department of Communicative Sciences and Disorders, Michigan State University, 1026 Red Cedar Rd, East Lansing, 48824, MI, USA.

Vocal Tract Shape Vocalizations Inverted Pendulum Flow Models

Jun 22, 2026cs.LG

Differential Spectral Damping Gap Adaptive Regularization for Ill-Conditioned Kernel Methods

Kernel methods requiring matrix inversion -- particularly Least-Squares Twin Support Vector Machines (LSTSVM) -- suffer from exponential eigenvalue decay in their system matrices, producing severely ill-conditioned problems where standard Tikhonov regularization applies uniform damping regardless of eigenvector reliability. We propose Differential Spectral Damping (DSD), a regularization formula that adapts its penalty to localized eigengap structure: preserving eigenvectors with large spectral gaps (reliable per Davis-Kahan perturbation theory) while aggressively suppressing those with small gaps (directionally corrupted beyond recovery). We motivate DSD through a principled design procedure grounded in the Davis-Kahan

\sin(Θ)

theorem, systematically deriving the requirements for a reliability-aware damping function and selecting the exponential form for its smoothness, differentiability, and natural saturation properties. Through rigorous paired testing with fairly optimized baselines (including gradient-optimized Tikhonov receiving equal optimization opportunity), we demonstrate that DSD improves LSTSVM classification accuracy by +4.8 percentage points on real-world GINA (

d=970

, Cohen's

d = 4.49

,

p < 0.0001

), +10.4 percentage points at

d=200

, and +2.6 percentage points on Madelon (

d=500

) -- all using only principled spectral initialization while Tikhonov receives grid search. For pre-image reconstruction on manifold data, DSD ties Tikhonov at high perturbation noise (

p=0.99

) but slightly underperforms at lower noise levels; both reduce naive inversion error by

66\times

. We characterize the precise operating regime (

d \geq 100

, condition number

> 10^3

) and document where simpler methods suffice, providing practitioners with clear deployment guidance.

Praveg Vashishtha

Department of Computer Science and Engineering, Indian Institute of Technology Patna, India · Sopra Banking Software India

Kernel Method Singular Value Decomposition Regularization Support Vector Machines Spectral Decomposition Spectral+1

Jun 21, 2026cs.RO

PenduMorph: Development and Motion Analysis of Pendulum-Actuated Rolling Reconfigurable Spherical Robot with Magnetic-Coupling

This paper presents "PenduMorph", a wireless reconfigurable rolling spherical robot designed as a modular platform for enclosed locomotion and inter-module interaction in challenging environments. The proposed robot extends our previous pendulum-actuated rolling disk concept to a fully enclosed spherical architecture integrating a 2-DoF internal pendulum, onboard control, battery-powered operation, and magnetic docking. The design aims to combine independent rolling mobility with protected hardware and reliable reconfigurability. We first present the robot design and an analytical study of the magnetic coupling mechanism to evaluate retention and interaction between coupled modules. We then experimentally investigate key motion behaviors at both the single-module and dual-module levels, including independent rolling, magnetic coupling, and coordinated coupled motion. The results show that the proposed platform enables stable wireless operation and a set of distinctive reconfigurable rolling behaviors, providing a useful foundation for future modular spherical robots operating in contact-rich and demanding environments.

Aung Myat, Peter Noyce, May Forgan +2

Geometric Mechanics and Mechatronics in Robotics (gm2R) Lab, the School of Engineering, Cardiff University, Cardiff, CF24 3AA, United Kingdom

Inverted Pendulum Locomotion Magnetic Tunnel Junction Robot Systems Motion

Jun 17, 2026cs.RO

SRL: Combining SLIP Model and Reinforcement Learning for Agile Robotic Jumping

Robotic jumping is pivotal in applications such as search and rescue and logistics, where crossing obstacles and enhancing mobility efficiency are critical. The Spring-Loaded Inverted Pendulum (SLIP) model leverages simplified spring-mass dynamics that naturally encode biologically plausible hopping motions, yet its performance degrades on irregular terrain due to idealized assumptions regarding contact and joint dynamics. Meanwhile, Reinforcement Learning (RL) can adapt to diverse and complex environments but often requires extensive data from unguided exploration. The complementary strengths of SLIP's physically grounded baseline and RL's adaptive capabilities motivate a hybrid framework that overcomes these individual limitations. We therefore propose Spring-loaded Reinforcement Learning (SRL), which integrates SLIP-based feedforward control signals with RL-driven real-time feedback, enabling continuous optimization of robotic jumping. Experimental results demonstrate that SRL can achieve more stable jumps with much less training time than the baseline method, maintaining an average position tracking error below 0.1 m and velocity tracking errors within +/-3% of the target values. Through bipedal and quadrupedal simulations of ground and stair jumping, as well as sim-to-sim and sim-to-real validations, SRL exhibits robust adaptability to various task requirements and environmental complexities, underscoring its potential for real-world deployment.

Xiaowen Hu, Linqi Ye, Yudi Zhu +4

Institute of Artificial Intelligence, Shanghai University, Shangda Road 99, Baoshan District, 200444, Shanghai, China · Institute of Machine Intelligence, University of Shanghai for Science and Technology, Jungong Road 516, Yangpu District, 200093, Shanghai, China

Scalable Robot Learning Reinforcement Learning Control Offline Reinforcement Learning Inverted Pendulum

Jun 11, 2026cs.RO

Learning Dynamic Swing-Up of an Inverted Pendulum using Remote Magnetic Actuation

Electromagnetic Navigation Systems (eMNS) have gained considerable attention for minimally invasive surgery and targeted drug delivery. While most of the literature relies on quasi-static control of these systems, recent work has demonstrated the benefits of dynamic approaches. However, trajectory tracking far from equilibrium states remains largely unaddressed. We close this gap by demonstrating the first swing-up of a magnetically actuated inverted pendulum using the clinically-ready Navion eMNS. Although the inverted pendulum is not clinically relevant in itself, the proposed method utilizes torques and forces as control objectives, making it applicable to other magnetically actuated devices such as catheters and guidewires. Our approach combines trajectory optimization that accounts for internal eMNS dynamics with time-varying Linear Quadratic Regulator (LQR) state feedback and Iterative Learning Control (ILC), which leverages previous trial data and the system's dynamic model to progressively refine the feedforward command. While LQR alone fails due to the complex phenomena of magnetic actuation, ILC enables successful swing-up within six iterations. Furthermore, post-experimental analysis reveals that the learned ILC correction closely matches the torque discrepancy predicted by high-fidelity magnetic field model calibration, suggesting learning and adaptation as a promising tool to deal with uncertainties in electromagnetic actuation arising, e.g., from patient-specific physiological motion patterns and field model calibration inaccuracies.

Viacheslav Sydora, Jasan Zughaibi, Denis von Arx +2

Learning and Dynamical Systems, Max Planck Institute for Intelligent Systems, Tübingen, Germany · Multi-Scale Robotics Lab, Institute of Robotics and Intelligent Systems, D-MAVT, ETH Zürich, Zürich, Switzerland · Medical Robotics Lab, Institute of Robotics and Intelligent Systems, D-MAVT, ETH Zürich, Zürich, Switzerland

Inverted Pendulum Magnetic Tunnel Junction

Jun 8, 2026cs.RO

Robotic Nonprehensile Object Transportation with a Hanging Tray

We consider the nonprehensile object transportation task known as the waiter's problem, in which a robot must move an object balanced on a tray from one location to another. In contrast to prior works on the robotic waiter's problem, which make the robot tilt a tray rigidly held by its end effector (EE), we use a tray suspended from the EE by ropes, such that it behaves like a three-dimensional pendulum. Some prior works have actuated the robot so that the EE simulates the behavior of a pendulum, because pendular motion reduces the shear forces acting on the transported objects, minimizing the sliding of rigid objects and sloshing in containers of liquid. In contrast, our use of a real hanging tray allows us to obtain the benefits of pendular motion while only actuating a 3 degree-of-freedom (DOF) mobile base, rather than requiring a full 6-DOF manipulator arm. Our experiments in simulation and on real hardware show that the hanging tray substantially reduces both sliding and sloshing compared to a static, rigidly-grasped tray. Furthermore, we integrate the hanging tray into an interactive robot waiter demonstration, which uses computer vision to identify people with a raised hand and visual servoing to steer toward them and allow them to access the tray.

Adam Heins, Angela P. Schoellig

University of Toronto · Toronto, Canada · Technical University of Munich +1

Robot Systems Inverted Pendulum Objects

Jun 8, 2026cs.RO

Stabilizing Fast Dynamical Systems Using Time-of-Flight Cameras

Time-of-flight cameras are popular in robotics because they provide direct depth information and are compact, inexpensive, and less dependent on ambient visible light. However, their low spatial resolution and depth noise raise questions about their suitability for stabilizing fast, unstable dynamics. In this paper, we show that an inexpensive, low-resolution time-of-flight camera can provide angle feedback for reliable and precise balancing of an inverted pendulum on a cart, a canonical control benchmark. These results open the door to using compact, inexpensive, low-resolution time-of-flight cameras for precise feedback control of fast, unstable systems.

Anthony Czubarow, Antonio Terpin, Raffaello D'Andrea

Institute for Dynamic Systems and Control, ETH Zürich, Zürich, Switzerland

Inverted Pendulum Quadrotor Camera Inverse Dynamics Feedback

May 7, 2026cs.RO

On the Emergence of Pendular Structure in Multi-Contact Locomotion

LIPM is everywhere in legged-locomotion control, but almost always as a modeling choice rather than as something the controller's cost actually prefers. This note tries to make that link more explicit. Working from a small centroidal OCP that penalizes the rate of angular momentum, we look at what its optimum tends to look like. Three things come out. With full-rank stance, the optimum drifts toward a pendular force pattern at a rate determined by the SVD of the moment Jacobian; the constant is set by foot-span geometry and matches the experiments to within 16%. With N=2 stance, as in trot, the friction cone introduces a lower bound on

\|\dot{H}_G\|

that no amount of weight tuning fixes; we also see a non-smooth feasibility kink at a critical horizontal acceleration that we can write in closed form. Adding a task term that asks for a nonzero

\dot{H}_G

moves the optimum off the pendular set in a predictable way. None of this is far from the classical ZMP/DCM picture. We test these claims on a point-mass quadruped and on the Unitree Go1 in MuJoCo (open-loop QP and a torque-level closed-loop controller), and we note where the asymptotic story stops being a good description of what the closed loop actually does.

Lingxue Lyu, Zihui Liu

School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104, USA · Department of Aeronautics & Astronautics, Stanford University, Stanford, CA 94305, USA

Inverted Pendulum Torque Momentum Emergence Attitude

Apr 28, 2026eess.SY

Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Control

We develop a physics-informed learning framework for energy-shaping control of port-Hamiltonian (pH) systems from trajectory data. The proposed approach co-learns a pH system model and an optimal energy-balancing passivity-based controller (EB-PBC) through alternating optimization with policy-aware data collection. At each iteration, the system model is refined using trajectory data collected under the current control policy, and the controller is re-optimized on the updated model. Both components are parameterized by neural networks that embed the pH dynamics and EB-PBC structure, ensuring interpretability in terms of energy interactions. The learned controller renders the closed-loop system inherently passive and provably stable, and exploits passive plant dynamics without canceling the natural potential. A dissipation regularization enforces strict energy decay during training, thereby enhancing robustness to sim-to-real gaps. The proposed framework is validated on state-regulation and swing-up tasks for planar and torsional pendulum systems.

Ankur Kamboj, Biswadip Dey, Vaibhav Srivastava

Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824 · Meta Reality Labs, Redmond, WA 98052

Learning-Based Control Active Flow Control Hamiltonian Inverted Pendulum Passive

Apr 1, 2026eess.SY

Safe learning-based control via function-based uncertainty quantification

Uncertainty quantification is essential when deploying learning-based control methods in safety-critical systems. This is commonly realized by constructing uncertainty tubes that enclose the unknown function of interest, e.g., the reward and constraint functions or the underlying dynamics model, with high probability. However, existing approaches for uncertainty quantification typically rely on restrictive assumptions that encode smoothness properties of the unknown function, such as a known norm in a function space. Moreover, these methods usually struggle with discontinuities. In this paper, we model the unknown function as a random function from which independent and identically distributed realizations can be generated. We then construct uncertainty tubes via the scenario approach that hold with high probability. Our uncertainty tubes rely solely on sampled realizations and can therefore accommodate discontinuities represented by the sampling model. We integrate these uncertainty tubes into a safe Bayesian optimization algorithm with which we safely tune control parameters on a real Furuta pendulum.

Abdullah Tokmak, Toni Karvonen, Thomas B. Schön +1

Cyber-physical Systems Group, Aalto University, Espoo, Finland · School of Engineering Sciences, Lappeenranta–Lahti University of Technology LUT, Lappeenranta, Finland · Department of Information Technology, Uppsala University, Uppsala, Sweden

Control Barrier Functions Uncertainty Quantification Learning-Based Control Inverted Pendulum Uncertainty Multi-Objective Bayesian Optimization Algorithms

Mar 30, 2026cs.LG

Critical Damping as a Momentum Schedule: Multi-Seed Validation, a Hybrid Recipe, and an Exhaustive Negative Result on Surgical Layer Selection

The critical damping condition of the damped harmonic oscillator model of SGD with momentum (Qian, 1999) yields a momentum schedule with no tuned hyperparameters: mu(t) = 1 - 2*sqrt(alpha(t)). Across five seeds on ResNet-18/CIFAR-10 (200-epoch cosine schedule) it reaches 90% test accuracy 2.34x faster than constant mu=0.9 (range 1.71-2.86x, 5/5 seeds, one-sided paired t-test p=4e-4), at the cost of a real final-accuracy deficit of 0.46 pp (5/5 seeds, p=0.009). A short-schedule control rules out a schedule-length artifact: compressed baselines either pay 0.5-0.9 pp of accuracy or stay slower to 90% at equal accuracy. A hybrid recipe -- critical-damping momentum until 90%, then constant mu=0.9 -- removes the deficit and keeps the speedup: 95.45 +/- 0.05% final accuracy at 2.4x faster progress to 90% (n=5). The speedup generalizes across architectures (VGG-16 without skip connections: 1.72x, n=3); on CIFAR-100 early gains persist (2-4x to mid-training thresholds) but the accuracy cost grows (-1.7 pp), compressing the accuracy-matched gain to 1.14x. We also report an exhaustive negative result on surgical layer selection. Version 2 of this paper claimed that gradient attribution on misclassified images selects which layers to retrain; running the identical correction protocol on all 35 combinations of 3-of-7 layer groups ranks the selected triple 11th of 35 (exact p=0.31) -- no better than random. What survives is weaker but real: combinations containing the top-ranked layer outperform the rest (+6.2 vs -1.4 mean net error reduction), and the bottom of the gradient-norm ranking reliably predicts the most harmful interventions (down to -20 net errors). Gradient attribution on errors is a harm-avoidance signal, not a selector of repair targets. We release the full 35-combination landscape as a baseline for layer-selection claims.

Ivan Pasichnyk

We Label Data Inc.

Momentum Stochastic Gradient Descent Inverted Pendulum Correction Recipe

Mar 17, 2026cs.RO

Sampling-Based MuJoCo MPC for Double-Pendulum Sway Suppression on a Shipboard Crane

Transferring heavy payloads in maritime settings relies on efficient crane operation, limited by hazardous double-pendulum payload sway. This sway motion is further exacerbated in offshore environments by external perturbations from wind and ocean waves. Manual suppression of these oscillations on an underactuated crane system by human operators is challenging. Existing control methods struggle in such settings, often relying on simplified analytical models, while deep reinforcement learning (RL) approaches tend to generalise poorly to unseen conditions. Deploying a predictive controller onto compute-constrained, highly non-linear physical systems without relying on extensive offline training or complex analytical models remains a significant challenge. Here we show a complete real-time control pipeline centered on the MuJoCo MPC framework that leverages a cross-entropy method planner to evaluate candidate action sequences directly within a physics simulator. By using simulated rollouts, this sampling-based approach successfully reconciles the conflicting objectives of dynamic target tracking and sway damping without relying on complex analytical models. We demonstrate that the controller can run effectively on a resource-constrained embedded hardware, while outperforming traditional PID and RL baselines in counteracting external base perturbations. Furthermore, our system demonstrates robustness even when subjected to unmodeled physical discrepancies like the introduction of a second payload.

Oscar Pang, Lisa Coiffard, Paul Templier +3

Adaptive and Intelligent Robotics Lab, Department of Computing, Imperial College London, Exhibition Rd, London, SW7 2BX, United Kingdom

Model Predictive Control Inverted Pendulum Reinforcement Learning Control Mujoco

Jan 30, 2026cs.LG

Adaptive Momentum and Nonlinear Damping for Neural Network Training

Momentum Stochastic Gradient Descent (mSGD) relies on a fixed momentum coefficient shared across all parameters, failing to account for the heterogeneous structure of modern loss landscapes. In this work, we adopt a continuous-time formulation to introduce individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This mechanism automatically adjusts to evolving training dynamics to maintain stability without sacrificing convergence speed. We demonstrate that this adaptive friction is inextricably linked to cubic damping, a suppression mechanism from structural dynamics. We additionally introduce two optimization schemes by augmenting the continuous dynamics of mSGD and Adam with a cubic damping term. Empirically, our methods demonstrate robustness and match or outperform Adam on training ViT, BERT, and GPT2 tasks where mSGD typically struggles. We further provide theoretical results establishing the exponential convergence of the proposed schemes.

Aikaterini Karoni, Rajit Rajpal, Benedict Leimkuhler +1

School of Mathematics University of Bristol · School of Mathematics University of Edinburgh · CERMICS, CNRS, École des Ponts, Institut Polytechnique de Paris; Inria Paris, France

Momentum Stochastic Gradient Descent Neural Network Training Inverted Pendulum

May 16, 2025cs.RO

Bracing for Impact: Robust Humanoid Push Recovery and Locomotion with Reduced Order Models

Push recovery during locomotion will facilitate the deployment of humanoid robots in human-centered environments. In this paper, we present a unified framework for walking control and push recovery for humanoid robots, leveraging the arms for push recovery while dynamically walking. The key innovation is to use the environment, such as walls, to facilitate push recovery by combining Single Rigid Body model predictive control (SRB-MPC) with Hybrid Linear Inverted Pendulum (HLIP) dynamics to enable robust locomotion, push detection, and recovery by utilizing the robot's arms to brace against such walls and dynamically adjusting the desired contact forces and stepping patterns. Extensive simulation results on a humanoid robot demonstrate improved perturbation rejection and tracking performance compared to HLIP alone, with the robot able to recover from pushes up to 100N for 0.2s while walking at commanded speeds up to 0.5m/s. Robustness is further validated in scenarios with angled walls and multi-directional pushes.

Lizhi Yang, Blake Werner, Adrian B. Ghansah +1

AMBER Lab at the Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, USA

Locomotion Robot-Free Demonstrations Inverted Pendulum Model Predictive Control Reduced-Order Models Impact Analysis