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Koopman Operators in Robot Learning

Koopman operator theory offers a rigorous treatment of dynamics and has been emerging as an alternative modeling and learning-based control method across various robotics sub-domains. Due to its ability to represent nonlinear dynamics as a linear (but higher-dimensional) operator, Koopman theory offers a fresh lens through which to understand and tackle the modeling and control of complex robotic systems. Moreover, it enables incremental updates and is computationally inexpensive, thus making it particularly appealing for real-time applications and online active learning. This review delves deeply into the foundations of Koopman operator theory and systematically builds a bridge from theoretical principles to practical robotic applications. We begin by explaining the mathematical underpinnings of the Koopman framework and discussing approximation approaches for incorporating inputs into Koopman-based modeling. Foundational considerations, such as data collection strategies as well as the design of lifting functions for effective system embedding, are also discussed. We then explore how Koopman-based models serve as a unifying tool for a range of robotics tasks, including model-based control, real-time state estimation, and motion planning. The review proceeds to a survey of cutting-edge research that demonstrates the versatility and growing impact of Koopman methods across diverse robotics sub-domains: from aerial and legged platforms to manipulators, soft-bodied systems, and multi-agent networks. A presentation of more advanced theoretical topics, necessary to push forward the overall framework, is included. Finally, we reflect on some key open challenges that remain and articulate future research directions that will shape the next phase of Koopman-inspired robotics. To support practical adoption, we provide a hands-on tutorial with executable code at https://shorturl.at/ouE59.

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EmbodiedRSI: Active Continual Robot Learning Through Hypothesis-Guided Co-Evolution

Robot foundation models provide strong visuomotor control, yet their performance can degrade when object positions or task instructions change. Further improvements often require post-training on substantial robot data, which can be costly to collect through methods such as teleoperation. Agentic harnesses can adapt around the model, but current self-evolving harnesses use robot trials inefficiently when deciding which code and skill changes to pursue. We introduce EmbodiedRSI, a self-evolving agentic harness that autonomously decides where to explore next and turns the resulting physical interaction into improved code and skills. EmbodiedRSI realizes this through a Fast-Slow Dual-System Architecture, in which competing code and skill hypotheses are maintained in a Hypothesis Graph. Value-of-Information Experiment Selection chooses physical experiments that can distinguish these hypotheses. Their outcomes guide Code-Skill Co-Evolution. The Slow System builds Hierarchical Memory, and Reward-Grounded Memory Learning selects effective memory according to their value for later Fast-System improvement. On RoboCasa365, EmbodiedRSI reaches 77.0% overall success and 71.3% on Composite-Unseen, compared with 40.1% for the best baseline. EmbodiedRSI also reaches 86.8% overall success on LIBERO-Pro. Beyond benchmark performance, EmbodiedRSI transfers zero-shot to real-world robot, achieving 71.3% overall success across multiple challenging tasks.

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Articulated-Body Dynamics Network: Dynamics-Grounded Prior for Robot Learning

Recent work in reinforcement learning has shown that incorporating structural priors for articulated robots, such as link connectivity, into policy networks improves learning efficiency. However, dynamics properties, despite their fundamental role in determining how forces and motion propagate through the body, remain largely underexplored as an inductive bias for policy learning. To address this gap, we present the Articulated-Body Dynamics Network (ABD-Net), a novel graph neural network architecture grounded in the computational structure of forward dynamics. Specifically, we adapt the inertia propagation mechanism from the Articulated Body Algorithm, systematically aggregating inertial quantities from child to parent links in a tree-structured manner, while replacing physical quantities with learnable parameters. Embedding ABD-NET into the policy actor enables dynamics-informed representations that capture how actions propagate through the body, leading to efficient and robust policy learning. Through experiments with simulated humanoid, quadruped, and hopper robots, our approach demonstrates increased sample efficiency and generalization to dynamics shifts compared to transformer-based and GNN baselines. We further validate the learned policy on real Unitree G1 and Go2 robots, state-of-the-art humanoid and quadruped platforms, generating dynamic, versatile and robust locomotion behaviors through sim-to-real transfer with real-time inference.

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Learning Robot Manipulation from Cross-Morphology Demonstration

Some Learning from Demonstrations (LfD) methods handle small mismatches in the action spaces of the teacher and student. Here we address the case where the teacher's morphology is substantially different from that of the student. Our framework, Morphological Adaptation in Imitation Learning (MAIL), bridges this gap allowing us to train an agent from demonstrations by other agents with significantly different morphologies. MAIL learns from suboptimal demonstrations, so long as they provide $\textit{some}$ guidance towards a desired solution. We demonstrate MAIL on manipulation tasks with rigid and deformable objects including 3D cloth manipulation interacting with rigid obstacles. We train a visual control policy for a robot with one end-effector using demonstrations from a simulated agent with two end-effectors. MAIL shows up to $24\%$ improvement in a normalized performance metric over LfD and non-LfD baselines. It is deployed to a real Franka Panda robot, handles multiple variations in properties for objects (size, rotation, translation), and cloth-specific properties (color, thickness, size, material). An overview is on https://uscresl.github.io/mail .

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ARS: Agentic Reward System for Robot Learning

Progress reward modeling is the problem of estimating how a robot's behavior changes task progress over time. Reliable estimation requires distinguishing meaningful state changes from failed attempts and task-irrelevant actions. We introduce the Agentic Reward System (ARS), an inference framework for progress reward modeling with general-purpose vision-language models (VLMs), without additional reward-model training. Given an offline trajectory and a task instruction, ARS uses adaptive visual inspection for both event proposal and verification. A subagent proposes a task-relevant event timeline, which a primary agent verifies and revises before estimating per-frame progress. ARS can incorporate optional terminal outcome labels and visual references to inform its judgments. It can also audit progress estimates from external reward models. We evaluate ARS with a 27B VLM on a controlled semantic-mismatch benchmark and downstream policy learning in simulation and on a real robot. The benchmark reveals that several evaluated reward baselines assign spurious progress to wrong-object manipulation even in simple pick-and-place scenes. ARS better suppresses these errors and outperforms these baselines in simulation policy learning. We further demonstrate that ARS supports long-horizon policy learning from mixed-quality offline experience on real-robot multi-screw fastening in a full-scale laboratory replica of an industrial washing-machine assembly line. These results suggest that structured inference and verification can improve the usefulness of general-purpose VLMs for robot reward modeling. Code is at https://github.com/midea-ai/ars

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FLARE: Robot Learning with Implicit World Modeling

We introduce $\textbf{F}$uture $\textbf{LA}$tent $\textbf{RE}$presentation Alignment ($\textbf{FLARE}$), a novel framework that integrates predictive latent world modeling into robot policy learning. By aligning features from a diffusion transformer with latent embeddings of future observations, $\textbf{FLARE}$ enables a diffusion transformer policy to anticipate latent representations of future observations, allowing it to reason about long-term consequences while generating actions. Remarkably lightweight, $\textbf{FLARE}$ requires only minimal architectural modifications -- adding a few tokens to standard vision-language-action (VLA) models -- yet delivers substantial performance gains. Across two challenging multitask simulation imitation learning benchmarks spanning single-arm and humanoid tabletop manipulation, $\textbf{FLARE}$ achieves state-of-the-art performance, outperforming prior policy learning baselines by up to 26%. Moreover, $\textbf{FLARE}$ unlocks the ability to co-train with human egocentric video demonstrations without action labels, significantly boosting policy generalization to a novel object with unseen geometry with as few as a single robot demonstration. Our results establish $\textbf{FLARE}$ as a general and scalable approach for combining implicit world modeling with high-frequency robotic control.

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Skill Composition for Legged Robot Reinforcement Learning

Robots, and humanoid robots in particular, are increasingly competent at individual behaviors, each obtained by training a specialized controller. A specialized skill is quick to train, converges reliably because the problem it faces is narrow, and can be validated on its own, none of which is true of a single end-to-end policy asked to cover everything. What remains fragile is the transition between them. We argue that the composition of independent sub-policies deserves to be treated as a research problem in its own right, rather than as an implementation detail left to whatever mechanism happens to be at hand. Reliable composition is what turns a collection of separate skills into a repertoire that can be used, extended and shared. More fundamentally, if control can be passed between specialized policies safely, and at any moment, the choice of what the robot should do next can be delegated to a component of an entirely different nature, such as a planner, an automaton or a symbolic controller, whose behavior can be inspected in advance. The policies would then only ever have to act, and what the robot can be trusted to do would become verifiable.

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Network-in-the-Loop at Scale: GPU-Batched 5G Simulation for Massively Parallel Robot Learning

Massively parallel GPU simulators train multi-robot policies in thousands of environments, and many fleets use private Fifth-Generation (5G) networks, where each robot's delay depends on its teammates' traffic. Network-in-the-loop training places a simulated 5G network inside this loop. However, GPU robot simulators reduce the network to an independent delay per message, while packet-level simulators run one scenario per CPU process and cannot keep pace with thousands of parallel environments. To bridge this gap, we present Isaac-Net, a GPU-batched 5G New Radio (NR) module that advances the uplink of thousands of environments in lockstep with Isaac Lab physics. Isaac-Net simulates every slot, the 0.5~ms interval in which the base station decides which robots transmit, for all environments at once. Extensive experiments confirm that its NR engine reproduces the median delay of ns-3 5G-LENA across loads, with a median delay 5--10\% low on an unseen carrier and 9\% high at 32 robots per environment in closed loop. The engine also reproduces the Age of Information (AoI), the age of each robot's newest delivered report, while an independent delay per message leaves the AoI tail about three times too light. In a configuration validated against 5G-LENA, Isaac-Net keeps the network in the loop for about one million robots on one GPU at 83\% of the Isaac Lab rate without the network, measured under a random policy. Isaac-Net is open source at https://github.com/ZzZTripleZzZ/isaac-net

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Physical Twins: Accelerating and Enabling Robot Learning with Phantom Platforms

Improvements in human-robot physical interaction (pHRI) can have major implications for physical therapy, search and rescue, and telemedicine. However, a major challenge concerns human constraints and safety in human-robot physical experiments. Concerns about human studies also include repeatability, scalability, and participant diversity. To conduct such experiments, an IRB and willing human participants are required. In this work, we present an improved phantom device, a physical twin, that enables real-world RL-type testing for physically interactive algorithms. The new device not only replicates the ball-and-socket motion of the shoulder but also renders scapular and protraction/retraction motions. The experiments showcase the device's ability to render multiple 3D joint limits and demonstrate a Franka Panda arm sensing limits and interacting with the device as an arm for ADLs (activities of daily living) and pHRI tasks.

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Isaac Lab: A GPU-Accelerated Simulation Framework for Multi-Modal Robot Learning

We present Isaac Lab, the natural successor to Isaac Gym, which extends the paradigm of GPU-native robotics simulation into the era of large-scale multi-modal learning. Isaac Lab combines high-fidelity GPU parallel physics, photorealistic rendering, and a modular, composable architecture for designing environments and training robot policies. Beyond physics and rendering, the framework integrates actuator models, multi-frequency sensor simulation, data collection pipelines, and domain randomization tools, unifying best practices for reinforcement and imitation learning at scale within a single extensible platform. We highlight its application to a diverse set of challenges, including whole-body control, cross-embodiment mobility, contact-rich and dexterous manipulation, and the integration of human demonstrations for skill acquisition. Finally, we discuss upcoming integration with the differentiable, GPU-accelerated Newton physics engine, which promises new opportunities for scalable, data-efficient, and gradient-based approaches to robot learning. We believe Isaac Lab's combination of advanced simulation capabilities, rich sensing, and data-center scale execution will help unlock the next generation of breakthroughs in robotics research.

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DynaMimicGen: A Data Generation Framework for Robot Learning of Dynamic Tasks

Learning robust manipulation policies typically requires large and diverse datasets, the collection of which is time-consuming, labor-intensive, and often impractical for dynamic environments. In this work, we introduce DynaMimicGen (D-MG), a scalable dataset generation framework that enables policy training from minimal human supervision while uniquely supporting dynamic task settings. Given only a few human demonstrations, D-MG first segments the demonstrations into meaningful sub-tasks, then leverages Dynamic Movement Primitives (DMPs) to adapt and generalize the demonstrated behaviors to novel and dynamically changing environments. Improving prior methods that rely on static assumptions or simplistic trajectory interpolation, D-MG produces smooth, realistic, and task-consistent Cartesian trajectories that adapt in real time to changes in object poses, robot states, or scene geometry during task execution. Our method supports different scenarios - including scene layouts, object instances, and robot configurations - making it suitable for both static and highly dynamic manipulation tasks. We show that robot agents trained via imitation learning on D-MG-generated data achieve strong performance across long-horizon and contact-rich benchmarks, including tasks like cube stacking and placing mugs in drawers, even under unpredictable environment changes. By eliminating the need for extensive human demonstrations and enabling generalization in dynamic settings, D-MG offers a powerful and efficient alternative to manual data collection, paving the way toward scalable, autonomous robot learning.

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Robot Learning of Shifting Objects for Grasping in Cluttered Environments

Robotic grasping in cluttered environments is often infeasible due to obstacles preventing possible grasps. Then, pre-grasping manipulation like shifting or pushing an object becomes necessary. We developed an algorithm that can learn, in addition to grasping, to shift objects in such a way that their grasp probability increases. Our research contribution is threefold: First, we present an algorithm for learning the optimal pose of manipulation primitives like clamping or shifting. Second, we learn non-prehensible actions that explicitly increase the grasping probability. Making one skill (shifting) directly dependent on another (grasping) removes the need of sparse rewards, leading to more data-efficient learning. Third, we apply a real-world solution to the industrial task of bin picking, resulting in the ability to empty bins completely. The system is trained in a self-supervised manner with around 25000 grasp and 2500 shift actions. Our robot is able to grasp and file objects with 274 picks per hour. Furthermore, we demonstrate the system's ability to generalize to novel objects.

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UniBYD: A Unified Framework for Learning Robotic Manipulation Across Embodiments Beyond Imitation of Human Demonstrations

In embodied intelligence, the embodiment gap between robotic and human hands brings significant challenges for learning from human demonstrations. Although some studies have attempted to bridge this gap using reinforcement learning, they remain confined to merely reproducing human manipulation, resulting in limited task performance. Moreover, current methods struggle to support diverse robotic hand configurations. In this paper, we propose UniBYD, a unified framework that uses a dynamic reinforcement learning algorithm to discover manipulation policies aligned with the robot's physical characteristics. To enable consistent modeling across diverse robotic hand morphologies, UniBYD incorporates a unified morphological representation (UMR). Building on UMR, we design a dynamic PPO with an annealed reward schedule, enabling reinforcement learning to transition from offline-informed imitation of human demonstrations to online-adaptive exploration of policies better adapted to diverse robotic morphologies, thereby going beyond mere imitation of human hands. To address the severe state drift caused by the incapacity of early-stage policies, we design a hybrid Markov-based shadow engine that provides fine-grained guidance to anchor the imitation within the expert's manifold. To evaluate UniBYD, we propose UniManip, the first benchmark for cross-embodiment manipulation spanning diverse robotic morphologies. Experiments demonstrate a 44.08% average improvement in success rate over the current state-of-the-art. Our project page is https://zhanheng-creator.github.io/UniBYD.

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Learning Robot Safety from Sparse Human Feedback using Conformal Prediction

Ensuring robot safety can be challenging; user-defined constraints can miss edge cases, policies can become unsafe even when trained from safe data, and safety can be subjective. Thus, we learn about robot safety by showing policy trajectories to a human who flags unsafe behavior. From this binary feedback, we use the statistical method of conformal prediction to identify a region of states, potentially in learned latent space, guaranteed to contain a user-specified fraction of future policy errors. Our method is sample-efficient, as it builds on nearest neighbor classification and avoids withholding data as is common with conformal prediction. By alerting if the robot reaches the suspected unsafe region, we obtain a warning system that mimics the human's safety preferences with guaranteed miss rate. From video labeling, our system can detect when a quadcopter visuomotor policy will fail to steer through a designated gate. We present an approach for policy improvement by avoiding the suspected unsafe region. With it we improve a model predictive controller's safety, as shown in experimental testing with 30 quadcopter flights across 6 navigation tasks. Code and videos are provided.

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Sim-to-Real Robot Learning from Pixels with Progressive Nets

Applying end-to-end learning to solve complex, interactive, pixel-driven control tasks on a robot is an unsolved problem. Deep Reinforcement Learning algorithms are too slow to achieve performance on a real robot, but their potential has been demonstrated in simulated environments. We propose using progressive networks to bridge the reality gap and transfer learned policies from simulation to the real world. The progressive net approach is a general framework that enables reuse of everything from low-level visual features to high-level policies for transfer to new tasks, enabling a compositional, yet simple, approach to building complex skills. We present an early demonstration of this approach with a number of experiments in the domain of robot manipulation that focus on bridging the reality gap. Unlike other proposed approaches, our real-world experiments demonstrate successful task learning from raw visual input on a fully actuated robot manipulator. Moreover, rather than relying on model-based trajectory optimisation, the task learning is accomplished using only deep reinforcement learning and sparse rewards.

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Robot Learning in Homes: Improving Generalization and Reducing Dataset Bias

Data-driven approaches to solving robotic tasks have gained a lot of traction in recent years. However, most existing policies are trained on large-scale datasets collected in curated lab settings. If we aim to deploy these models in unstructured visual environments like people's homes, they will be unable to cope with the mismatch in data distribution. In such light, we present the first systematic effort in collecting a large dataset for robotic grasping in homes. First, to scale and parallelize data collection, we built a low cost mobile manipulator assembled for under 3K USD. Second, data collected using low cost robots suffer from noisy labels due to imperfect execution and calibration errors. To handle this, we develop a framework which factors out the noise as a latent variable. Our model is trained on 28K grasps collected in several houses under an array of different environmental conditions. We evaluate our models by physically executing grasps on a collection of novel objects in multiple unseen homes. The models trained with our home dataset showed a marked improvement of 43.7% over a baseline model trained with data collected in lab. Our architecture which explicitly models the latent noise in the dataset also performed 10% better than one that did not factor out the noise. We hope this effort inspires the robotics community to look outside the lab and embrace learning based approaches to handle inaccurate cheap robots.

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Safe Robot Learning in Assistive Devices through Neural Network Repair

Assistive robotic devices are a particularly promising field of application for neural networks (NN) due to the need for personalization and hard-to-model human-machine interaction dynamics. However, NN based estimators and controllers may produce potentially unsafe outputs over previously unseen data points. In this paper, we introduce an algorithm for updating NN control policies to satisfy a given set of formal safety constraints, while also optimizing the original loss function. Given a set of mixed-integer linear constraints, we define the NN repair problem as a Mixed Integer Quadratic Program (MIQP). In extensive experiments, we demonstrate the efficacy of our repair method in generating safe policies for a lower-leg prosthesis.

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Using Temperature Sampling to Effectively Train Robot Learning Policies on Imbalanced Datasets

Increasingly large datasets of robot actions and sensory observations are being collected to train ever-larger neural networks. These datasets are collected based on tasks and while these tasks may be distinct in their descriptions, many involve very similar physical action sequences (e.g., 'pick up an apple' versus 'pick up an orange'). As a result, many datasets of robotic tasks are substantially imbalanced in terms of the physical robotic actions they represent. In this work, we propose a simple sampling strategy for policy training that mitigates this imbalance. Our method requires only a few lines of code to integrate into existing codebases and improves generalization. We evaluate our method in both pre-training small models and fine-tuning large foundational models. Our results show substantial improvements on low-resource tasks compared to prior state-of-the-art methods, without degrading performance on high-resource tasks. This enables more effective use of model capacity for multi-task policies. We also further validate our approach in a real-world setup on a Franka Panda robot arm across a diverse set of tasks.

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