Covariance-Regulated Recursive Koopman Learning for Nonlinear Systems with Uncertain Time-Varying Dynamics

Offline models for autonomous robots often fail under time-varying dynamics outside their training distribution. Koopman operator theory offers a linear representation of nonlinear dynamics via lifting, but its transition to real-time recursive estimation may suffer numerical vulnerabilities: covariance windup under low excitation when using exponential forgetting, and vanishing gain without forgetting. This paper introduces a Covariance-Regulated Recursive Koopman Learning (CR-RKL) framework with two complementary strategies--error dead-zone gating and constant-trace normalization--each independently capable of preventing covariance explosion and parameter freezing, with the latter additionally preserving the geometric structure of uncertainty. Validated on a non-holonomic differential-drive robot with wheel slip and Stribeck friction and on a 26-gram butterfly-inspired flapping-wing micro aerial vehicle, CR-RKL achieves numerically stable and accurate online modeling, and when embedded in model predictive control, it maintains reliable tracking performance under uncertain, time-varying dynamics.

Neuromorphic Control of a Flapping-Wing Robot on Resource-Constrained Hardware

Flapping-Wing Micro Aerial Vehicles (FWMAVs) provide exceptional maneuverability and aerodynamic efficiency but pose significant challenges for onboard control due to nonlinear dynamics and stringent Size, Weight, and Power (SWaP) constraints, as exemplified by a butterfly-inspired robot less than 30 gram. To this end, we present a hierarchical neuromorphic control framework that enables fully onboard, closed-loop flight on a widely available, resource-constrained ESP32 microcontroller with a unit cost of approximately $5. Specifically, our method deploys two lightweight Spiking Neural Networks (SNNs) onboard: one for state estimation from raw sensory feedback and another for control via modulation of a Central Pattern Generator (CPG) for wing actuation. Trained by imitation learning, the system achieves stable pitch and heading angle tracking during untethered real-world flight. Experimental results further reveal that the SNN-based controller reduces latency by 36% (1059us to 680us) and power by 18% (0.033W to 0.027W) for inference compared to the conventional Artificial Neural Network (ANN) baseline, demonstrating the viability of spike-based computation without specialized hardware. To the best of our knowledge, this work constitutes the first demonstration of fully onboard neuromorphic control for autonomous flight of a FWMAV, highlighting the potential of SNNs to enable energy-efficient autonomy under stringent SWaP constraints. Visual abstract: http://bit.ly/4nI8ECY

Koopman Identification of Nonlinear Systems via Reservoir Liftings

Learning tractable linear representations of nonlinear dynamical systems via Koopman operator theory is often hindered by dictionary selection, temporal memory encoding, and numerical ill-conditioning. Inspired by Reservoir Computing (RC) paradigm, this paper introduces the RC-Koopman framework, which interprets reservoir as a stateful, finite-dimensional Koopman dictionary whose temporal depth is explicitly controlled by its spectral radius. We show that the Echo State Property (ESP) guarantees well-posedness and favorable numerical conditioning of the lifted Koopman approximation. A correlation-based spectral radius selection algorithm aligns reservoir memory with dominant system timescales. Analysis reveals how the finite memory of the reservoir determines which Koopman eigenfunctions remain observable from the lifted features. Evaluation on synthetic benchmarks demonstrates that RC-Koopman achieves a favorable balance between reconstruction accuracy of the underlying nonlinear dynamics and dynamical stability, compared to Extended Dynamic Mode Decomposition (EDMD) and Hankel-based lifting approaches. Code available at: https://github.com/NEAR-the-future/RC-Koopman.git

A 26-Gram Butterfly-Inspired Robot Achieving Autonomous Tailless Flight

Flapping-wing micro air vehicles (FWMAVs) have demonstrated remarkable bio-inspired agility, yet tailless two-winged configurations remain largely unexplored due to their complex fluid-structure and wing-body coupling. Here we present \textit{AirPulse}, a 26-gram butterfly-inspired FWMAV that achieves fully onboard, closed-loop, untethered flight without auxiliary control surfaces. The AirPulse robot replicates key biomechanical traits of butterfly flight, including low wing aspect ratio, compliant carbon-fiber-reinforced wings, and low-frequency, high-amplitude flapping that induces cyclic variations in the center of gravity and moment of inertia, producing characteristic body undulation. We establish a quantitative mapping between flapping modulation parameters and force-torque generation, and introduce the Stroke Timing Asymmetry Rhythm (STAR) generator, enabling smooth, stable, and linearly parameterized wingstroke asymmetry for flapping control. Integrating these with an attitude controller, the AirPulse robot maintains pitch and yaw stability despite strong oscillatory dynamics. Free-flight experiments demonstrate stable climbing and turning maneuvers via either angle offset or stroke timing modulation, marking the first onboard controlled flight of the lightest two-winged, tailless butterfly-inspired FWMAV reported in peer-reviewed literature. This work corroborates a foundational platform for lightweight, collision-proof FWMAVs, bridging biological inspiration with practical aerial robotics. Their non-invasive maneuverability is ideally suited for real-world applications, such as confined-space inspection and ecological monitoring, inaccessible to traditional drones, while their biomechanical fidelity provides a physical model to decode the principles underlying the erratic yet efficient flight of real butterflies.

DISCOVERSE: Efficient Robot Simulation in Complex High-Fidelity Environments

We present the first unified, modular, open-source 3DGS-based simulation framework for Real2Sim2Real robot learning. It features a holistic Real2Sim pipeline that synthesizes hyper-realistic geometry and appearance of complex real-world scenarios, paving the way for analyzing and bridging the Sim2Real gap. Powered by Gaussian Splatting and MuJoCo, Discoverse enables massively parallel simulation of multiple sensor modalities and accurate physics, with inclusive supports for existing 3D assets, robot models, and ROS plugins, empowering large-scale robot learning and complex robotic benchmarks. Through extensive experiments on imitation learning, Discoverse demonstrates state-of-the-art zero-shot Sim2Real transfer performance compared to existing simulators. For code and demos: https://air-discoverse.github.io/.

An Real-Sim-Real (RSR) Loop Framework for Generalizable Robotic Policy Transfer with Differentiable Simulation

The sim-to-real gap remains a critical challenge in robotics, hindering the deployment of algorithms trained in simulation to real-world systems. This paper introduces a novel Real-Sim-Real (RSR) loop framework leveraging differentiable simulation to address this gap by iteratively refining simulation parameters, aligning them with real-world conditions, and enabling robust and efficient policy transfer. A key contribution of our work is the design of an informative cost function that encourages the collection of diverse and representative real-world data, minimizing bias and maximizing the utility of each data point for simulation refinement. This cost function integrates seamlessly into existing reinforcement learning algorithms (e.g., PPO, SAC) and ensures a balanced exploration of critical regions in the real domain. Furthermore, our approach is implemented on the versatile Mujoco MJX platform, and our framework is compatible with a wide range of robotic systems. Experimental results on several robotic manipulation tasks demonstrate that our method significantly reduces the sim-to-real gap, achieving high task performance and generalizability across diverse scenarios of both explicit and implicit environmental uncertainties.