arXiv subjects

M. Ani Hsieh

Publications and source records attributed to M. Ani Hsieh.

At least 19 recordsLinked to original sources

arXiv2026

Flatness-Preserving Residual Learning for Real-Time Tight Quadrotor Formation Flight

Quadrotors flying in tight formations are severely affected by turbulent aerodynamic interactions, such as downwash, that can cause catastrophic collisions if left unmodeled. To compensate for these effects, we propose a physics-informed residual dynamics learning framework that captures complex aerodynamic interactions while ensuring the joint multi-quadrotor system remains differentially flat. We leverage this preserved flatness to design a computationally efficient feedback linearization controller that is easily tunable with linear control techniques and cancels aerodynamic disturbances via feedforward compensation. Hardware experiments demonstrate our framework reduces average tracking errors by 31% compared to nominal baselines. Crucially, our lightweight approach matches the tracking performance of state-of-the-art nonlinear model predictive control (NMPC) while requiring an order of magnitude less computation. We are the first to show that stable, tight formation flight can be achieved with under 30 seconds of training data and a 5ms loop rate, unlocking high-fidelity aerodynamic compensation for compute-constrained flight stacks. The video of our physical experiments can be found at https://www.youtube.com/watch?v=uF26IkRFQMk

cs.RO↗

arXiv2026

Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs

We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries. To this end, we introduce General-Geometry Neural Whitney Forms (Geo-NeW): a data-driven finite element method. We jointly learn a differential operator and compatible reduced finite element spaces defined on the underlying geometry. The resulting model is solved to generate predictions, while exactly preserving physical conservation laws through Finite Element Exterior Calculus. Geometry enters the model as a discretized mesh both through a transformer-based encoding and as the basis for the learned finite element spaces. This explicitly connects the underlying geometry and imposed boundary conditions to the solution, providing a powerful inductive bias for learning neural PDEs, which we demonstrate improves generalization to unseen domains. We provide a novel parameterization of the constitutive model ensuring the existence and uniqueness of the solution. Our approach demonstrates state-of-the-art performance on several steady-state PDE benchmarks, and provides a significant improvement over conventional baselines on out-of-distribution geometries.

cs.LG↗

arXiv2026

Neural Navigation Functions for Zero-Shot Generalizable Motion Planning

We introduce Neural Navigation Functions (Neural-NF), a learned reactive navigation function capable of zero-shot transfer across unseen environment geometries. Neural-NF places data-driven adaptation within a structured elliptic planner, where the navigation objective is learned while planner structure is preserved by construction. Specifically, intrinsic Laplacian-derived features are mapped to local PDE coefficients, and solving the resulting boundary value problem produces a globally consistent value function on each target domain. For every admissible learned model, the resulting policy is collision-free, provides monotonic descent and a global minimum at the goal by construction. This admits a linearly-solvable optimal-control interpretation for any parameter setting. Empirically, Neural-NF achieves strong zero-shot transfer across diverse geometries and outperforms learned planners that directly predict the value function by up to a $5\times$ improvement.

cs.RO↗

arXiv2026

Local Input-to-State Stability for Consensus in the Presence of Intermittent Communication and Input Saturation

This paper addresses the problem of reaching consensus under input saturation and intermittent communication, which can hinder the convergence of the system. We propose a method that translates the consensus into an equivalent stability problem. Then, we compute bounded sets that enclose the initial conditions and the evolution of trajectories leading to local input-to-state stability for systems interconnected over directed intermittent topologies. Our contributions include sufficient conditions for stability and stabilization of multi-agent systems under intermittent interactions and saturating inputs, with the ability to evaluate disturbance tolerance and rejection based on the regions that enclose the system's trajectories. We define disturbance rejection in terms of the $\mathscr{L}_2$ gain, and formulate stability and controller design conditions as convex optimization problems. Our method enable the maximization of regions that ensure local input-to-state stability, we provide numerical examples highlighting the trade-offs between mean frequency of intermittent interactions, disturbance energy, and convergence region size.

eess.SY↗

arXiv2026

Learned Lagrangian Models of PDEs via Euler-Lagrange Residual Minimization

We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range predictions. We develop an optimization-based integrator that minimizes the squared Euler--Lagrange residual via a mesh-free near-symplectic construction on local space-time patches. Different from integrators for analytical models, integrators for learned models should decouple model error (phase error) from integration error (conservation error). By relying on optimization rather than time-stepping, we bypass the global coupling inherent to fixed discretizations, which slows time- and space-stepping and complicates learning. Our method scales linearly with domain size via Jacobi iteration, and places no structural requirements on the learned network, allowing it to be coupled with existing physics-guided machine learning (ML) methods. We validate our approach on a learned representation of a double pendulum, a one-dimensional wave equation, and a two-dimensional wave equation. Our method achieves error comparable to classical symplectic methods while generalizing to spatially varying dynamics and arbitrary boundary conditions without retraining.

cs.LG↗

arXiv2026

A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds

We introduce a meshfree exterior calculus (MEEC) for learning structure-preserving descriptions of physics on point clouds, and use it to build MEEC-Net, a data-efficient surrogate that transfers across resolutions, geometries, and physical parameters. MEEC equips an $\varepsilon$-ball graph with virtual node and edge measures via a single sparse Schur complement solve; the resulting complex satisfies discrete conservation exactly, is end-to-end differentiable in the point positions, and exposes a direct geometry-to-physics link without the mesh-generation step required by conventional structure-preserving discretizations. MEEC-Net learns unknown physics as a shared edge-wise flux law in an SO($d$)-invariant local frame, so the same kernel produces compatible fluxes on any point cloud whose features lie in the training range. We prove a solution-error bound that splits into discretization and kernel-approximation terms which is independent of problem geometry, explaining the observed transfer from very few examples. We show that single-solution training transfers to unseen geometries, boundary conditions, and physical parameters. On five canonical PDE benchmarks MEEC-Net achieves 1-2 orders of magnitude lower out-of-distribution error than baseline neural-operator approaches. On the SimJEB structural-bracket benchmark it achieves competitive error while using substantially fewer training geometries.

cs.LG↗

arXiv2025

KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning

In this work, we propose a novel flow field-based motion planning method that drives a robot from any initial state to a desired reference trajectory such that it converges to the trajectory's end point. Despite demonstrated efficacy in using Koopman operator theory for modeling dynamical systems, Koopman does not inherently enforce convergence to desired trajectories nor to specified goals - a requirement when learning from demonstrations (LfD). We present KoopMotion which represents motion flow fields as dynamical systems, parameterized by Koopman Operators to mimic desired trajectories, and leverages the divergence properties of the learnt flow fields to obtain smooth motion fields that converge to a desired reference trajectory when a robot is placed away from the desired trajectory, and tracks the trajectory until the end point. To demonstrate the effectiveness of our approach, we show evaluations of KoopMotion on the LASA human handwriting dataset and a 3D manipulator end-effector trajectory dataset, including spectral analysis. We also perform experiments on a physical robot, verifying KoopMotion on a miniature autonomous surface vehicle operating in a non-static fluid flow environment. Our approach is highly sample efficient in both space and time, requiring only 3\% of the LASA dataset to generate dense motion plans. Additionally, KoopMotion provides a significant improvement over baselines when comparing metrics that measure spatial and temporal dynamics modeling efficacy. Code at: \href{https://alicekl.github.io/koop-motion/}{\color{blue}{https://alicekl.github.io/koop-motion}}.

cs.RO↗

arXiv2025

Online Adaptation for Flying Quadrotors in Tight Formations

The task of flying in tight formations is challenging for teams of quadrotors because the complex aerodynamic wake interactions can destabilize individual team members as well as the team. Furthermore, these aerodynamic effects are highly nonlinear and fast-paced, making them difficult to model and predict. To overcome these challenges, we present L1 KNODE-DW MPC, an adaptive, mixed expert learning based control framework that allows individual quadrotors to accurately track trajectories while adapting to time-varying aerodynamic interactions during formation flights. We evaluate L1 KNODE-DW MPC in two different three-quadrotor formations and show that it outperforms several MPC baselines. Our results show that the proposed framework is capable of enabling the three-quadrotor team to remain vertically aligned in close proximity throughout the flight. These findings show that the L1 adaptive module compensates for unmodeled disturbances most effectively when paired with an accurate dynamics model. A video showcasing our framework and the physical experiments is available here: https://youtu.be/9QX1Q5Ut9Rs

cs.RO↗

arXiv2025

Multi-robot Multi-source Localization in Complex Flows with Physics-Preserving Environment Models

Source localization in a complex flow poses a significant challenge for multi-robot teams tasked with localizing the source of chemical leaks or tracking the dispersion of an oil spill. The flow dynamics can be time-varying and chaotic, resulting in sporadic and intermittent sensor readings, and complex environmental geometries further complicate a team's ability to model and predict the dispersion. To accurately account for the physical processes that drive the dispersion dynamics, robots must have access to computationally intensive numerical models, which can be difficult when onboard computation is limited. We present a distributed mobile sensing framework for source localization in which each robot carries a machine-learned, finite element model of its environment to guide information-based sampling. The models are used to evaluate an approximate mutual information criterion to drive an infotaxis control strategy, which selects sensing regions that are expected to maximize informativeness for the source localization objective. Our approach achieves faster error reduction compared to baseline sensing strategies and results in more accurate source localization compared to baseline machine learning approaches.

cs.RO↗

arXiv2025

Physics-informed sensor coverage through structure preserving machine learning

We present a machine learning framework for adaptive source localization in which agents use a structure-preserving digital twin of a coupled hydrodynamic-transport system for real-time trajectory planning and data assimilation. The twin is constructed with conditional neural Whitney forms (CNWF), coupling the numerical guarantees of finite element exterior calculus (FEEC) with transformer-based operator learning. The resulting model preserves discrete conservation, and adapts in real time to streaming sensor data. It employs a conditional attention mechanism to identify: a reduced Whitney-form basis; reduced integral balance equations; and a source field, each compatible with given sensor measurements. The induced reduced-order environmental model retains the stability and consistency of standard finite-element simulation, yielding a physically realizable, regular mapping from sensor data to the source field. We propose a staggered scheme that alternates between evaluating the digital twin and applying Lloyd's algorithm to guide sensor placement, with analysis providing conditions for monotone improvement of a coverage functional. Using the predicted source field as an importance function within an optimal-recovery scheme, we demonstrate recovery of point sources under continuity assumptions, highlighting the role of regularity as a sufficient condition for localization. Experimental comparisons with physics-agnostic transformer architectures show improved accuracy in complex geometries when physical constraints are enforced, indicating that structure preservation provides an effective inductive bias for source identification.

cs.LG↗

arXiv2025

Air-Ground Collaboration for Language-Specified Missions in Unknown Environments

As autonomous robotic systems become increasingly mature, users will want to specify missions at the level of intent rather than in low-level detail. Language is an expressive and intuitive medium for such mission specification. However, realizing language-guided robotic teams requires overcoming significant technical hurdles. Interpreting and realizing language-specified missions requires advanced semantic reasoning. Successful heterogeneous robots must effectively coordinate actions and share information across varying viewpoints. Additionally, communication between robots is typically intermittent, necessitating robust strategies that leverage communication opportunities to maintain coordination and achieve mission objectives. In this work, we present a first-of-its-kind system where an unmanned aerial vehicle (UAV) and an unmanned ground vehicle (UGV) are able to collaboratively accomplish missions specified in natural language while reacting to changes in specification on the fly. We leverage a Large Language Model (LLM)-enabled planner to reason over semantic-metric maps that are built online and opportunistically shared between an aerial and a ground robot. We consider task-driven navigation in urban and rural areas. Our system must infer mission-relevant semantics and actively acquire information via semantic mapping. In both ground and air-ground teaming experiments, we demonstrate our system on seven different natural-language specifications at up to kilometer-scale navigation.

cs.RO↗

arXiv2025

Deploying Foundation Model-Enabled Air and Ground Robots in the Field: Challenges and Opportunities

The integration of foundation models (FMs) into robotics has enabled robots to understand natural language and reason about the semantics in their environments. However, existing FM-enabled robots primary operate in closed-world settings, where the robot is given a full prior map or has a full view of its workspace. This paper addresses the deployment of FM-enabled robots in the field, where missions often require a robot to operate in large-scale and unstructured environments. To effectively accomplish these missions, robots must actively explore their environments, navigate obstacle-cluttered terrain, handle unexpected sensor inputs, and operate with compute constraints. We discuss recent deployments of SPINE, our LLM-enabled autonomy framework, in field robotic settings. To the best of our knowledge, we present the first demonstration of large-scale LLM-enabled robot planning in unstructured environments with several kilometers of missions. SPINE is agnostic to a particular LLM, which allows us to distill small language models capable of running onboard size, weight and power (SWaP) limited platforms. Via preliminary model distillation work, we then present the first language-driven UAV planner using on-device language models. We conclude our paper by proposing several promising directions for future research.

cs.RO↗

arXiv2024

EnKode: Active Learning of Unknown Flows with Koopman Operators

In this letter, we address the task of adaptive sampling to model vector fields. When modeling environmental phenomena with a robot, gathering high resolution information can be resource intensive. Actively gathering data and modeling flows with the data is a more efficient alternative. However, in such scenarios, data is often sparse and thus requires flow modeling techniques that are effective at capturing the relevant dynamical features of the flow to ensure high prediction accuracy of the resulting models. To accomplish this effectively, regions with high informative value must be identified. We propose EnKode, an active sampling approach based on Koopman Operator theory and ensemble methods that can build high quality flow models and effectively estimate model uncertainty. For modeling complex flows, EnKode provides comparable or better estimates of unsampled flow regions than Gaussian Process Regression models with hyperparameter optimization. Additionally, our active sensing scheme provides more accurate flow estimates than comparable strategies that rely on uniform sampling. We evaluate EnKode using three common benchmarking systems: the Bickley Jet, Lid-Driven Cavity flow with an obstacle, and real ocean currents from the National Oceanic and Atmospheric Administration (NOAA).

cs.RO↗

arXiv2024

Flying Quadrotors in Tight Formations using Learning-based Model Predictive Control

Flying quadrotors in tight formations is a challenging problem. It is known that in the near-field airflow of a quadrotor, the aerodynamic effects induced by the propellers are complex and difficult to characterize. Although machine learning tools can potentially be used to derive models that capture these effects, these data-driven approaches can be sample inefficient and the resulting models often do not generalize as well as their first-principles counterparts. In this work, we propose a framework that combines the benefits of first-principles modeling and data-driven approaches to construct an accurate and sample efficient representation of the complex aerodynamic effects resulting from quadrotors flying in formation. The data-driven component within our model is lightweight, making it amenable for optimization-based control design. Through simulations and physical experiments, we show that incorporating the model into a novel learning-based nonlinear model predictive control (MPC) framework results in substantial performance improvements in terms of trajectory tracking and disturbance rejection. In particular, our framework significantly outperforms nominal MPC in physical experiments, achieving a 40.1% improvement in the average trajectory tracking errors and a 57.5% reduction in the maximum vertical separation errors. Our framework also achieves exceptional sample efficiency, using only a total of 46 seconds of flight data for training across both simulations and physical experiments. Furthermore, with our proposed framework, the quadrotors achieve an exceptionally tight formation, flying with an average separation of less than 1.5 body lengths throughout the flight. A video illustrating our framework and physical experiments is given here: https://youtu.be/Hv-0JiVoJGo

cs.RO↗

arXiv2024

EvMAPPER: High Altitude Orthomapping with Event Cameras

Traditionally, unmanned aerial vehicles (UAVs) rely on CMOS-based cameras to collect images about the world below. One of the most successful applications of UAVs is to generate orthomosaics or orthomaps, in which a series of images are integrated together to develop a larger map. However, the use of CMOS-based cameras with global or rolling shutters mean that orthomaps are vulnerable to challenging light conditions, motion blur, and high-speed motion of independently moving objects under the camera. Event cameras are less sensitive to these issues, as their pixels are able to trigger asynchronously on brightness changes. This work introduces the first orthomosaic approach using event cameras. In contrast to existing methods relying only on CMOS cameras, our approach enables map generation even in challenging light conditions, including direct sunlight and after sunset.

cs.RO↗

arXiv2024

Collision-free time-optimal path parameterization for multi-robot teams

Coordinating the motion of multiple robots in cluttered environments remains a computationally challenging task. We study the problem of minimizing the execution time of a set of geometric paths by a team of robots with state-dependent actuation constraints. We propose a Time-Optimal Path Parameterization (TOPP) algorithm for multiple car-like agents, where the modulation of the timing of every robot along its assigned path is employed to ensure collision avoidance and dynamic feasibility. This is achieved through the use of a priority queue to determine the order of trajectory execution for each robot while taking into account all possible collisions with higher priority robots in a spatiotemporal graph. We show a 10-20% reduction in makespan against existing state-of-the-art methods and validate our approach through simulations and hardware experiments.

cs.RO↗

arXiv2024

Knowledge-based Neural Ordinary Differential Equations for Cosserat Rod-based Soft Robots

Soft robots have many advantages over rigid robots thanks to their compliant and passive nature. However, it is generally challenging to model the dynamics of soft robots due to their high spatial dimensionality, making it difficult to use model-based methods to accurately control soft robots. It often requires direct numerical simulation of partial differential equations to simulate soft robots. This not only requires an accurate numerical model, but also makes soft robot modeling slow and expensive. Deep learning algorithms have shown promises in data-driven modeling of soft robots. However, these algorithms usually require a large amount of data, which are difficult to obtain in either simulation or real-world experiments of soft robots. In this work, we propose KNODE-Cosserat, a framework that combines first-principle physics models and neural ordinary differential equations. We leverage the best from both worlds -- the generalization ability of physics-based models and the fast speed of deep learning methods. We validate our framework in both simulation and real-world experiments. In both cases, we show that the robot model significantly improves over the baseline models under different metrics.

cs.RO↗

arXiv2024

Spectrally Informed Learning of Fluid Flows

Accurate and efficient fluid flow models are essential for applications relating to many physical phenomena including geophysical, aerodynamic, and biological systems. While these flows may exhibit rich and multiscale dynamics, in many cases underlying low-rank structures exist which describe the bulk of the motion. These structures tend to be spatially large and temporally slow, and may contain most of the energy in a given flow. The extraction and parsimonious representation of these low-rank dynamics from high-dimensional data is a key challenge. Inspired by the success of physics-informed machine learning methods, we propose a spectrally-informed approach to extract low-rank models of fluid flows by leveraging known spectral properties in the learning process. We incorporate this knowledge by imposing regularizations on the learned dynamics, which bias the training process towards learning low-frequency structures with corresponding higher power. We demonstrate the effectiveness of this method to improve prediction and produce learned models which better match the underlying spectral properties of prototypical fluid flows.

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