arXiv subjects

Taeyoung Lee

Publications and source records attributed to Taeyoung Lee.

At least 19 recordsLinked to original sources

arXiv2026

Knowing When to Ask: Resolving Uncertainty in Human-Robot Joint Planning via Explicit Dialogue and Implicit Intent Cues

Effective human-robot collaboration in open-world environments requires joint planning under uncertainty about the task, the environment, and the human teammate. Communication is the most direct means of resolving such uncertainty, yet most existing systems support only one-way communication: robots listen and act, treating humans as passive supervisors rather than conversational teammates capable of two-way dialogue. We propose a unified human-robot joint planning system in which the robot actively resolves uncertainty through two complementary communication channels. When uncertainty is decision-critical, an uncertainty-mitigation joint planning module engages the human in clarification dialogue: it grounds ambiguous instructions via an LLM-assisted active elicitation mechanism, enumerates traversability hypotheses through a hypothesis-augmented A* search, and computes a cost-optimal querying policy via dynamic programming, so that the robot asks only the questions whose answers actually matter for the plan. When explicit dialogue is unnecessary or impractical, a real-time intent-aware collaboration module instead reads implicit, nonverbal cues, maintaining a probabilistic belief over the human's latent task intent from spatial and directional signals to enable coordination-aware task selection without any communication overhead. We validate the proposed system in both Gazebo simulations and real-world UAV deployments, integrated with a voice dialogue interface and a Vision-Language Model (VLM)-based 3D semantic perception pipeline. Experimental results show that cost-optimal clarification dialogue cuts the interaction cost by 51.9% while maintaining a 100% task success rate, and implicit intent reading reduces the cooperative task execution time by 25.4% compared to the baselines.

cs.RO↗

arXiv2026

Hardware- and Vision-in-the-Loop Validation of Deep Monocular Pose Estimation for Autonomous Maritime UAV Flight

Autonomous UAV operations on ships require reliable vision-based relative pose estimation, yet at-sea validation is costly, weather-dependent, and risky. This paper presents a hardware-validated vision-in-the-loop framework that enables fully autonomous indoor flight while emulating photorealistic maritime environments. Rendered maritime views are processed onboard by a deep transformer-based monocular pose estimator. Delayed vision measurements are fused with high-rate IMU data using a delayed Kalman filter to provide consistent state estimates for geometric control. The system captures critical embedded effects, including perception latency, asynchronous updates, and computational constraints, that are absent in pure simulation. Autonomous takeoff, trajectory tracking, and landing experiments demonstrate stable closed-loop flight. The results establish a safe and hardware-realistic intermediate stage for developing maritime UAV autonomy prior to shipboard deployment.

cs.RO↗

arXiv2026

Max-Entropy Moment Filtering for Stochastic Hybrid Systems

Stochastic hybrid systems combine continuous-time stochastic dynamics with discrete reset events, producing intrinsically non-Gaussian and often multimodal uncertainty. A consistent propagation law must also account for boundary-induced probability flux across guard sets, making direct density propagation through hybrid Fokker-Planck equations expensive. We develop a hybrid extension of the Max-Entropy Moment Kalman Filter (MEM-KF) that performs filtering from partial statistical information by propagating a finite collection of moments through stochastic hybrid dynamics and reconstructing beliefs using moment-constrained maximum-entropy distributions. The key step is a moment propagation rule derived from Dynkin's formula with a jump-sum, in which reset effects appear as a boundary-flux correction over the guard set. This yields tractable moment dynamics without solving the underlying hybrid PDE. In a stochastic bouncing-ball example, the proposed method captures reset-induced non-Gaussianity through corrected moment equations while retaining the MEM-KF's optimization-based maximum-entropy representation.

eess.SY↗

arXiv2026

The Score Kalman Filter

A central obstacle in nonlinear Bayesian filtering is representing the belief distribution. Moment-based filters address this by propagating polynomial moments and reconstructing a density from them. Recent work completes the predict-update loop via the maximum-entropy (MaxEnt) principle, but each step requires the partition function and its gradient, both $n$-dimensional integrals whose cost scales exponentially, restricting the demonstrated MaxEnt moment filtering to $n \le 4$. We avoid the partition function entirely by combining score matching with Stein's identity. In our setting, score matching reduces the density fit to a single linear solve whose coefficients are assembled directly from the propagated moments. The same parameters then drive Stein's identity to close the moment hierarchy during prediction and to recover posterior moments after each Bayesian update, keeping the full predict-update loop free of partition function evaluation. The resulting Score Kalman Filter (SKF) reduces to the classical information-form Kalman filter as a special case and performs every step through linear algebra. On nonlinear coupled-oscillator networks, the SKF runs through $n=20$ and reports lower RMSE than the EKF, UKF, EnKF, and particle-filter baselines on the tested synthetic benchmarks.

eess.SY↗

arXiv2026

Transfer Operators for Stochastic Hybrid Systems on Manifolds with Guard-Induced Resets

This paper develops a transfer operator framework for stochastic hybrid systems with guard-induced resets, encompassing both the Koopman and Frobenius--Perron operators. Exploiting their duality, we derive a unified formulation in which observables and probability densities evolve under adjoint generators corresponding to the backward and forward Kolmogorov equations. The formulation is developed in a global and intrinsic manner on differentiable manifolds, ensuring consistency with the underlying geometric structure of the state space. In addition, we propose a finite volume computational scheme on manifolds that preserves total probability mass while accurately capturing fluxes across guards and reset-induced transfers. The proposed framework provides a unified and geometrically consistent approach to uncertainty propagation in stochastic hybrid systems, bridging continuous stochastic dynamics and hybrid transitions within a transfer operator perspective.

math.DS↗

arXiv2026

Uncertainty Propagation in Stochastic Hybrid Systems with Dimension-Varying Resets

This paper studies probability density evolution for stochastic hybrid systems with reset maps that change the dimension of the continuous state across modes. Existing Frobenius--Perron formulations typically represent reset-induced probability transfer through boundary conditions, which is insufficient when resets map guard sets into the interior or onto lower-dimensional subsets of another mode. We develop a weak-form formulation in which reset-induced transfer is represented by the pushforward of probability flux across the guard, yielding a unified description for such systems. The proposed framework naturally captures both cases: when the reset decreases dimension, the transferred probability appears as an interior source density, whereas when the reset increases dimension, it generally appears as a singular source supported on a lower-dimensional subset. The approach is illustrated using a stochastic hybrid model in which two particles merge into one and later split back into two, demonstrating how dimension-changing resets lead to source terms beyond classical boundary-condition-based formulations.

math.OC↗

arXiv2026

Global Tensor Field Formulation of the Fokker-Planck Equation on Riemannian Manifolds

This paper presents a global, coordinate-free formulation of the Fokker-Planck equation on Riemannian manifolds. In the Stratonovich formulation, the infinitesimal generator is expressed intrinsically through Lie derivatives, and its adjoint is derived via the divergence theorem, yielding a concise geometric form of the Fokker-Planck equation. In the Ito formulation, a diffusion tensor field is introduced to generalize the Euclidean diffusion matrix, and a tensor-field-based analysis establishes an intrinsic double-divergence representation of the Fokker-Planck equation. The proposed framework provides a globally valid and geometrically consistent interpretation of diffusion and probability transport on Riemannian manifolds, supported by compact and intuitive proofs.

math.PR↗

arXiv2026

Deep Transformer Network for Monocular Pose Estimation of Shipborne Unmanned Aerial Vehicle

This paper introduces a deep transformer network for estimating the relative 6D pose of a Unmanned Aerial Vehicle (UAV) with respect to a ship using monocular images. A synthetic dataset of ship images is created and annotated with 2D keypoints of multiple ship parts. A Transformer Neural Network model is trained to detect these keypoints and estimate the 6D pose of each part. The estimates are integrated using Bayesian fusion. The model is tested on synthetic data and in-situ flight experiments, demonstrating robustness and accuracy in various lighting conditions. The position estimation error is approximately 0.8\% and 1.0\% of the distance to the ship for the synthetic data and the flight experiments, respectively. The method has potential applications for ship-based autonomous UAV landing and navigation.

cs.CV↗

arXiv2025

Invariant Kalman Filter for Relative Dynamics

This paper develops a geometric framework for invariant filtering of relative dynamics on Lie groups. We first revisit the notion of state trajectory independence, under which the estimation error evolves autonomously, and derive new equivalent conditions by decomposing the system vector field into left-invariant, intrinsic, and right-invariant components. Building on this result, we introduce the concept of relative trajectory independence to characterize when the relative motion between two dynamical systems is autonomous. A key theoretical finding is that relative trajectory independence automatically ensures state trajectory independence for the corresponding estimation error. This connection provides the foundation for constructing invariant filters that preserve the Lie group structure, maintain exact linearization of the error dynamics, and enable consistent covariance propagation. These are illustrated with numerical examples.

eess.SY↗

arXiv2025

Geometric Interpretation of Brownian Motion on Riemannian Manifolds

This paper presents a unified geometric framework for Brownian motion on manifolds, encompassing intrinsic Riemannian manifolds, embedded submanifolds, and Lie groups. The approach constructs the stochastic differential equation by injecting noise along each axis of an orthonormal frame and designing the drift term so that the resulting generator coincides with the Laplace--Beltrami operator. Both Stratonovich and Itô formulations are derived explicitly, revealing the geometric origin of curvature-induced drift. The drift is shown to correspond to the covariant derivatives of the frame fields for intrinsic manifolds, the mean curvature vector for embedded manifolds, and the adjoint-trace term for Lie groups, which vanishes for unimodular cases. The proposed formulation provides a geometrically transparent and mathematically consistent foundation for diffusion processes on nonlinear configuration spaces.

math.PR↗

arXiv2025

Equivariant Reinforcement Learning Frameworks for Quadrotor Low-Level Control

Improving sampling efficiency and generalization capability is critical for the successful data-driven control of quadrotor unmanned aerial vehicles (UAVs) that are inherently unstable. While various reinforcement learning (RL) approaches have been applied to autonomous quadrotor flight, they often require extensive training data, posing multiple challenges and safety risks in practice. To address these issues, we propose data-efficient, equivariant monolithic and modular RL frameworks for quadrotor low-level control. Specifically, by identifying the rotational and reflectional symmetries in quadrotor dynamics and encoding these symmetries into equivariant network models, we remove redundancies of learning in the state-action space. This approach enables the optimal control action learned in one configuration to automatically generalize into other configurations via symmetry, thereby enhancing data efficiency. Experimental results demonstrate that our equivariant approaches significantly outperform their non-equivariant counterparts in terms of learning efficiency and flight performance.

cs.RO↗

arXiv2025

Vision-in-the-loop Simulation for Deep Monocular Pose Estimation of UAV in Ocean Environment

This paper proposes a vision-in-the-loop simulation environment for deep monocular pose estimation of a UAV operating in an ocean environment. Recently, a deep neural network with a transformer architecture has been successfully trained to estimate the pose of a UAV relative to the flight deck of a research vessel, overcoming several limitations of GPS-based approaches. However, validating the deep pose estimation scheme in an actual ocean environment poses significant challenges due to the limited availability of research vessels and the associated operational costs. To address these issues, we present a photo-realistic 3D virtual environment leveraging recent advancements in Gaussian splatting, a novel technique that represents 3D scenes by modeling image pixels as Gaussian distributions in 3D space, creating a lightweight and high-quality visual model from multiple viewpoints. This approach enables the creation of a virtual environment integrating multiple real-world images collected in situ. The resulting simulation enables the indoor testing of flight maneuvers while verifying all aspects of flight software, hardware, and the deep monocular pose estimation scheme. This approach provides a cost-effective solution for testing and validating the autonomous flight of shipboard UAVs, specifically focusing on vision-based control and estimation algorithms.

cs.CV↗

arXiv2024

Uncertainty propagation of stochastic hybrid systems: a case study for types of jump

Stochastic hybrid systems are dynamic systems that undergo both random continuous-time flows and random discrete jumps. Depending on how randomness is introduced into the continuous dynamics, discrete transitions, or both, stochastic hybrid systems exhibit distinct characteristics. This paper investigates the role of uncertainties in the interplay between continuous flows and discrete jumps by studying probability density propagation. Specifically, we formulate stochastic Koopman/Frobenius-Perron operators for three types of one-dimensional stochastic hybrid systems to uncover their unique dynamic characteristics and verify them using Monte Carlo simulations.

math.OC↗

arXiv2024

Mean Field Game and Control for Switching Hybrid Systems

Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate continuous dynamics with discrete transitions, effectively modeling the complex interplay between continuous flows and instantaneous jumps in a unified framework. This paper formulates mean field game and control strategies for switching hybrid systems and proposes computational methods to solve the resulting integro-partial differential equation. This approach enables scalable, decentralized decision-making in large-scale switching systems, which is illustrated through numerical examples in an emergency evacuation scenario with sudden changes in the surrounding environment.

math.OC↗

arXiv2024

Collaborative AI Teaming in Unknown Environments via Active Goal Deduction

With the advancements of artificial intelligence (AI), we're seeing more scenarios that require AI to work closely with other agents, whose goals and strategies might not be known beforehand. However, existing approaches for training collaborative agents often require defined and known reward signals and cannot address the problem of teaming with unknown agents that often have latent objectives/rewards. In response to this challenge, we propose teaming with unknown agents framework, which leverages kernel density Bayesian inverse learning method for active goal deduction and utilizes pre-trained, goal-conditioned policies to enable zero-shot policy adaptation. We prove that unbiased reward estimates in our framework are sufficient for optimal teaming with unknown agents. We further evaluate the framework of redesigned multi-agent particle and StarCraft II micromanagement environments with diverse unknown agents of different behaviors/rewards. Empirical results demonstrate that our framework significantly advances the teaming performance of AI and unknown agents in a wide range of collaborative scenarios.

cs.AI↗

arXiv2024

Multi-Agent Reinforcement Learning for the Low-Level Control of a Quadrotor UAV

By leveraging the underlying structures of the quadrotor dynamics, we propose multi-agent reinforcement learning frameworks to innovate the low-level control of a quadrotor, where independent agents operate cooperatively to achieve a common goal. While single-agent reinforcement learning has been successfully applied in quadrotor controls, training a large monolithic network is often data-intensive and time-consuming. Moreover, achieving agile yawing control remains a significant challenge due to the strongly coupled nature of the quadrotor dynamics. To address this, we decompose the quadrotor dynamics into translational and yawing components and assign collaborative reinforcement learning agents to each part to facilitate more efficient training. Additionally, we introduce regularization terms to mitigate steady-state errors and prevent excessive maneuvers. Benchmark studies, including sim-to-sim transfer verification, demonstrate that our proposed training schemes substantially improve the convergence rate of training, while enhancing flight control performance and stability compared to traditional single-agent approaches.

cs.RO↗

arXiv2023

Equivariant Reinforcement Learning for Quadrotor UAV

This paper presents an equivariant reinforcement learning framework for quadrotor unmanned aerial vehicles. Successful training of reinforcement learning often requires numerous interactions with the environments, which hinders its applicability especially when the available computational resources are limited, or when there is no reliable simulation model. We identified an equivariance property of the quadrotor dynamics such that the dimension of the state required in the training is reduced by one, thereby improving the sampling efficiency of reinforcement learning substantially. This is illustrated by numerical examples with popular reinforcement learning techniques of TD3 and SAC.

cs.LG↗

arXiv2022

Constrained Imitation Learning for a Flapping Wing Unmanned Aerial Vehicle

This paper presents a data-driven optimal control policy for a micro flapping wing unmanned aerial vehicle. First, a set of optimal trajectories are computed off-line based on a geometric formulation of dynamics that captures the nonlinear coupling between the large angle flapping motion and the quasi-steady aerodynamics. Then, it is transformed into a feedback control system according to the framework of imitation learning. In particular, an additional constraint is incorporated through the learning process to enhance the stability properties of the resulting controlled dynamics. Compared with conventional methods, the proposed constrained imitation learning eliminates the need to generate additional optimal trajectories on-line, without sacrificing stability. As such, the computational efficiency is substantially improved. Furthermore, this establishes the first nonlinear control system that stabilizes the coupled longitudinal and lateral dynamics of flapping wing aerial vehicle without relying on averaging or linearization. These are illustrated by numerical examples for a simulated model inspired by Monarch butterflies.

cs.RO↗