Taeyoung Lee

Taeyoung Lee, Melvin Leok, N. Harris McClamroch

This paper provides new results for control of complex flight maneuvers for a quadrotor unmanned aerial vehicle (UAV). The flight maneuvers are defined by a concatenation of flight modes or primitives, each of which is achieved by a nonlinear controller that solves an output tracking problem. A mathematical model of the quadrotor UAV rigid body dynamics, defined on the configuration space $\SE$, is introduced as a basis for the analysis. The quadrotor UAV has four input degrees of freedom, namely the magnitudes of the four rotor thrusts; each flight mode is defined by solving an asymptotic optimal tracking problem. Although many flight modes can be studied, we focus on three output tracking problems, namely (1) outputs given by the vehicle attitude, (2) outputs given by the three position variables for the vehicle center of mass, and (3) output given by the three velocity variables for the vehicle center of mass. A nonlinear tracking controller is developed on the special Euclidean group $\SE$ for each flight mode, and the closed loop is shown to have desirable closed loop properties that are almost global in each case. Several numerical examples, including one example in which the quadrotor recovers from being initially upside down and another example that includes switching and transitions between different flight modes, illustrate the versatility and generality of the proposed approach.

Taeyoung Lee

This paper provides new results for a robust adaptive tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid complexities and ambiguities associated with other attitude representations such as Euler angles or quaternions. By designing an adaptive law for the inertia matrix of a rigid body, the proposed control system can asymptotically follow an attitude command without the knowledge of the inertia matrix, and it is extended to guarantee boundedness of tracking errors in the presence of unstructured disturbances. These are illustrated by numerical examples and experiments for the attitude dynamics of a quadrotor UAV.

Taeyoung Lee, Melvin Leok, N. Harris McClamroch

This paper presents an analytical model and a geometric numerical integrator for a system of rigid bodies connected by ball joints, immersed in an irrotational and incompressible fluid. The rigid bodies can translate and rotate in three-dimensional space, and each joint has three rotational degrees of freedom. This model characterizes the qualitative behavior of three-dimensional fish locomotion. A geometric numerical integrator, refereed to as a Lie group variational integrator, preserves Hamiltonian structures of the presented model and its Lie group configuration manifold. These properties are illustrated by a numerical simulation for a system of three connected rigid bodies.

Beomyeol Yu, Taeyoung Lee

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.

Shankar Kulumani, Christopher Poole, Taeyoung Lee

This paper presents a new geometric adaptive control system with state inequality constraints for the attitude dynamics of a rigid body. The control system is designed such that the desired attitude is asymptotically stabilized, while the controlled attitude trajectory avoids undesired regions defined by an inequality constraint. In addition, we develop an adaptive update law that enables attitude stabilization in the presence of unknown disturbances. The attitude dynamics and the proposed control systems are developed on the special orthogonal group such that singularities and ambiguities of other attitude parameterizations, such as Euler angles and quaternions are completely avoided. The effectiveness of the proposed control system is demonstrated through numerical simulations and experimental results.

Taeyoung Lee, Melvin Leok, N. Harris McClamroch

Euler-Lagrange equations and variational integrators are developed for Lagrangian mechanical systems evolving on a product of two-spheres. The geometric structure of a product of two-spheres is carefully considered in order to obtain global equations of motion. Both continuous equations of motion and variational integrators completely avoid the singularities and complexities introduced by local parameterizations or explicit constraints. We derive global expressions for the Euler-Lagrange equations on two-spheres which are more compact than existing equations written in terms of angles. Since the variational integrators are derived from Hamilton's principle, they preserve the geometric features of the dynamics such as symplecticity, momentum maps, or total energy, as well as the structure of the configuration manifold. Computational properties of the variational integrators are illustrated for several mechanical systems.

Dong Eui Chang, Taeyoung Lee

We propose a 12-dimensional, global, continuous, and exponentially convergent observer for gyro bias and attitude of a rigid body. Any attitude observer developed on the special orthogonal group suffers from the topological restriction that prohibits global attractivity in continuous flow. In this paper, the observer is designed in the set of 3 by 3 real matrices, thus making the topological obstruction on the special orthogonal group irrelevant. The efficacy of the proposed approach against other attitude observers is illustrated by an indoor experiment utilizing visual landmarks.

Kaito Iwasaki, Tejaswi K. C., Anthony Bloch et al.

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.

Kaito Iwasaki, Anthony Bloch, Taeyoung Lee et al.

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.

Tejaswi K. C., Taeyoung Lee

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.

Zuyuan Zhang, Hanhan Zhou, Mahdi Imani et al.

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.

Zeyu Fang, Yuxin Lin, Cheng Liu et al.

Effective human-robot collaboration in open-world environments requires joint planning under uncertain conditions. However, existing approaches often treat humans as passive supervisors, preventing autonomous agents from becoming human-like teammates that can actively model teammate behaviors, reason about knowledge gaps, query, and elicit responses through communication to resolve uncertainties. To address these limitations, we propose a unified human-robot joint planning system designed to tackle dual sources of uncertainty: task-relevant knowledge gaps and latent human intent. Our system operates in two complementary modes. First, an uncertainty-mitigation joint planning module enables two-way conversations to resolve semantic ambiguity and object uncertainty. It utilizes an LLM-assisted active elicitation mechanism and a hypothesis-augmented A^* search, subsequently computing an optimal querying policy via dynamic programming to minimize interaction and verification costs. Second, a real-time intent-aware collaboration module maintains a probabilistic belief over the human's latent task intent via spatial and directional cues, enabling dynamic, coordination-aware task selection for agents without explicit communication. We validate the proposed system in both Gazebo simulations and real-world UAV deployments integrated with a Vision-Language Model (VLM)-based 3D semantic perception pipeline. Experimental results demonstrate that the system significantly cuts the interaction cost by 51.9% in uncertainty-mitigation planning and reduces the task execution time by 25.4% in intent-aware cooperation compared to the baselines.

Maneesha Wickramasuriya, Beomyeol Yu, Taeyoung Lee et al.

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.

Maneesha Wickramasuriya, Taeyoung Lee, Murray Snyder

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.

Hai H. Tran, Sumyeong Ahn, Taeyoung Lee et al.

In this paper, we study the problem of unsupervised domain adaptation that aims at obtaining a prediction model for the target domain using labeled data from the source domain and unlabeled data from the target domain. There exists an array of recent research based on the idea of extracting features that are not only invariant for both domains but also provide high discriminative power for the target domain. In this paper, we propose an idea of empowering the discriminativeness: Adding a new, artificial class and training the model on the data together with the GAN-generated samples of the new class. The trained model based on the new class samples is capable of extracting the features that are more discriminative by repositioning data of current classes in the target domain and therefore drawing the decision boundaries more effectively. Our idea is highly generic so that it is compatible with many existing methods such as DANN, VADA, and DIRT-T. We conduct various experiments for the standard data commonly used for the evaluation of unsupervised domain adaptations and demonstrate that our algorithm achieves the SOTA performance for many scenarios.

Daewoo Kim, Sangwoo Moon, David Hostallero et al.

Many real-world reinforcement learning tasks require multiple agents to make sequential decisions under the agents' interaction, where well-coordinated actions among the agents are crucial to achieve the target goal better at these tasks. One way to accelerate the coordination effect is to enable multiple agents to communicate with each other in a distributed manner and behave as a group. In this paper, we study a practical scenario when (i) the communication bandwidth is limited and (ii) the agents share the communication medium so that only a restricted number of agents are able to simultaneously use the medium, as in the state-of-the-art wireless networking standards. This calls for a certain form of communication scheduling. In that regard, we propose a multi-agent deep reinforcement learning framework, called SchedNet, in which agents learn how to schedule themselves, how to encode the messages, and how to select actions based on received messages. SchedNet is capable of deciding which agents should be entitled to broadcasting their (encoded) messages, by learning the importance of each agent's partially observed information. We evaluate SchedNet against multiple baselines under two different applications, namely, cooperative communication and navigation, and predator-prey. Our experiments show a non-negligible performance gap between SchedNet and other mechanisms such as the ones without communication and with vanilla scheduling methods, e.g., round robin, ranging from 32% to 43%.

Mahdis Bisheban, Taeyoung Lee

This paper proposes a geometric adaptive controller for a quadrotor unmanned aerial vehicle with artificial neural networks. It is assumed that the dynamics of a quadrotor is disturbed by arbitrary, unstructured forces and moments caused by wind. To address this, the proposed control system is augmented with multilayer neural networks, and the weights of neural networks are adjusted online according to an adaptive law. By utilizing the universal approximation theorem, it is shown that the effects of unknown disturbances can be mitigated. More specifically, under the proposed control system, the tracking errors in the position and the heading direction are uniformly ultimately bounded where the ultimate bound can be reduced arbitrarily. These are developed directly on the special Euclidean group to avoid complexities or singularities inherent to local parameterizations. The efficacy of the proposed control system is first illustrated by numerical examples. Then, several indoor flight experiments are presented to demonstrate that the proposed controller successfully rejects the effects of wind disturbances even for aggressive, agile maneuvers.

Mahdis Bisheban, Taeyoung Lee

This paper presents a geometric adaptive control scheme for a quadrotor unmanned aerial vehicle, where the effects of unknown, unstructured disturbances are mitigated by a multilayer neural network that is adjusted online. The stability of the proposed controller is analyzed with Lyapunov stability theory on the special Euclidean group, and it is shown that the tracking errors are uniformly ultimately bounded with an ultimate bound that can be abridged arbitrarily. A mathematical model of wind disturbance on the quadrotor dynamics is presented, and it is shown that the proposed adaptive controller is capable of rejecting the effects of wind disturbances successfully. These are illustrated by numerical examples.

Shankar Kulumani, Kuya Takami, Taeyoung Lee

This paper considers the coupled orbit and attitude dynamics of a dumbbell spacecraft around an asteroid. Geometric methods are used to derive the coupled equations of motion, defined on the configuration space of the special Euclidean group, and then a nonlinear controller is designed to enable trajectory tracking of desired landing trajectories. Rather than relying on sliding mode control or optimization based methods, the proposed approach avoids the increased control utilization and computational complexity inherent in other techniques. The nonlinear controller is used to track a desired landing trajectory to the asteroid surface. A monocular imaging sensor is used to provide position and attitude estimates using visual odometry to enable relative state estimates. We demonstrate this control scheme with a landing simulation about asteroid Itokawa.

Taeyoung Lee, Melvin Leok, N. Harris McClamroch

This paper provides nonlinear tracking control systems for a quadrotor unmanned aerial vehicle (UAV) that are robust to bounded uncertainties. A mathematical model of a quadrotor UAV is defined on the special Euclidean group, and nonlinear output-tracking controllers are developed to follow (1) an attitude command, and (2) a position command for the vehicle center of mass. The controlled system has the desirable properties that the tracking errors are uniformly ultimately bounded, and the size of the ultimate bound can be arbitrarily reduced by control system parameters. Numerical examples illustrating complex maneuvers are provided.

Taeyoung Lee, Melvin Leok, N. Harris McClamroch

This paper presents an analytical model and a geometric numerical integrator for a rigid body connected to an elastic string, acting under a gravitational potential. Since the point where the string is attached to the rigid body is displaced from the center of mass of the rigid body, there exist nonlinear coupling effects between the string deformation and the rigid body dynamics. A geometric numerical integrator, refereed to as a Lie group variational integrator, is developed to numerically preserve the Hamiltonian structure of the presented model and its Lie group configuration manifold. These properties are illustrated by a numerical simulation.

Eugene G. Fahnestock, Taeyoung Lee, Melvin Leok et al.

We present a combination of tools which allows for investigation of the coupled orbital and rotational dynamics of two rigid bodies with nearly arbitrary shape and mass distribution, under the influence of their mutual gravitational potential. Methods for calculating that mutual potential and resulting forces and moments for a polyhedral body representation are simple and efficient. Discrete equations of motion, referred to as the Lie Group Variational Integrator (LGVI), preserve the structure of the configuration space, SE(3), as well as the geometric features represented by the total energy and the total angular momentum. The synthesis of these approaches allows us to simulate the full two body problem accurately and efficiently. Simulation results are given for two octahedral rigid bodies for comparison with other integration methods and to show the qualities of the results thus obtained. A significant improvement is seen over other integration methods while correctly capturing the interesting effects of strong orbit and attitude dynamics coupling, in multiple scenarios.

Taeyoung Lee, Melvin Leok, N. Harris McClamroch

We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of rigid body configurations. Both continuous equations of motion and variational integrators are developed in Lagrangian and Hamiltonian forms, and the reduction from the inertial frame to a relative coordinate system is also carried out. The Lie group variational integrators are shown to be symplectic, to preserve conserved quantities, and to guarantee exact evolution on the configuration space. One of these variational integrators is used to simulate the dynamics of two rigid dumbbell bodies.