arXiv subjects

Taeyoung Lee

Publications and source records attributed to Taeyoung Lee.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2022

Bayesian Shape Reconstruction and Optimal Guidance for Autonomous Landing on Asteroids

Construction of the precise shape of an asteroid is critical for spacecraft operations as the gravitational potential is determined by spatial mass distribution. The typical approach to shape determination requires a prolonged mapping phase of the mission over which extensive measurements are collected and transmitted for Earth-based processing. This paper presents a set of approaches to explore an unknown asteroid with onboard calculations, and to land on its surface area selected in an optimal fashion. The main motivation is to avoid the extended period of mapping or preliminary ground observations that are commonly required in spacecraft missions around asteroids. First, range measurements from the spacecraft to the surface are used to incrementally correct an initial shape estimate according to the Bayesian framework. Then, an optimal guidance scheme is proposed to control the vantage point of the range sensor to construct a complete 3D model of the asteroid shape. This shape model is then used in a nonlinear controller to track a desired trajectory about the asteroid. Finally, a multi resolution approach is presented to construct a higher fidelity shape representation in a specified location while avoiding the inherent burdens of a uniformly high resolution mesh. This approach enables for an accurate shape determination around a potential landing site. We demonstrate this approach using several radar shape models of asteroids and provide a full dynamical simulation about asteroid 4769 Castalia.

astro-ph.EP↗

arXiv2022

Uncertainty Propagation for General Stochastic Hybrid Systems on Compact Lie Groups

This paper deals with uncertainty propagation of general stochastic hybrid systems (GSHS) where the continuous state space is a compact Lie group. A computational framework is proposed to solve the Fokker-Planck (FP) equation that describes the time evolution of the probability density function for the state of GSHS. The FP equation is split into two parts: the partial differential operator corresponding to the continuous dynamics, and the integral operator arising from the discrete dynamics. These two parts are solved alternatively using the operator splitting technique. Specifically, the partial differential equation is solved by the spectral method where the density function is decomposed into a linear combination of a complete orthonormal function basis brought forth by the Peter-Weyl theorem, thereby resulting an ordinary differential equation. Next, the integral equation is solved by approximating the integral by a finite summation using a quadrature rule. The proposed method is then applied to a three-dimensional rigid body pendulum colliding with a wall, evolving on the product of the three-dimensional special orthogonal group and the Euclidean space. It is illustrated that the proposed method exhibits numerical results consistent with a Monte Carlo simulation, while explicitly generating the density function that carries the complete stochastic information of the hybrid state.

math.OC↗

arXiv2022

Iterative Supervised Learning for Regression with Constraints

Regression in supervised learning often requires the enforcement of constraints to ensure that the trained models are consistent with the underlying structures of the input and output data. This paper presents an iterative procedure to perform regression under arbitrary constraints. It is achieved by alternating between a learning step and a constraint enforcement step, to which an affine extension function is incorporated. We show this leads to a contraction mapping under mild assumptions, from which the convergence is guaranteed analytically. The presented proof of convergence in regression with constraints is the unique contribution of this paper. Furthermore, numerical experiments illustrate improvements in the trained model in terms of the quality of regression, the satisfaction of constraints, and also the stability in training, when compared to other existing algorithms.

math.OC↗

arXiv2021

Geometric Optimal Controls for Flapping Wing UAV on a Lie Group

Inspired by flight characteristics captured from live Monarch butterflies, an optimal control problem is presented while accounting the effects of low-frequency flapping and abdomen undulation. A flapping-wing aerial vehicle is modeled as an articulated rigid body, and its dynamics are developed according to Lagrangian mechanics on an abstract Lie group. This provides an elegant, global formulation of the dynamics for flapping-wing aerial vehicles, avoiding complexities and singularities associated with local coordinates. This is utilized to identify an optimal periodic motion that minimizes energy variations, and an optimal control is formulated to stabilize the periodic motion. Furthermore, the outcome of this paper can be applied to optimal control for any Lagrangian system on a Lie group with a configuration-dependent inertia.

math.OC↗

arXiv2021

On the Observability of Attitude with Single Direction Measurements

The attitude of a rigid body evolves on the three-dimensional special orthogonal group, and it is often estimated by measuring reference directions, such as gravity or magnetic field, using an onboard sensor. As a single direction measurement provides a two-dimensional constraint, it has been widely accepted that at least two non-parallel reference directions should be measured, or the reference direction should change over time, to determine the attitude completely. This paper uncovers an intriguing fact that the attitude can actually be estimated by using multiple measurements of a single, fixed reference direction, provided that the angular velocity and the direction measurements are resolved in appropriate frames, respectively. More specifically, after recognizing that the attitude uncertainties propagated over the left-trivialized stochastic kinematics are distinct from those over the right-trivialized one, stochastic attitude observability with single direction measurements is formulated by an information theoretic analysis. These are further illustrated by numerical simulations and experiments.

math.OC↗

arXiv2021

Impact of Fe$_{80}$B$_{20}$ insertion on the properties of dual-MgO perpendicular magnetic tunnel junctions

We explore the impact of Fe80B20 inserted at both Co$_{20}$Fe$_{80}$B$_{20}$/MgO interfaces of dual-MgO free layers (FLs) in bottom-pinned magnetic tunnel junctions (MTJs). MTJ stacks are annealed for 30 min at 350 $^\circ$C and 400 $^\circ$C in a vacuum after film deposition. Current-in-plane tunneling measurements are carried out to characterize magnetotransport properties of the MTJs. Conventional magnetometry measurements and ferromagnetic resonance are conducted to estimate the saturation magnetization, the effective perpendicular anisotropy field and the Gilbert damping of dual-MgO FLs as a function of the Fe$_{80}$B$_{20}$ thickness and annealing temperatures. With ultrathin Fe$_{80}$B$_{20}$ (0.2 - 0.4 nm) inserted, perpendicular magnetic anisotropy (PMA) of FLs increases with similar tunnel magneto-resistance (TMR) and low damping values. As Fe$_{80}$B$_{20}$ layer thickness further increases (0.6 - 1.2 nm), both TMR and PMA degrade, and damping increases dramatically. This study demonstrates a novel approach to tune properties of MTJ stacks with dual-MgO FLs up to 400 $^\circ$C annealing, which enables MTJ stacks for various applications.

physics.app-ph↗

arXiv2021

Variational Symplectic Accelerated Optimization on Lie Groups

There has been significant interest in generalizations of the Nesterov accelerated gradient descent algorithm due to its improved performance guarantee compared to the standard gradient descent algorithm, and its applicability to large scale optimization problems arising in deep learning. A particularly fruitful approach is based on numerical discretizations of differential equations that describe the continuous time limit of the Nesterov algorithm, and a generalization involving time-dependent Bregman Lagrangian and Hamiltonian dynamics that converges at an arbitrarily fast rate to the minimum. We develop a Lie group variational discretization based on an extended path space formulation of the Bregman Lagrangian on Lie groups, and analyze its computational properties with two examples in attitude determination and vision-based localization.

math.OC↗

arXiv2021

Dynamics and Control of a Flapping Wing UAV with Abdomen Undulation Inspired by Monarch Butterfly

This paper presents a dynamic model and a control system for a flapping-wing unmanned aerial vehicle. Inspired by flight characteristics captured from live Monarch butterflies, a new dynamic model is presented to account the effects of low-frequency flapping and abdomen undulation. We developed it according to Lagrangian mechanics on a Lie group to obtain an elegant, global formulation of dynamics. Then, a feedback control system is presented to asymptotically stabilize periodic motions with active motion of abdomen, and its stability is verified according to Floquet theory. In particular, it is illustrated that the abdomen undulation has the desirable effects of reducing the variation of the total energy and also improving the stability of the proposed control system.

eess.SY↗

arXiv2020

Matrix Fisher-Gaussian Distribution on $\mathrm{SO}(3)\times\mathbb{R}^n$ for Attitude Estimation with a Gyro Bias

In this paper, a new probability distribution, referred to as the matrix Fisher-Gaussian (MFG) distribution, is proposed on the nonlinear manifold $\mathrm{SO}(3)\times\mathbb{R}^n$. It is constructed by conditioning a (9+n)-variate Gaussian distribution from the ambient Euclidean space into $\mathrm{SO}(3)\times\mathbb{R}^n$, while imposing a certain geometric interpretation of the correlation terms to avoid over-parameterization. The unique feature is that it may represent large uncertainties in attitudes, linear variables of an arbitrary dimension, and angular-linear correlations between them in a global fashion without singularities associated with local parameterizations. Various stochastic properties and an approximate maximum likelihood estimator of MFG are developed. Furthermore, two methods are developed to propagate uncertainties though a stochastic differential equation representing attitude kinematics. Based on these, a Bayesian estimator is proposed to estimate the attitude and time-varying gyro bias concurrently. Numerical studies indicate that the proposed estimator exhibits a better accuracy against the well-established multiplicative extended Kalman filter for two challenging cases.

math.OC↗

arXiv2020

Bayesian Attitude Estimation with the Matrix Fisher Distribution on SO(3)

This paper focuses on a stochastic formulation of Bayesian attitude estimation on the special orthogonal group. In particular, an exponential probability density model for random matrices, referred to as the matrix Fisher distribution is used to represent the uncertainties of attitude estimates and measurements in a global fashion. Various stochastic properties of the matrix Fisher distribution are derived on the special orthogonal group, and based on these, two types of intrinsic frameworks for Bayesian attitude estimation are constructed. These avoid complexities or singularities of the attitude estimators developed in terms of quaternions. The proposed approaches are particularly useful to deal with large estimation errors or large uncertainties for complex maneuvers to obtain accurate estimates of the attitude.

math.OC↗

arXiv2020

Spectral Bayesian Estimation for General Stochastic Hybrid Systems

General Stochastic Hybrid Systems (GSHS) have been formulated to represent various types of uncertainties in hybrid dynamical systems. In this paper, we propose computational techniques for Bayesian estimation of GSHS. In particular, the Fokker-Planck equation that describes the evolution of uncertainty distributions along GSHS is solved by spectral techniques, where an arbitrary form of probability density of the hybrid state is represented by a mixture of Fourier series. The method is based on splitting the Fokker-Planck equation represented by an integro-partial differential equation into the partial differentiation part for continuous diffusion and the integral part for discrete transition, and integrating the solution of each part. The propagated density function is used with a likelihood function in the Bayes' formula to estimate the hybrid state for given sensor measurements. The unique feature of the proposed technique is that the probability density describing complete stochastic properties of the hybrid state is constructed without relying on the common Gaussian assumption, in contrast to other methods that compute certain expected values such as mean or variance. We apply the proposed method to the estimation of two examples: the bouncing ball model and the Dubins vehicle model. We show that the proposed technique yields propagated densities consistent with Monte Carlo simulations, more accurate estimates over the Gaussian based approach and some computational benefits over a particle filter.

math.OC↗

arXiv2020

Enlarging Discriminative Power by Adding an Extra Class in Unsupervised Domain Adaptation

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.

cs.LG↗

arXiv2019

Adaptive Learning Kalman Filter with Gaussian Process

This paper presents an adaptive Kalman filter for a linear dynamic system perturbed by an additive disturbance. The objective is to estimate both of the state and the unknown disturbance concurrently, while learning the disturbance as a stochastic process of the state vector. This is achieved by estimating the state according to the extended Kalman filtering applied to the marginal distribution of the state, and by estimating the disturbance from a backward smoothing technique. The corresponding pair of the estimated states and disturbances are fetched to a Gaussian process, which is constantly updated to resemble the disturbance process. The unique feature is that all of uncertainties in the estimated state and disturbance are accounted throughout the learning process. The efficacy of the proposed approach is illustrated by a numerical example.

math.OC↗

arXiv2019

A Global, Continuous, and Exponentially Convergent Observer for Gyro Bias and Attitude of a Rigid Body

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.

math.OC↗

arXiv2019

Attitude Observer on SO(3) with Time-Varying Reference Directions

This paper introduces an advanced Lyapunov stability analysis for an attitude observer that has been developed on the special orthogonal group. In particular, when the attitude observer is constructed based on multiple direction measurements toward known reference points, a local exponential stability has been established by linearization, under the assumption that those reference points are fixed in the inertial frame. Several modifications have been proposed to deal with reference directions changing over time. Here, we present an alternative Lyapunov analysis to show that the attitude observer still exhibits exponential stability for time-varying reference directions, under the assumption that the observer gain is sufficiently large relative to the rate of change of the reference directions. These are illustrated by a numerical example, followed by experimental results with visual marker detection in an indoor space.

math.OC↗

arXiv2019

Geometric Adaptive Control with Neural Networks for a Quadrotor UAV in Wind fields

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.

math.OC↗

arXiv2019

Learning to Schedule Communication in Multi-agent Reinforcement Learning

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%.

cs.AI↗