arXiv subjects

Taeyoung Lee

Publications and source records attributed to Taeyoung Lee.

At least 55 records · Page 3Linked to original sources

arXiv2018

Real Harmonic Analysis on the Special Orthogonal Group

This paper presents theoretical analysis and software implementation for real harmonics analysis on the special orthogonal group. Noncommutative harmonic analysis for complex-valued functions on the special orthogonal group has been studied extensively. However, it is customary to treat real harmonic analysis as a special case of complex harmonic analysis, and there have been limited results developed specifically for real-valued functions. Here, we develop a set of explicit formulas for real-valued irreducible unitary representations on the special orthogonal group, and provide several operational properties, such as derivatives, sampling, and Clebsch-Gordon coefficients. Furthermore, we implement both of complex and real harmonics analysis on the special orthogonal group into an open source software package that utilizes parallel processing through the OpenMP library. The efficacy of the presented results are illustrated by benchmark studies and an application to spherical shape matching.

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arXiv2018

Geometric Adaptive Control for a Quadrotor UAV with Wind Disturbance Rejection

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.

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arXiv2017

Constrained Geometric Attitude Control on SO(3)

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.

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arXiv2017

Geometric Control for Autonomous Landing on Asteroid Itokawa using Visual Localization

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.

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arXiv2017

Semi-Global Attitude Controls Bypassing the Topological Obstruction on SO(3)

This paper presents global tracking strategies for the attitude dynamics of a rigid body. It is well known that global attractivity is prohibited for continuous attitude control systems on the special orthogonal group. Such topological restriction has been dealt with either by constructing smooth attitude control systems that exclude a set of measure zero in the region of attraction, or by introducing hybrid control systems to obtain global asymptotic stability. This paper proposes alternative attitude control systems that are continuous in time to achieve exponential stability, where the region of attraction covers the entire special orthogonal group. The main contribution of this paper is providing a new framework to overcome the topological restriction in attitude controls without relying on discontinuities through the controlled maneuvers. The efficacy of the proposed methods is illustrated by numerical simulations and experiments.

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arXiv2016

Low-Thrust Trajectory Design Using Reachability Sets near Asteroid 4769 Castalia

We present a computational approach for the design of continuous low thrust transfers around an asteroid. These transfers are computed through the use of a reachability set generated on a lower dimensional Poincaré surface. Complex, long duration transfer trajectories are highly sensitive to the initial guess and generally have a small region of convergence. Computation of the reachable set alleviates the need to generate an accurate initial guess for optimization. From the reachable set, we chose a trajectory which minimizes a distance metric towards the desired target. Successive computation of the reachable set allows for the design of general transfer trajectories which iteratively approach the target. We demonstrate this method by determining a transfer trajectory about the asteroid 4769 Castalia.

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arXiv2016

Extended Kalman Filter on SE(3) for Geometric Control of a Quadrotor UAV

An extended Kalman filter (EKF) is developed on the special Euclidean group, SE(3) for geometric control of a quadrotor UAV. It is obtained by performing an extensive linearization on SE(3) to estimate the state of the quadrotor from noisy measurements. Proposed estimator considers all the coupling effects between rotational and translational dynamics, and it is developed in a coordinate-free fashion. The desirable features of the proposed EKF are illustrated by numerical examples and experimental results for several scenarios. The proposed estimation scheme on SE(3) has been unprecedented and these results can be particularly useful for aggressive maneuvers in GPS denied environments or in situations where parts of onboard sensors fail.

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arXiv2016

Geometric Adaptive Control of Attitude Dynamics on SO(3) with State Inequality Constraints

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arXiv2016

Global Unscented Attitude Estimation via the Matrix Fisher Distributions on SO(3)

This paper is focused on probabilistic estimation for the attitude dynamics of a rigid body on the special orthogonal group. We select the matrix Fisher distribution to represent the uncertainties of attitude estimates and measurements in a global fashion without need for local coordinates. Several properties of the matrix Fisher distribution on the special orthogonal group are presented, and an unscented transform is proposed to approximate a matrix Fisher distribution by selected sigma points. Based on these, an intrinsic, global framework for Bayesian attitude estimation is developed. It is shown that the proposed approach can successfully deal with large initial estimator errors and large uncertainties over complex maneuvers to obtain accurate estimates of the attitude.

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arXiv2015

Stabilization of a Rigid Body Payload with Multiple Cooperative Quadrotors

This paper presents the full dynamics and control of arbitrary number of quadrotor unmanned aerial vehicles (UAV) transporting a rigid body. The rigid body is connected to the quadrotors via flexible cables where each flexible cable is modeled as a system of arbitrary number of serially connected links. It is shown that a coordinate-free form of equations of motion can be derived for the complete model without any simplicity assumptions that commonly appear in other literature, according to Lagrangian mechanics on a manifold. A geometric nonlinear controller is presented to transport the rigid body to a fixed desired position while aligning all of the links along the vertical direction. A rigorous mathematical stability proof is given and the desirable features of the proposed controller are illustrated by numerical examples and experimental results.

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arXiv2015

Systematic Design of Optimal Low-Thrust Transfers for the Three-Body Problem

A computational approach is developed for the design of continuous low thrust transfers in the planar circular restricted three-body problem. The transfer design method of invariant manifolds is extended with the addition of continuous low thrust propulsion. A reachable region is generated and it is used to determine transfer opportunities, analogous to the intersection of invariant manifolds. The reachable set is developed on a lower dimensional Poincare section and used to design transfer trajectories. This is solved numerically as a discrete optimal control problem using a variational integrator. This provides for a geometrically exact and numerically efficient method for the motion in the three-body problem. A numerical simulation is provided developing a transfer from a $L_1$ periodic orbit in the Earth-Moon system to a target orbit about the Moon.

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arXiv2015

Geometric Controls for a Tethered Quadrotor UAV

This paper deals with the dynamics and controls of a quadrotor unmanned aerial vehicle that is connected to a fixed point on the ground via a tether. Tethered quadrotors have been envisaged for long-term aerial surveillance with high-speed communications. This paper presents an intrinsic form of the dynamic model of a tethered quadrotor including the coupling between deformations of the tether and the motion of the quadrotor, and it constructs geometric control systems to asymptotically stabilize the coupled dynamics of the quadrotor and the tether. The proposed global formulation of dynamics and control also avoids complexities and singularities associated with local coordinates. These are illustrated by numerical examples.

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arXiv2015

Hybrid Attitude Observer on SO(3) with Global Asymptotic Stability

This paper presents a deterministic hybrid observer for the attitude dynamics of a rigid body that guarantees global asymptotical stability. Any smooth attitude observer suffers from the inherent topological restriction that it is impossible to achieve global attractivity, and as such, attitude observers have been developed with almost global asymptotic stability. We demonstrate that such attitude observer may yields very slow initial convergence rates, and motivated by this, we propose a hybrid attitude observer that guarantees global asymptotic stability on the special orthogonal group. We illustrate that the proposed observer exhibits substantially improved convergence rate uniformly via numerical examples and experiments.

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arXiv2015

Angular Velocity Observer on the Special Orthogonal Group for Velocity-Free Rigid-Body Attitude Tracking Control

This paper studies a rigid body attitude tracking control problem with attitude measurements only, when angular velocity measurements are not available. An angular velocity observer is constructed such that the estimated angular velocity is guaranteed to converge to the true angular velocity asymptotically from almost all initial estimates. As it is developed directly on the special orthogonal group, it completely avoids singularities, complexities, or discontinuities caused by minimal attitude representations or quaternions. Then, the presented observer is integrated with a proportional-derivative attitude tracking controller to show a separation type property, where exponential stability is guaranteed for the combined observer and attitude control system.

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arXiv2015

Global Formulations of Lagrangian and Hamiltonian Mechanics on Two-Spheres

This paper provides global formulations of Lagrangian and Hamiltonian variational dynamics evolving on the product of an arbitrary number of two-spheres. Four types of Euler-Lagrange equations and Hamilton's equations are developed in a coordinate-free fashion on two-spheres, without relying on local parameterizations that may lead to singularities and cumbersome equations of motion. The proposed intrinsic formulations of Lagrangian and Hamiltonian dynamics are novel in that they incorporate the geometry of two-spheres, resulting in equations of motion that are expressed compactly, and they are useful in analysis and computation of the global dynamics.

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arXiv2015

Geometric Adaptive Control for Aerial Transportation of a Rigid Body

This paper is focused on tracking control for a rigid body payload, that is connected to an arbitrary number of quadrotor unmanned aerial vehicles via rigid links. A geometric adaptive controller is constructed such that the payload asymptotically follows a given desired trajectory for its position and attitude in the presence of uncertainties. The coupled dynamics between the rigid body payload, links, and quadrotors are explicitly incorporated into control system design and stability analysis. These are developed directly on the nonlinear configuration manifold in a coordinate-free fashion to avoid singularities and complexities that are associated with local parameterizations. The desirable features of the proposed control system are illustrated by a numerical example.

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arXiv2015

Dynamics and Control of Quadrotor UAVs Transporting a Rigid Body Connected via Flexible Cables

This paper is focused on the dynamics and control of arbitrary number of quadrotor UAVs transporting a rigid body payload. The rigid body payload is connected to quadrotors via flexible cables where each flexible cable is modeled as a system of serially-connected links. It is shown that a coordinate-free form of equations of motion can be derived for arbitrary numbers of quadrotors and links according to Lagrangian mechanics on a manifold. A geometric nonlinear controller is presented to transport the rigid body to a fixed desired position while aligning all of the links along the vertical direction. Numerical results are provided to illustrate the desirable features of the proposed control system.

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arXiv2014

Global Exponential Attitude Tracking Controls on SO(3)

This paper presents four types of tracking control systems for the attitude dynamics of a rigid body. First, a smooth control system is constructed to track a given desired attitude trajectory, while guaranteeing almost semi-global exponential stability. It is extended to achieve global exponential stability by using a hybrid control scheme based on multiple configuration error functions. They are further extended to obtain robustness with respect to a fixed disturbance using an integral term. The resulting robust, global exponential stability for attitude tracking is the unique contribution of this paper, and these are developed directly on the special orthogonal group to avoid singularities of local coordinates, or ambiguities associated with quaternions. The desirable features are illustrated by numerical examples.

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