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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., Comment: 23 pages, 25 figures, 3 tables

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.

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., Comment: 8 pages, 5 figures, 3 tables

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.

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., Comment: 8 pages, 7 figures

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., Comment: J Astronaut Sci (2022)

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.

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.

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., Comment: Full version (8 pages) of LHMNC 2021 paper

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.

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.

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., Comment: Full version (8 pages) of ACC 2021 paper

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.

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.

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.

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.

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.

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.

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.

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%., Comment: Accepted in ICLR 2019

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.

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.

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.

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., Comment: Published: Kulumani, S. and Lee, T. Constrained Geometric Attitude Control on SO(3), International Journal of Control, Automation, and Systems, 2017, vol. 15, no. 6

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., Comment: arXiv admin note: text overlap with arXiv:1602.03511

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.

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., Comment: Presented at 2017 AAS Astrodynamics Specialist Conference Stevenson, WA

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 Poincar\'e 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., Comment: Accepted 2016 AIAA/AAS Space Conference, Long Beach, CA

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., Comment: arXiv admin note: text overlap with arXiv:1304.6765, arXiv:1411.2986

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., Comment: 2016 American Control Conference (ACC)

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.

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., Comment: arXiv admin note: substantial text overlap with arXiv:1501.04910

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., Comment: Presented at AAS Astrodynamics Specialist Conference Vail, CO August 2015

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.

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.