СИНТЕЗ FPGA-АРХИТЕКТУР БАНКОВ ФИЛЬТРОВ НА ОСНОВЕ БЛОЧНОЙ ЛЕСТНИЧНОЙ ФАКТОРИЗАЦИИ В АЛГЕБРЕ КВАТЕРНИОНОВ (ЧАСТЬ 1)

Nowadays the methodology for designing systems on a chip is based on highly parameterized IP components which provide a wide range of adjustment of costs in resources, fixed point arithmetic data formats and system performance for a specific target application. The article presents a systematic approach for synthesizing FPGA architectures of integer reversible paraunitary filter banks in quaternion algebra (Int-Q-PUBB) for L2L (lossless-to-lossy) image transformed encoding. It is shown that the basic elementary transformation of the filter bank is the operation of quaternion multiplication (Q-MUL), the block-lifting factorization of which and the distributed arithmetic on the adder are the basis of the parametrizable Q-MUL IP-component.В настоящее время методологии проектирования систем на кристалле основываются на высокопараметризированных IP-компонентах (IP – intellectual property), которые для конкретного целевого приложения обеспечивают широкий диапазон регулировки затрат ресурсов, форматов данных арифметики с фиксированной запятой и производительности системы. В статье представлен систематический подход к синтезу FPGA-архитектур целочисленных обратимых параунитарных банков фильтров в алгебре кватернионов (Int-Q-ПУБФ) для трансформационного кодирования изображений по схеме L2L (lossless-to-lossy). Показывается, что базовым элементарным преобразованием банка фильтров является операция умножения кватернионов (Q-MUL). Блочная лестничная факторизация данной операции и распределенная арифметика на сумматорах положены в основу параметризируемого Q-MUL IP-компонента

Noncommutative geometry of the Moyal plane: translation isometries, Connes' distance on coherent states, Pythagoras equality

We study the metric aspect of the Moyal plane from Connes' noncommutative geometry point of view. First, we compute Connes' spectral distance associated with the natural isometric action of R^2 on the algebra of the Moyal plane A. We show that the distance between any state of A and any of its translated is precisely the amplitude of the translation. As a consequence, we obtain the spectral distance between coherent states of the quantum harmonic oscillator as the Euclidean distance on the plane. We investigate the classical limit, showing that the set of coherent states equipped with Connes' spectral distance tends towards the Euclidean plane as the parameter of deformation goes to zero. The extension of these results to the action of the symplectic group is also discussed, with particular emphasize on the orbits of coherent states under rotations. Second, we compute the spectral distance in the double Moyal plane, intended as the product of (the minimal unitization of) A by C^2. We show that on the set of states obtained by translation of an arbitrary state of A, this distance is given by Pythagoras theorem. On the way, we prove some Pythagoras inequalities for the product of arbitrary unital & non-degenerate spectral triples. Applied to the Doplicher-Fredenhagen-Roberts model of quantum spacetime [DFR], these two theorems show that Connes' spectral distance and the DFR quantum length coincide on the set of states of optimal localization. Some of the results of this paper can be thought as a continuation of arXiv:0912.0906, as well as a companion to arXiv:1106.0261.Comment: 32 pages, 1 figure. Section on the generalities of the Moyal plane shortened. One section added on symplectic orbits. To be published in Commun. Math. Phy

A custom computing framework for orientation and photogrammetry

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.Includes bibliographical references (p. 211-223).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.There is great demand today for real-time computer vision systems, with applications including image enhancement, target detection and surveillance, autonomous navigation, and scene reconstruction. These operations generally require extensive computing power; when multiple conventional processors and custom gate arrays are inappropriate, due to either excessive cost or risk, a class of devices known as Field-Programmable Gate Arrays (FPGAs) can be employed. FPGAs per the flexibility of a programmable solution and nearly the performance of a custom gate array. When implementing a custom algorithm in an FPGA, one must be more efficient than with a gate array technology. By tailoring the algorithms, architectures, and precisions, the gate count of an algorithm may be sufficiently reduced to t into an FPGA. The challenge is to perform this customization of the algorithm, while still maintaining the required performance. The techniques required to perform algorithmic optimization for FPGAs are scattered across many fields; what is currently lacking is a framework for utilizing all these well known and developing techniques. The purpose of this thesis is to develop this framework for orientation and photogrammetry systems.by Paul D. Fiore.Ph.D

Linearized Rigid-Body Static and Dynamic Stability of an Aircraft With a Bio-Inspired Rotating Empennage

The United States Air Force (USAF) will likely seek to remove the vertical tail of next-generation fighter aircraft. This work seeks to characterize the static and dynamic stability and handling qualities of a vertical-tailless aircraft concept that would satisfy the USAF’s goal. This concept aircraft, one modified with a Bio-Inspired Rotating Empennage (BIRE), does not have a vertical tail, and is instead capable of rotating the horizontal tail about the fuselage axis for maneuvering. The dynamic characteristics of the BIRE-modified aircraft are compared to a baseline unmodified aircraft, similar to the F16, with a traditional vertical tail. Linearized aerodynamic models for each aircraft, based on previous work, are used alongside a set of coupled dynamic equations of motion for asymmetric aircraft, derived in this work, to estimate the dynamic response of each aircraft to disturbances from steady level and banked trim conditions.The static stability analysis suggests that modifying the baseline with a BIRE decreases the aircraft’s static pitch, roll and yaw stability. The dynamic stability analysis suggests that modifying the baseline aircraft with a BIRE; 1) slightly decreases the aircraft’s short period damping and slightly increases the aircraft’s short period frequency, 2) decreases the aircraft’s phugoid damping and slightly increases the aircraft’s phugoid frequency, 3) slightly increases the aircraft’s roll damping, 4) decreases the aircraft’s spiral damping for steady level flight and increases the aircraft’s spiral damping sensitivity to center of gravity location when banked, and 5) produces a non-traditional dutch roll mode. The handling quality analysis suggests that modifying the baseline aircraft with a BIRE decreases only the aircraft’s dutch roll handling quality levels

Aerodynamic Implications of a Bio‐Inspired Rotating Empennage Design for Control of a Fighter Aircraft

This dissertation presents an analysis of the aerodynamics for an aircraft using a novel, bio-inspired control system. The control system is a rotating tail, that is inspired by the way in which birds use their tail to control their flight. An aerodynamic model for a baseline aircraft and a bio-inspired variant are created by referencing well-known relationships for the aerodynamics of flight, which are then used to analyze the available flight envelope at which each aircraft can reach two different equilibrium states. An analysis of the total aerodynamic control authority of each aircraft is also included along with a preliminary control system to bring the aircraft back to equilibrium when influenced by a wind gust. These studies indicate some of the benefits and trade-offs of using this bio-inspired rotating tail design

분산된 로터로 구동되는 비행 스켈레톤 시스템의 디자인 상태추정 및 제어

학위논문(박사)--서울대학교 대학원 :공과대학 기계항공공학부,2020. 2. 이동준.In this thesis, we present key theoretical components for realizing flying aerial skeleton system called LASDRA (large-size aerial skeleton with distributed rotor actuation). Aerial skeletons are articulated aerial robots actuated by distributed rotors including both ground connected type and flying type. These systems have recently attracted interest and are being actively researched in several research groups, with the expectation of applying those for aerial manipulation in distant/narrow places, or for the performance with entertaining purpose such as drone shows. Among the aerial skeleton systems, LASDRA system, proposed by our group has some significant advantages over the other skeleton systems that it is capable of free SE(3) motion by omni-directional wrench generation of each link, and also the system can be operated with wide range of configuration because of the 3DOF (degrees of freedom) inter-link rotation enabled by cable connection among the link modules. To realize this LASDRA system, following three components are crucial: 1) a link module that can produce omni-directional force and torque and enough feasible wrench space; 2) pose and posture estimation algorithm for an articulated system with high degrees of freedom; and 3) a motion generation framework that can provide seemingly natural motion while being able to generate desired motion (e.g., linear and angular velocity) for the entire body. The main contributions of this thesis is theoretically developing these three components, and verifying these through outdoor flight experiment with a real LASDRA system. First of all, a link module for the LASDRA system is designed with proposed constrained optimization problem, maximizing the guaranteed feasible force and torque for any direction while also incorporating some constraints (e.g., avoiding inter-rotor air-flow interference) to directly obtain feasible solution. Also, an issue of ESC-induced (electronic speed control) singularity is first introduced in the literature which is inevitably caused by bi-directional thrust generation with sensorless actuators, and handled with a novel control allocation called selective mapping. Then for the state estimation of the entire LASDRA system, constrained Kalman filter based estimation algorithm is proposed that can provide estimation result satisfying kinematic constraint of the system, also along with a semi-distributed version of the algorithm to endow with system scalability. Lastly, CPG-based motion generation framework is presented that can generate natural biomimetic motion, and by exploiting the inverse CPG model obtained with machine learning method, it becomes possible to generate certain desired motion while still making CPG generated natural motion.본 논문에서는 비행 스켈레톤 시스템 LASDRA (large-size aerial skeleton with distributed rotor actuation) 의 구현을 위해 요구되는 핵심 기법들을 제안하며, 이를 실제 LASDRA 시스템의 실외 비행을 통해 검증한다. 제안된 기법은 1) 전방향으로 힘과 토크를 낼 수 있고 충분한 가용 렌치공간을 가진 링크 모듈, 2) 높은 자유도의 다관절구조 시스템을 위한 위치 및 자세 추정 알고리즘, 3) 자연스러운 움직임을 내는 동시에 전체 시스템이 속도, 각속도 등 원하는 움직임을 내도록 할 수 있는 모션 생성 프레임워크로 구성된다. 본 논문에서는 우선 링크 모듈의 디자인을 위해 전방향으로 보장되는 힘과 토크의 크기를 최대화하는 구속 최적화를 사용하고, 실제 적용가능한 해를 얻기 위해 몇가지 구속조건(로터 간 공기 흐름 간섭의 회피 등)을 고려한다. 또한 센서가 없는 액츄에이터로 양방향 추력을 내는 것에서 야기되는 ESC 유발 특이점 (ESC-induced singularity) 이라는 문제를 처음으로 소개하고, 이를 해결하기 위해 선택적 맵핑 (selective mapping) 이라는 기법을 제시한다. 전체 LASDRA 시스템의 상태추정을 위해 시스템의 기구학적 구속조건을 만족하는 결과를 얻을 수 있도록 구속 칼만 필터 기반의 상태추정 기법을 제시하고, 시스템 확장성을 고려하여 반 분산 (semi-distributed) 개념의 알고리즘을 함께 제시한다. 마지막으로 본 논문에서는 자연스러운 움직임의 생성을 위하여 CPG 기반의 모션 생성 프레임워크를 제안하며, 기계 학습 방법을 통해 CPG 역연산 모델을 얻음으로써 전체 시스템이 원하는 움직임을 낼 수 있도록 한다.1 Introduction 1 1.1 Motivation and Background 1 1.2 Research Problems and Approach 3 1.3 Preview of Contributions 5 2 Omni-Directional Aerial Robot 7 2.1 Introduction 7 2.2 Mechanical Design 12 2.2.1 Design Description 12 2.2.2 Wrench-Maximizing Design Optimization 13 2.3 System Modeling and Control Design 20 2.3.1 System Modeling 20 2.3.2 Pose Trajectory Tracking Control 22 2.3.3 Hybrid Pose/Wrench Control 22 2.3.4 PSPM-Based Teleoperation 24 2.4 Control Allocation with Selective Mapping 27 2.4.1 Infinity-Norm Minimization 27 2.4.2 ESC-Induced Singularity and Selective Mapping 29 2.5 Experiment 38 2.5.1 System Setup 38 2.5.2 Experiment Results 41 2.6 Conclusion 49 3 Pose and Posture Estimation of an Aerial Skeleton System 51 3.1 Introduction 51 3.2 Preliminary 53 3.3 Pose and Posture Estimation 55 3.3.1 Estimation Algorithm via SCKF 55 3.3.2 Semi-Distributed Version of Algorithm 59 3.4 Simulation 62 3.5 Experiment 65 3.5.1 System Setup 65 3.5.2 Experiment of SCKF-Based Estimation Algorithm 66 3.6 Conclusion 69 4 CPG-Based Motion Generation 71 4.1 Introduction 71 4.2 Description of Entire Framework 75 4.2.1 LASDRA System 75 4.2.2 Snake-Like Robot & Pivotboard 77 4.3 CPG Model 79 4.3.1 LASDRA System 79 4.3.2 Snake-Like Robot 80 4.3.3 Pivotboard 83 4.4 Target Pose Calculation with Expected Physics 84 4.5 Inverse Model Learning 86 4.5.1 LASDRA System 86 4.5.2 Snake-Like Robot 89 4.5.3 Pivotboard 90 4.6 CPG Parameter Adaptation 93 4.7 Simulation 94 4.7.1 LASDRA System 94 4.7.2 Snake-Like Robot & Pivotboard 97 4.8 Conclusion 101 5 Outdoor Flight Experiment of the F-LASDRA System 103 5.1 System Setup 103 5.2 Experiment Results 104 6 Conclusion 111 6.1 Summary 111 6.2 Future Works 112Docto

Parametric reduced-order aeroelastic modelling for analysis, dynamic system interpolation and control of flexible aircraft

This work presents an integral framework to derive aeroelastic models for very flexible aircraft that can be used in design routines, operational envelope analysis and control applications. Aircraft are modelled using a nonlinear geometrically-exact beam model coupled with an Unsteady Vortex-Lattice Method aerodynamic solver, capable of capturing important nonlinear couplings and effects that significantly impact the flight characteristics of very flexible aircraft. Then, complete linearised expressions of the aircraft system about trim reference conditions at possibly large deformations are presented. The nature of the aerodynamic models results in a high-dimensional system that requires of model reduction methods for efficient analysis and manipulation. Krylov-subspace model reduction methods are implemented to reduce the dimensionality of the multi-input multi-output linearised aerodynamic model and achieve a very significant reduction in the size of the size of the system. The reduced aerodynamic model is then coupled with a modal expression of the linearised beam model, resulting in a compact aeroelastic state-space that can be efficiently used on desktop hardware for linear analysis or as part of internal control models. These have been used to explore the design space of a very flexible wing with complex aeroelastic properties to determine the flutter boundaries, for which experimental data has become available that validates the methods presented herein. Additionally, they have been integrated in a model predictive control framework, where the reduced linear aerodynamic model is part of the control model, and the simulation plant is the nonlinear flight dynamic/aeroelastic model connected as a hardware-in-the-loop platform. Finally, in order to accelerate the design space exploration of very flexible structures, state-space interpolation methods are sought to obtain, with a few linearised models sampled across the domain, interpolated state-spaces anywhere in the parameter-space in a fast and accurate manner. The performance of the interpolation schemes is heavily dependent on the location of the sampling points on the design space, therefore, a novel adaptive Bayesian sampling scheme is presented to choose these points in an optimal approach that minimises the interpolation error function.Open Acces