1,025 research outputs found

    A survey on fractional order control techniques for unmanned aerial and ground vehicles

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    In recent years, numerous applications of science and engineering for modeling and control of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) systems based on fractional calculus have been realized. The extra fractional order derivative terms allow to optimizing the performance of the systems. The review presented in this paper focuses on the control problems of the UAVs and UGVs that have been addressed by the fractional order techniques over the last decade

    Adaptive and Optimal Motion Control of Multi-UAV Systems

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    This thesis studies trajectory tracking and coordination control problems for single and multi unmanned aerial vehicle (UAV) systems. These control problems are addressed for both quadrotor and fixed-wing UAV cases. Despite the fact that the literature has some approaches for both problems, most of the previous studies have implementation challenges on real-time systems. In this thesis, we use a hierarchical modular approach where the high-level coordination and formation control tasks are separated from low-level individual UAV motion control tasks. This separation helps efficient and systematic optimal control synthesis robust to effects of nonlinearities, uncertainties and external disturbances at both levels, independently. The modular two-level control structure is convenient in extending single-UAV motion control design to coordination control of multi-UAV systems. Therefore, we examine single quadrotor UAV trajectory tracking problems to develop advanced controllers compensating effects of nonlinearities and uncertainties, and improving robustness and optimality for tracking performance. At fi rst, a novel adaptive linear quadratic tracking (ALQT) scheme is developed for stabilization and optimal attitude control of the quadrotor UAV system. In the implementation, the proposed scheme is integrated with Kalman based reliable attitude estimators, which compensate measurement noises. Next, in order to guarantee prescribed transient and steady-state tracking performances, we have designed a novel backstepping based adaptive controller that is robust to effects of underactuated dynamics, nonlinearities and model uncertainties, e.g., inertial and rotational drag uncertainties. The tracking performance is guaranteed to utilize a prescribed performance bound (PPB) based error transformation. In the coordination control of multi-UAV systems, following the two-level control structure, at high-level, we design a distributed hierarchical (leader-follower) 3D formation control scheme. Then, the low-level control design is based on the optimal and adaptive control designs performed for each quadrotor UAV separately. As particular approaches, we design an adaptive mixing controller (AMC) to improve robustness to varying parametric uncertainties and an adaptive linear quadratic controller (ALQC). Lastly, for planar motion, especially for constant altitude flight of fixed-wing UAVs, in 2D, a distributed hierarchical (leader-follower) formation control scheme at the high-level and a linear quadratic tracking (LQT) scheme at the low-level are developed for tracking and formation control problems of the fixed-wing UAV systems to examine the non-holonomic motion case. The proposed control methods are tested via simulations and experiments on a multi-quadrotor UAV system testbed

    The Phoenix Drone: An Open-Source Dual-Rotor Tail-Sitter Platform for Research and Education

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    In this paper, we introduce the Phoenix drone: the first completely open-source tail-sitter micro aerial vehicle (MAV) platform. The vehicle has a highly versatile, dual-rotor design and is engineered to be low-cost and easily extensible/modifiable. Our open-source release includes all of the design documents, software resources, and simulation tools needed to build and fly a high-performance tail-sitter for research and educational purposes. The drone has been developed for precision flight with a high degree of control authority. Our design methodology included extensive testing and characterization of the aerodynamic properties of the vehicle. The platform incorporates many off-the-shelf components and 3D-printed parts, in order to keep the cost down. Nonetheless, the paper includes results from flight trials which demonstrate that the vehicle is capable of very stable hovering and accurate trajectory tracking. Our hope is that the open-source Phoenix reference design will be useful to both researchers and educators. In particular, the details in this paper and the available open-source materials should enable learners to gain an understanding of aerodynamics, flight control, state estimation, software design, and simulation, while experimenting with a unique aerial robot.Comment: In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'19), Montreal, Canada, May 20-24, 201

    Attitude Estimation and Control Using Linear-Like Complementary Filters: Theory and Experiment

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    This paper proposes new algorithms for attitude estimation and control based on fused inertial vector measurements using linear complementary filters principle. First, n-order direct and passive complementary filters combined with TRIAD algorithm are proposed to give attitude estimation solutions. These solutions which are efficient with respect to noise include the gyro bias estimation. Thereafter, the same principle of data fusion is used to address the problem of attitude tracking based on inertial vector measurements. Thus, instead of using noisy raw measurements in the control law a new solution of control that includes a linear-like complementary filter to deal with the noise is proposed. The stability analysis of the tracking error dynamics based on LaSalle's invariance theorem proved that almost all trajectories converge asymptotically to the desired equilibrium. Experimental results, obtained with DIY Quad equipped with the APM2.6 auto-pilot, show the effectiveness and the performance of the proposed solutions.Comment: Submitted for Journal publication on March 09, 2015. Partial results related to this work have been presented in IEEE-ROBIO-201

    An Application of UAV Attitude Estimation Using a Low-Cost Inertial Navigation System

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    Unmanned Aerial Vehicles (UAV) are playing an increasing role in aviation. Various methods exist for the computation of UAV attitude based on low cost microelectromechanical systems (MEMS) and Global Positioning System (GPS) receivers. There has been a recent increase in UAV autonomy as sensors are becoming more compact and onboard processing power has increased significantly. Correct UAV attitude estimation will play a critical role in navigation and separation assurance as UAVs share airspace with civil air traffic. This paper describes attitude estimation derived by post-processing data from a small low cost Inertial Navigation System (INS) recorded during the flight of a subscale commercial off the shelf (COTS) UAV. Two discrete time attitude estimation schemes are presented here in detail. The first is an adaptation of the Kalman Filter to accommodate nonlinear systems, the Extended Kalman Filter (EKF). The EKF returns quaternion estimates of the UAV attitude based on MEMS gyro, magnetometer, accelerometer, and pitot tube inputs. The second scheme is the complementary filter which is a simpler algorithm that splits the sensor frequency spectrum based on noise characteristics. The necessity to correct both filters for gravity measurement errors during turning maneuvers is demonstrated. It is shown that the proposed algorithms may be used to estimate UAV attitude. The effects of vibration on sensor measurements are discussed. Heuristic tuning comments pertaining to sensor filtering and gain selection to achieve acceptable performance during flight are given. Comparisons of attitude estimation performance are made between the EKF and the complementary filter

    Validation and Experimental Testing of Observers for Robust GNSS-Aided Inertial Navigation

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    This chapter is the study of state estimators for robust navigation. Navigation of vehicles is a vast field with multiple decades of research. The main aim is to estimate position, linear velocity, and attitude (PVA) under all dynamics, motions, and conditions via data fusion. The state estimation problem will be considered from two different perspectives using the same kinematic model. First, the extended Kalman filter (EKF) will be reviewed, as an example of a stochastic approach; second, a recent nonlinear observer will be considered as a deterministic case. A comparative study of strapdown inertial navigation methods for estimating PVA of aerial vehicles fusing inertial sensors with global navigation satellite system (GNSS)-based positioning will be presented. The focus will be on the loosely coupled integration methods and performance analysis to compare these methods in terms of their stability, robustness to vibrations, and disturbances in measurements

    Cooperative monocular-based SLAM for multi-UAV systems in GPS-denied environments

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    This work presents a cooperative monocular-based SLAM approach for multi-UAV systems that can operate in GPS-denied environments. The main contribution of the work is to show that, using visual information obtained from monocular cameras mounted onboard aerial vehicles flying in formation, the observability properties of the whole system are improved. This fact is especially notorious when compared with other related visual SLAM configurations. In order to improve the observability properties, some measurements of the relative distance between the UAVs are included in the system. These relative distances are also obtained from visual information. The proposed approach is theoretically validated by means of a nonlinear observability analysis. Furthermore, an extensive set of computer simulations is presented in order to validate the proposed approach. The numerical simulation results show that the proposed system is able to provide a good position and orientation estimation of the aerial vehicles flying in formation.Peer ReviewedPostprint (published version

    Gain-Scheduled Complementary Filter Design for a MEMS Based Attitude and Heading Reference System

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    This paper describes a robust and simple algorithm for an attitude and heading reference system (AHRS) based on low-cost MEMS inertial and magnetic sensors. The proposed approach relies on a gain-scheduled complementary filter, augmented by an acceleration-based switching architecture to yield robust performance, even when the vehicle is subject to strong accelerations. Experimental results are provided for a road captive test during which the vehicle dynamics are in high-acceleration mode and the performance of the proposed filter is evaluated against the output from a conventional linear complementary filter

    MEMS ์„ผ์„œ๋ฅผ ํ™œ์šฉํ•œ ๋ฉ€ํ‹ฐ๋กœํ„ฐํ˜• ๋ฌด์ธํ•ญ๊ณต๊ธฐ์˜ ์ €๋น„์šฉ ๋น„ํ–‰์ œ์–ด์‹œ์Šคํ…œ์˜ ์„ค๊ณ„์— ๊ด€ํ•œ ์—ฐ๊ตฌ

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    ํ•™์œ„๋…ผ๋ฌธ(์„์‚ฌ)--์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› :๊ณต๊ณผ๋Œ€ํ•™ ๊ธฐ๊ณ„ํ•ญ๊ณต๊ณตํ•™๋ถ€,2019. 8. ์—ฌ์žฌ์ต.ํ”ํžˆ ๋“œ๋ก (Drone)์ด๋ผ๊ณ  ๋ถˆ๋ฆฌ๋Š” ๋ฉ€ํ‹ฐ๋กœํ„ฐํ˜• ๋ฌด์ธํ•ญ๊ณต๊ธฐ๋Š” ์ €๋ ดํ•˜๊ณ  ์กฐ์ข…ํ•˜๊ธฐ ์‰ฌ์šฐ๋ฉฐ ๊ฐ„๋‹จํ•œ ๊ตฌ์กฐ์™€ ์ˆ˜์ง ์ด์ฐฉ๋ฅ™์ด ๊ฐ€๋Šฅํ•˜์—ฌ ๊ตฐ์‚ฌ์ ์ธ ์šฉ๋„๋ฅผ ๋น„๋กฏํ•˜์—ฌ ์ƒ์—…์ ์ธ ์šฉ๋„๋กœ ๋„๋ฆฌ ์“ฐ์ด๊ณ  ์žˆ๋‹ค. ๋ฉ€ํ‹ฐ๋กœํ„ฐํ˜• ๋ฌด์ธํ•ญ๊ณต๊ธฐ๋Š” ๊ฐ€์†๋„ ์„ผ์„œ, ์ž์ด๋กœ์Šค์ฝ”ํ”„ ์„ผ์„œ๋ฅผ ํฌํ•จํ•˜๋Š” ๊ด€์„ฑ ์ธก์ • ์œ ๋‹›(IMU)์„ ์ด์šฉํ•˜์—ฌ ์ง€ํ‘œ๋ฉด์— ๋Œ€ํ•œ ์ž์„ธ๋ฅผ ์ธก์ •ํ•˜์—ฌ ๊ฐ ๋ชจํ„ฐ์˜ ํšŒ์ „์†๋„๋ฅผ ์ œ์–ดํ•˜๋Š” ๋ฐฉ์‹์œผ๋กœ ๋น„ํ–‰ํ•˜๋ฉฐ, ๋น„ํ–‰ ๋ฐฉํ–ฅ์„ ์ถ”์ •ํ•  ์ˆ˜ ์žˆ๋Š” ์ง€์ž๊ธฐ ์„ผ์„œ์™€ ๊ณ ๋„๋ฅผ ์ธก์ •ํ•  ์ˆ˜ ์žˆ๋Š” ๊ธฐ์••๊ณ„๋ฅผ ๋‚ด์žฅํ•œ๋‹ค. ๋น„ํ–‰์ฒด์— ํƒ‘์žฌ๋˜๋Š” ๋น„ํ–‰์ œ์–ด์œ ๋‹›(Flight Control Unit, FCU)์€ ์ด๋Ÿฌํ•œ ์„ผ์„œ ๋ฐ์ดํ„ฐ์™€ ์กฐ์ข… ๋ช…๋ น์„ ์ด์šฉํ•˜์—ฌ ๊ฐ ๋ชจํ„ฐ๋ฅผ ์ œ์–ดํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ๊ณ„์‚ฐ์„ ์ˆ˜ํ–‰ํ•˜๊ธฐ ์œ„ํ•ด์„œ ๊ธฐ์กด์˜ ๋น„ํ–‰ ์ œ์–ด ์‹œ์Šคํ…œ์€ ํ•˜๋‚˜ ์ด์ƒ์˜ 32-bit ๋งˆ์ดํฌ๋กœํ”„๋กœ์„ธ์„œ๋ฅผ ์‚ฌ์šฉํ•˜๋ฉฐ ์ด์— ๋”ฐ๋ผ ๋น„ํ–‰์ œ์–ด๋ฅผ ์œ„ํ•œ ํŽŒ์›จ์–ด๋ฅผ ๊ฐœ๋ฐœํ•˜๋Š”๋ฐ ์žˆ์–ด ํšŒ๋กœ ๋ฐ ํŒจํ„ด ์„ค๊ณ„ ๋ฐ ์†Œํ”„ํŠธ์›จ์–ด ๊ฐœ๋ฐœ ํ™˜๊ฒฝ(SDK)์„ ๊ตฌ์„ฑํ•˜๋Š”๋ฐ ์žˆ์–ด ๋งŽ์€ ์‹œ๊ฐ„๊ณผ ์ธ๋ ฅ, ๋น„์šฉ์„ ํ•„์š”๋กœ ํ•˜์—ฌ ์ „์ฒด ์‹œ์Šคํ…œ์˜ ๊ฐ€๊ฒฉ์ด ์ €๋ ดํ•˜์ง€ ์•Š๋‹ค. ๋˜ํ•œ ์ž‘์€ ํฌ๊ธฐ์˜ ๋ฉ€ํ‹ฐ๋กœํ„ฐ์— ์‚ฌ์šฉ๋˜๋Š” ์ €๋ ดํ•œ ๋น„ํ–‰์ œ์–ด์œ ๋‹›์€ ํ”„๋กœ๊ทธ๋ž˜๋ฐ์ด ๋ถˆ๊ฐ€๋Šฅํ•˜๊ฑฐ๋‚˜ ํ™•์žฅ์„ฑ์— ์ œ์•ฝ์ด ์žˆ์–ด ํ•˜๋‚˜์˜ ์ œ์–ด ์‹œ์Šคํ…œ์œผ๋กœ ํ•˜๋‚˜์˜ ๋น„ํ–‰์ฒด ๋ชจ๋ธ์—๋งŒ ์ ์šฉํ•˜๋Š” ํ•œ๊ณ„๊ฐ€ ์žˆ๋‹ค. ๋”ฐ๋ผ์„œ ๋น ๋ฅด๊ณ  ๊ฐ„ํŽธํ•˜๊ฒŒ ํ”„๋กœ๊ทธ๋ž˜๋ฐ์ด ๊ฐ€๋Šฅํ•˜๋ฉฐ ์ €๋ ดํ•˜๊ณ  ๊ตฌํ•˜๊ธฐ ์‰ฌ์šด 8-bit AVR ํ”„๋กœ์„ธ์„œ์™€ MEMS ์„ผ์„œ, C/C++์–ธ์–ด๋ฅผ ์ด์šฉํ•˜์—ฌ ๋น„ํ–‰์ œ์–ด์‹œ์Šคํ…œ์„ ๊ตฌ์„ฑํ•˜์˜€์œผ๋ฉฐ ๊ทธ ๊ฒฐ๊ณผ ํ™•์žฅ์„ฑ์„ ๊ฐ–์ถ”๋ฉด์„œ ๊ฐ€๊ฒฉ์ด ์ €๋ ดํ•˜๋ฉด์„œ ํšจ์œจ์ ์ธ ๋น„ํ–‰ ์ œ์–ด ์‹œ์Šคํ…œ์„ ๊ตฌ์„ฑํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ๋ถ€์กฑํ•œ 8-bit ํ”„๋กœ์„ธ์„œ์˜ ์„ฑ๋Šฅ์€ ํ”„๋กœ์„ธ์„œ์˜ ์ˆ˜๋Ÿ‰์„ ๋Š˜๋ฆฌ๋Š” ๋ณ‘๋ ฌ ์ปดํ“จํŒ… ๋ฐฉ๋ฒ•์œผ๋กœ ํ•ด๊ฒฐํ•  ์ˆ˜ ์žˆ์—ˆ์œผ๋ฉฐ ์ƒ๋ณดํ•„ํ„ฐ์˜ ๊ฐ„๊ฒฐํ•œ ๊ตฌ์กฐ๋กœ ์ธํ•ด 8-bit ํ”„๋กœ์„ธ์„œ์˜ ๋‚ฎ์€ ์ปดํ“จํŒ… ์„ฑ๋Šฅ์œผ๋กœ๋„ ์ดˆ๋‹น ์•ฝ 250Hz์˜ ์ œ์–ด ์ฃผ๊ธฐ๋ฅผ ๊ฐ€์งˆ ์ˆ˜ ์žˆ์—ˆ๋‹ค. ์ž์„ธ ์ œ์–ด ์•Œ๊ณ ๋ฆฌ์ฆ˜์œผ๋กœ Cascade controller๋ฅผ ์„ ํƒํ•˜์—ฌ ์™ธ๋ž€์— ๊ฐ•ํ•˜๋ฉฐ ๋น ๋ฅธ ์ œ์–ด ์†๋„๋ฅผ ์–ป์„ ์ˆ˜ ์žˆ์—ˆ๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ ์ง„๋™์ด ์ƒ๋Œ€์ ์œผ๋กœ ํฐ ํŒœ ์‚ฌ์ด์ฆˆ์˜ ์ฟผ๋“œ๋กœํ„ฐ UAV์—์„œ๋„ ์•ˆ์ •์ ์ธ ๋น„ํ–‰ ์„ฑ๋Šฅ์„ ๊ตฌํ˜„ํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค.1. Introduction ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 1 1. 1. About Research ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 4 1. 2. Basic Theory ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 6 1. 2. 1. Attitude Estimation ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 8 1. 2. 2. Cascade PID Controller ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 14 1. 3. Research Goal ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 17 2. Hardware Design ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 18 2. 1. PCB Design ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 20 2. 1. 1. Design of Flight Controller ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 20 2. 1. 2. Design of PMU for BLDC System ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 29 2. 2. Body Frame Design ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 33 2. 2. 1. DC Motor Powered Quadcopter ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 34 2. 2. 2. BLDC Motor Powered Hexacopter ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 36 3. Software Design ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 38 3. 1. Flight Software Design ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 38 3. 1. 1. Attitude Reference System ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 39 3. 1. 2. Cascade PID Controller ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 44 3. 1. 3. Bluetooth-based Control System ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 46 3. 2. IMU & Attitude Reference System ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 51 3. 2. Attitude Control Performance ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 51 4. Conclusion ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 53 ์ฐธ๊ณ ๋ฌธํ—Œ ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 55 Abstract ยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยทยท 57Maste
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