• 제목/요약/키워드: Closed-form equation

검색결과 215건 처리시간 0.022초

평면대수곡선을 기반으로 한 스테레오 비젼 (Stereo Vision based on Planar Algebraic Curves)

  • 안민호;이정림
    • 한국정보과학회논문지:소프트웨어및응용
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    • 제27권1호
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    • pp.50-61
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    • 2000
  • 최근 원추곡선에 기반한 스테레오 비젼에 대한 연구가 주목을 받고 있는데, 이는 원추곡선이 행렬표현, 대응관계설정의 용이성, 그리고 실세계에서 쉽게 찾을 수 있다는 좋은 성질을 갖는다는 점에서 당연한 현상이라 여겨진다. 하지만, 일반적인 고차의 대수곡선에 대한 확장은 아직 성공적으로 이루어지지 못하고 있는 실정이다. 기약인 대수곡선 (irreducible algebraic curve)은 실세계에서 많지 않지만, 직선과 원추곡선은 무수히 많고, 따라서 이들의 곱으로 주어지는 높은 차수의 대수곡선도 무수히 많다. 본고에서는 2이상의 임의의 차수를 가지는 대수곡선을 calibration된 두 대의 카메라를 가지고 스테레오 문제를 푼다. 대응관계설정과 복원, 두 가지 문제 모두에 대한 closed form solution을 제시한다. $f_1,\;f_2,\;{\pi}$를 각각 두 이미지 곡선, 공간상의 평면이라 하고, $VC_P(g)$를 평면곡선 g와 점 P로 만들어지는 원추곡선이라 하면, $VC_{O1}(f_1)\;=\;VC_{O1}(VC_{O2}(f_2)\;∩\;{\pi})$ 의 관계를 이용하여 미지수인 평면 ${\pi}$의 계수들, $d_1,\;d_2,\;d_3$에 대한 다항 방정식들을 얻을 수 있다. 약간의 변형을 통하여 $d_1$에 대한 다항 방정식을 얻을 수 있고, 이 방정식의 유일한 양수해는 나머지 과정에서 매우 중요한 역할을 한다. 그 이후에는 $O(n^2)$개의 일변수 다항식에 대한 계산만으로 모든 스테레오 문제를 해결한다. 이는 과거의 여러 개의 다변수 다항식의 공통근을 구해야 했던 방법에 비교된다. synthetic 데이터와 실제 이미지에 대한 실험은 우리의 알고리듬이 옳음을 보여준다.

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기준점 배치에 따른 쿼터니언기반 공간후방교회법의 정확도 분석 (Analysis of the Accuracy of Quaternion-Based Spatial Resection Based on the Layout of Control Points)

  • 김의명;최한승
    • 한국측량학회지
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    • 제36권4호
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    • pp.255-262
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    • 2018
  • 사진측량에서 3차원 위치를 결정하기 위한 사전단계로 외부표정요소를 결정하는 공간후방교회법을 수행해야한다. 기존의 공선조건식 기반의 공간후방교회법은 비선형 방정식으로 외부표정요소의 초기값이 필요하며 짐벌락 현상이 나타날 수 있는 문제점이 있다. 이에 반해 쿼터니언 기반의 공간후방교회법은 외부표정요소의 초기값이 필요없고 짐벌락의 문제를 제거할 수 있는 방법이다. 본 연구에서는 쿼터니언기반의 공간후방교회법 안정성을 분석하기 위해 기준점의 배치를 달리하여 외부표정요소를 결정하고 이를 기존의 공선조건식 기반의 공간후방교회법을 적용한 것과 비교 하였다. 그 결과 비교적 쿼터니언 기반의 공간후방교회법은 기준점 배치에 따라 공간후방교회법의 정확도가 많은 영향을 받는 것을 알 수 있었다. 따라서 외부표정요소의 초기값을 얻을 수 없다면 쿼터니언 기반의 공간후방교회법으로 초기값을 추정한 후 이를 공선조건식 기반의 공간후방교회법에 적용하는 것이 효과적으로 외부표정요소를 결정할 수 있는 방법으로 나타났다.

Dynamic Control Allocation for Shaping Spacecraft Attitude Control Command

  • Choi, Yoon-Hyuk;Bang, Hyo-Choong
    • International Journal of Aeronautical and Space Sciences
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    • 제8권1호
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    • pp.10-20
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    • 2007
  • For spacecraft attitude control, reaction wheel (RW) steering laws with more than three wheels for three-axis attitude control can be derived by using a control allocation (CA) approach.1-2 The CA technique deals with a problem of distributing a given control demand to available sets of actuators.3-4 There are many references for CA with applications to aerospace systems. For spacecraft, the control torque command for three body-fixed reference frames can be constructed by a combination of multiple wheels, usually four-wheel pyramid sets. Multi-wheel configurations can be exploited to satisfy a body-axis control torque requirement while satisfying objectives such as minimum control energy.1-2 In general, the reaction wheel steering laws determine required torque command for each wheel in the form of matrix pseudo-inverse. In general, the attitude control command is generated in the form of a feedback control. The spacecraft body angular rate measured by gyros is used to estimate angular displacement also.⁵ Combination of the body angular rate and attitude parameters such as quaternion and MRPs(Modified Rodrigues Parameters) is typically used in synthesizing the control command which should be produced by RWs.¹ The attitude sensor signals are usually corrupted by noise; gyros tend to contain errors such as drift and random noise. The attitude determination system can estimate such errors, and provide best true signals for feedback control.⁶ Even if the attitude determination system, for instance, sophisticated algorithm such as the EKF(Extended Kalman Filter) algorithm⁶, can eliminate the errors efficiently, it is quite probable that the control command still contains noise sources. The noise and/or other high frequency components in the control command would cause the wheel speed to change in an undesirable manner. The closed-loop system, governed by the feedback control law, is also directly affected by the noise due to imperfect sensor characteristics. The noise components in the sensor signal should be mitigated so that the control command is isolated from the noise effect. This can be done by adding a filter to the sensor output or preventing rapid change in the control command. Dynamic control allocation(DCA), recently studied by Härkegård, is to distribute the control command in the sense of dynamics⁴: the allocation is made over a certain time interval, not a fixed time instant. The dynamic behavior of the control command is taken into account in the course of distributing the control command. Not only the control command requirement, but also variation of the control command over a sampling interval is included in the performance criterion to be optimized. The result is a control command in the form of a finite difference equation over the given time interval.⁴ It results in a filter dynamics by taking the previous control command into account for the synthesis of current control command. Stability of the proposed dynamic control allocation (CA) approach was proved to ensure the control command is bounded at the steady-state. In this study, we extended the results presented in Ref. 4 by adding a two-step dynamic CA term in deriving the control allocation law. Also, the strict equality constraint, between the virtual and actual control inputs, is relaxed in order to construct control command with a smooth profile. The proposed DCA technique is applied to a spacecraft attitude control problem. The sensor noise and/or irregular signals, which are existent in most of spacecraft attitude sensors, can be handled effectively by the proposed approach.

2차원 트러스 구조물에 대한 제어/구조 시스템의 동시최적설계 (Simultaneous Optimal Design of Control-Structure Systems for 2-D Truss Structure)

  • 박중현;김순호
    • 제어로봇시스템학회논문지
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    • 제7권10호
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    • pp.812-818
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    • 2001
  • This paper proposes an optimum design method of structural and control systems, taking a 2-D truss structure as an example. The structure is supposed to be subjected to initial static loads and disturbances. For the structure, a FEM model is formed, and using modal transformation, the equation of motion is transformed into that of modal coordinates in order to reduce the D.O.F. of the FEM model. The structure is controlled by an output feedback $H^$\infty$$ controller to suppress the effect of the disturbances. The design variables of the simultaneous optimal design of control-structure systems are the cross sectional areas of truss members. The structural objective function is the structural weight. The control objective function is the $H^$\infty$$ norm, that is, the performance index of control. The second structural objective function is the energy of the response related to the initial state, which is derived from the time integration of the quadratic form of the state in the closed-loop system. In a numerical example, simulations have been carried out. Through the consideration of structural weight and $H^$\infty$$ norm, an advantage of the simultaneous optimum design of structural and control systems is shown. Moreover, while the optimized performance index of control is almost kept, we can acquire better design of structural strength.

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DEVELOPMENT OF AN OPTIMIZATION TECHNIQUE OF A WARM SHRINK FITTING PROCESS FOR AN AUTOMOTIVE TRANSMISSION PARTS

  • Kim, H.Y.;Kim, C.;Bae, W.B.
    • International Journal of Automotive Technology
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    • 제7권7호
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    • pp.847-852
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    • 2006
  • A fitting process carried out in the automobile transmission assembly line is classified into three classes; heat fitting, press fitting, and their combined fitting. Heat fitting is a method that applies heat in the outer diameter of a gear to a suitable range under the tempering temperature and assembles the gear and the shaft made larger than the inner radius of the gear. Its stress depends on the yield strength of a gear. Press fitting is a method that generally squeezes gear toward that of a shaft at room temperature by a press. Another method heats warmly gear and safely squeezes it toward that of a shaft. A warm shrink fitting process for an automobile transmission part is now gradually increased, but the parts (shaft/gear) assembled by the process produced dimensional change in both outer diameter and profile of the gear so that it may cause noise and vibration between gears. In order to solve these problems, we need an analysis of a warm shrink fitting process in which design parameters such as contact pressure according to fitting interference between outer diameter of a shaft and inner diameter of a gear, fitting temperature, and profile tolerance of gear are involved. In this study, an closed form equation to predict the contact pressure and fitting load was proposed in order to develop an optimization technique of a warm shrink fitting process and verified its reliability through the experimental results measured in the field and FEM, thermal-structural coupled field analysis. Actual loads measured in the field have a good agreement with the results obtained from theoretical and finite element analysis and also the expanded amounts of the outer diameters of the gears have a good agreement with the results.

고수압 조건에서 쉴드터널 세그먼트 라이닝 구조설계에 관한 연구 (A study on the design of shield tunnel lining in high water pressure condition)

  • 이영준;김기림;정건웅;홍의준;김선홍;전덕찬
    • 한국터널지하공간학회 논문집
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    • 제17권3호
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    • pp.227-236
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    • 2015
  • 양호한 암반조건이나 균질한 점토지반 등 불투수성 지반의 경우에도 불연속면에 의하여 수압이 작용될 수 있으므로, 설계시 지반조건에 상관없이 수압조건을 고려하고 있다. 그러나, 세그먼트 라이닝의 형상이 원형임에 따라 수압을 고려하는 경우가 오히려 라이닝에 발생되는 부재력을 감소시킬 수가 있으므로, 고수압 조건에서는 이에 대한 설계개념정립이 중요하다. 따라서, 본 논문에서는 고수압의 불투수성 지반조건에서 하중조건 및 하중조합에 따른 부재력 크기 등을 비교함으로서, 세그먼트 라이닝 설계시 합리적이고 적절한 설계개념에 대하여 서술하였다.

Influence of loose bonding, initial stress and reinforcement on Love-type wave propagating in a functionally graded piezoelectric composite structure

  • Singh, Abhishek K.;Parween, Zeenat;Chaki, Mriganka S.;Mahto, Shruti
    • Smart Structures and Systems
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    • 제22권3호
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    • pp.341-358
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    • 2018
  • This present study investigates Love-type wave propagation in composite structure consists of a loosely bonded functionally graded piezoelectric material (FGPM) stratum lying over a functionally graded initially-stressed fibre-reinforced material (FGIFM) substrate. The closed-form expressions of the dispersion relation have been obtained analytically for both the cases of electrically open and electrically short conditions. Some special cases of the problem have also been studied and the obtained results are found in well-agreement with the classical Love wave equation. The emphatic influence of wave number, bonding parameter associated with bonding of stratum with substrate of the composite structure, piezoelectric coefficient as well as dielectric constant of the piezoelectric stratum, horizontal initial stresses, and functional gradedness of the composite structure on the phase velocity of Love-type wave has been reported and illustrated through numerical computation along with graphical demonstration in both the cases of electrically open and electrically short condition for the reinforced and reinforced-free composite structure. Comparative study has been carried out to analyze the distinct cases associated with functional gradedness of the composite structure and also various cases which reveals the influence of piezoelectricity, reinforcement and horizontal initial stress acting in the composite structure, and bonding of the stratum and substrate of the composite structure in context of the present problem which serves as one of the major highlights of the study.

Effect of porosity on vibrational characteristics of non-homogeneous plates using hyperbolic shear deformation theory

  • Mouaici, Fethi;Benyoucef, Samir;Atmane, Hassen Ait;Tounsi, Abdelouahed
    • Wind and Structures
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    • 제22권4호
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    • pp.429-454
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    • 2016
  • In this paper, a shear deformation plate theory based on neutral surface position is developed for free vibration analysis of functionally graded material (FGM) plates. The material properties of the FGM plates are assumed to vary through the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. During manufacture, defects such as porosities can appear. It is therefore necessary to consider the vibration behavior of FG plates having porosities in this investigation. The proposed theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The equation of motion for FG rectangular plates is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Numerical results are presented and the influences of the volume fraction index and porosity volume fraction on frequencies of FGM plates are clearly discussed.

램버트 W 함수를 사용한 라플라스 신호의 최소 평균제곱오차 양자화 (The Lambert W Function in the Design of Minimum Mean Square-Error Quantizers for a Laplacian Source)

  • 송현정;나상신
    • 한국통신학회논문지
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    • 제27권6A호
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    • pp.524-532
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    • 2002
  • 이 논문은, 램버트 W 함수가 라플라스 신호원에 대한 최적 (최소평균제곱오차) 양자기의 비반복적 설계에 이용될 수 있다는 사실을 보고한다. 구체적으로, 라플라스 신호원에 최적인 양자기의 비반복적 설계법을 고찰하며, 설계에 필수적인 비선형 방정식의 점화식의 풀이가 램버트 W 함수를 사용한 닫힌 식으로 표현된다는 것을 발견하였고, 또 이 논문에서는 이 설계법이 지수함수 형태나 라플라스 확률밀도함수 형태를 갖는 신호원에만 적용된다는 것을 증명하였다. 이 논문의 기여점은, 양자기의 설계가 비반복적이며, 원하는 만큼의 정확도로 설계되기 때문에 설계에 필요한 계산 회수가 감소되고, 양자점과 경계값을 구하는데 있어 높은 정확도를 갖는다는 점이다. 또한, 수치결과를 통하여 최적 양자 왜곡이 팬터-다잇 상수에 단조 증기적으로 수렴하는 과정을 관찰하였으며, 최적 양자기의 최외곽 경계값인 중요변수의 근사식을 유도하였다.

에너지와 대기시간을 고려한 우주비행체 랑데부 (Spacecraft Rendezvous Considering Orbital Energy and Wait Time)

  • 오승렬;이현재
    • 한국항공우주학회지
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    • 제45권9호
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    • pp.775-783
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    • 2017
  • 본 논문에서는 서로 다른 궤도상에 있는 두 우주비행체의 랑데부를 위한 최소 에너지 순간추력을 구하는 문제를 다룬다. 두 우주비행체의 궤도는 공면 궤도나 원 궤도 같이 특정 지어진 궤도가 아닌 일반적인 궤도이다. 이러한 최적화 문제를 다루기 위해 범용변수를 사용한 케플러 방정식과 두 우주비행체의 최종 위치 및 속도를 구속조건으로 사용하며, 전이 궤도의 정보를 얻기 위해 라그랑지 계수를 이용한다. 이 방법은 최소 에너지를 고려한 예시와 대기시간까지 고려한 예시를 통해 보여 지며, 최소 에너지 궤도로 알려진 호만 궤도와 비교함으로써 검증된다. 비록 닫힌 형태의 해를 얻을 수는 없었지만, 수치해석적 방식을 적용함으로써 다양한 궤도 전이 문제의 해를 구할 수 있음을 보여준다.