• Title/Summary/Keyword: curvature of space curve

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MYLLER CONFIGURATIONS IN FINSLER SPACES. APPLICATIONS TO THE STUDY OF SUBSPACES AND OF TORSE FORMING VECTOR FIELDS

  • Constantinescu, Oana
    • Journal of the Korean Mathematical Society
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    • v.45 no.5
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    • pp.1443-1482
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    • 2008
  • In this paper we define a Myller configuration in a Finsler space and use some special configurations to obtain results about Finsler subspaces. Let $F^{n}$ = (M,F) be a Finsler space, with M a real, differentiable manifold of dimension n. Using the pull back bundle $({\pi}^{*}TM,\tilde{\pi},\widetilde{TM})$ of the tangent bundle $(TM,{\pi},M)$ by the mapping $\tilde{\pi}={\pi}/TM$ and the Cartan Finsler connection of a Finsler space, we obtain an orthonormal frame of sections of ${\pi}^{*}TM$ along a regular curve in $\widetilde{TM}$ and a system of invariants, geometrically associated to the Myller configuration. The fundamental equations are written in a very simple form and we prove a fundamental theorem. Important lines in a Finsler subspace are defined like special lines in a Myller configuration, geometrically associated to the subspace: auto parallels, lines of curvature, asymptotes. Torse forming vector fields with respect to the Cartan Finsler connection are characterized by means of the invariants of the Frenet frame of a versor field along a curve, and the new notion of torse forming vector fields in the sense of Myller is introduced. The particular cases of concurrence and parallelism in the sense of Myller are completely studied, for vector fields from the distribution $T^m$ of the Myller configuration and also from the normal distribution $T^p$.

SLANT HELICES IN MINKOWSKI SPACE E13

  • Ali, Ahmad T.;Lopez, Rafael
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.159-167
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    • 2011
  • We consider a curve $\alpha$= $\alpha$(s) in Minkowski 3-space $E_1^3$ and denote by {T, N, B} the Frenet frame of $\alpha$. We say that $\alpha$ is a slant helix if there exists a fixed direction U of $E_1^3$ such that the function is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of $\alpha$. Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in $E_1^3$.

Stereovision by Active Surface Model

  • Yokomichi, M.;Sugiyama, H.;Kono, M.
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.1990-1993
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    • 2005
  • Stereovision is known to be one of the most important tools for robot vision systems. Previously, 2D active contour model has been applied to stereovision by defining the contour on the 3D space instead of image plane. However, the proposed model is still that of curve so that some complex shapes such as surfaces with high curvature can not be properly estimated because of occlusion phenomena. In this paper, the authors extend the curve model to the surface model. The surface is approximated by polygons and new energy function and its optimization method for surface estimation is proposed. Its effectiveness is examined by experiments with real stereo images.

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Fast Axis Estimation from 3D Axially-Symmetric Object's Fragment (3차원 회전축 대칭 물체 조각의 축 추정 방법)

  • Li, Liang;Han, Dong-Jin;Hahn, Hern-Soo
    • Journal of the Korean Institute of Intelligent Systems
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    • v.20 no.6
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    • pp.748-754
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    • 2010
  • To reduce the computational cost required for assembling vessel fragments using surface geometry, this paper proposes a fast axis estimation method. Using circular constraint of pottery and local planar patch assumption, it finds the axis of the symmetry. First, the circular constraint on each cylinder is used. A circular symmetric pot can be thought of unions of many cylinders with different radii. It selects one arbitrary point on the pot fragment surface and searches a path where a circumference exists on that point. The variance of curvature will be calculated along the path and the path with the minimum variance will be selected. The symmetric axis will pass through the center of that circle. Second, the planar patch assumption and profile curve is used. The surface of fragment is divided into small patches and each patch is assumed as plane. The surface normal of each patch will intersects the axis in 3D space since each planar patch faces the center of the pot. A histogram method and minimization of the profile curve error are utilized to find the probability distribution of the axis location. Experimental results demonstrate the improvement in speed and robustness of the algorithms.

Maximum Velocity Trajectory Planning for Mobile Robots Considering Wheel Velocity Limit (이동로봇의 바퀴 속도 제한을 고려한 최대 속도궤적 생성 방법)

  • Yang, Gil Jin;Choi, Byoung Wook
    • Journal of Institute of Control, Robotics and Systems
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    • v.21 no.5
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    • pp.471-476
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    • 2015
  • This paper presents a maximum velocity trajectory planning algorithm for differential mobile robots with wheel velocity constraint to cope with physical limits in the joint space for two-wheeled mobile robots (TMR). In previous research, the convolution operator was able to generate a central velocity that deals with the physical constraints of a mobile robot while considering the heading angles along a smooth curve in terms of time-dependent parameter. However, the velocity could not track the predefined path. An algorithm is proposed to compensate an error that occurs between the actual and driven distance by the velocity of the center of a TMR within a sampling time. The velocity commands in Cartesian space are also converted to actuator commands to drive two wheels. In the case that the actuator commands exceed the maximum velocity the trajectory is redeveloped with the compensated center velocity. The new center velocity is obtained according to the curvature of the path to provide a maximum allowable velocity meaning a time-optimal trajectory. The effectiveness of the algorithm is shown through numerical examples.

Dubins Path Generation and Tracking of UAVs With Angular Velocity Constraints (각속도 제한을 고려한 무인기의 Dubins 경로 생성 및 추적)

  • Yang, You-young;Jang, Seok-ho;Leeghim, Henzeh
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.49 no.2
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    • pp.121-128
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    • 2021
  • In this paper, we propose a path generation and tracking algorithm of an unmanned air vehicle in a two-dimensional plane given the initial and final points. The path generation algorithm using the Dubins curve proposed in this work has the advantage that it can be applied in real time to an unmanned air vehicle. The path tracking algorithm is an algorithm similar to the line-of-sight induction algorithm. In order to efficiently control the direction angle, a gain related to the look ahead distance concept is introduced. Most of UAVs have the limited maximum curvature due to the structural constraints. A numerical simulation is conducted to follow the path generated by the sliding mode controller considering the angular velocity limit. The path generation and tracking performance is verified by comparing the suggested controller with conventional control techniques.