Vector Field

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Zhuowen Tu - One of the best experts on this subject based on the ideXlab platform.

  • regularized Vector Field learning with sparse approximation for mismatch removal
    Pattern Recognition, 2013
    Co-Authors: Ji Zhao, Jinwen Tian, Zhuowen Tu
    Abstract:

    In Vector Field learning, regularized kernel methods such as regularized least-squares require the number of basis functions to be equivalent to the training sample size, N. The learning process thus has O(N^3) and O(N^2) in the time and space complexity, respectively. This poses significant burden on the Vector learning problem for large datasets. In this paper, we propose a sparse approximation to a robust Vector Field learning method, sparse Vector Field consensus (SparseVFC), and derive a statistical learning bound on the speed of the convergence. We apply SparseVFC to the mismatch removal problem. The quantitative results on benchmark datasets demonstrate the significant speed advantage of SparseVFC over the original VFC algorithm (two orders of magnitude faster) without much performance degradation; we also demonstrate the large improvement by SparseVFC over traditional methods like RANSAC. Moreover, the proposed method is general and it can be applied to other applications in Vector Field learning.

Yueqian Liang - One of the best experts on this subject based on the ideXlab platform.

  • combined Vector Field approach for planar curved path following with fixed wing uavs
    Advances in Computing and Communications, 2015
    Co-Authors: Yueqian Liang, Yingmin Jia, Zhuo Wang, Fumitoshi Matsuno
    Abstract:

    In this paper the problem of planar curved path following using fixed-wing unmanned aerial vehicles (UAVs) is studied. UAV input constraints and constant wind disturbance are considered. A combined Vector Field is proposed by trading off a conservative Vector Field and a solenoidal Vector Field. Accordingly a saturated course rate controller is designed, and its stability is discussed through the Lyapunov stability theory. Simulation examples show us the effectiveness of the approach.

  • Vector Field guidance for three dimensional curved path following with fixed wing uavs
    Advances in Computing and Communications, 2015
    Co-Authors: Yueqian Liang, Yingmin Jia, Jun Zhang
    Abstract:

    This paper investigates the three-dimensional (3D) curved path following problem using fixed-wing unmanned aerial vehicles (UAVs) in the presence of constant wind disturbance. Vector Field based approaches are used as the solution. Two Vector Fields are first developed, one is the tangent Vector Field based on path tangent Vector and coordinate transformation, and the other is the combined Vector Field based on the combination of a conservative Vector Field and a solenoidal Vector Field. A unified jointly saturated course rate and saturated climb rate controller is designed based on the proposed Vector Fields. Simulations are conducted to demonstrate the effectiveness of the proposed approach.

  • ACC - Combined Vector Field approach for planar curved path following with fixed-wing UAVs
    2015 American Control Conference (ACC), 2015
    Co-Authors: Yueqian Liang, Yingmin Jia, Zhuo Wang, Fumitoshi Matsuno
    Abstract:

    In this paper the problem of planar curved path following using fixed-wing unmanned aerial vehicles (UAVs) is studied. UAV input constraints and constant wind disturbance are considered. A combined Vector Field is proposed by trading off a conservative Vector Field and a solenoidal Vector Field. Accordingly a saturated course rate controller is designed, and its stability is discussed through the Lyapunov stability theory. Simulation examples show us the effectiveness of the approach.

  • ACC - Vector Field guidance for three-dimensional curved path following with fixed-wing UAVs
    2015 American Control Conference (ACC), 2015
    Co-Authors: Yueqian Liang, Yingmin Jia, Jun Zhang
    Abstract:

    This paper investigates the three-dimensional (3D) curved path following problem using fixed-wing unmanned aerial vehicles (UAVs) in the presence of constant wind disturbance. Vector Field based approaches are used as the solution. Two Vector Fields are first developed, one is the tangent Vector Field based on path tangent Vector and coordinate transformation, and the other is the combined Vector Field based on the combination of a conservative Vector Field and a solenoidal Vector Field. A unified jointly saturated course rate and saturated climb rate controller is designed based on the proposed Vector Fields. Simulations are conducted to demonstrate the effectiveness of the proposed approach.

Jun Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Vector Field guidance for three dimensional curved path following with fixed wing uavs
    Advances in Computing and Communications, 2015
    Co-Authors: Yueqian Liang, Yingmin Jia, Jun Zhang
    Abstract:

    This paper investigates the three-dimensional (3D) curved path following problem using fixed-wing unmanned aerial vehicles (UAVs) in the presence of constant wind disturbance. Vector Field based approaches are used as the solution. Two Vector Fields are first developed, one is the tangent Vector Field based on path tangent Vector and coordinate transformation, and the other is the combined Vector Field based on the combination of a conservative Vector Field and a solenoidal Vector Field. A unified jointly saturated course rate and saturated climb rate controller is designed based on the proposed Vector Fields. Simulations are conducted to demonstrate the effectiveness of the proposed approach.

  • ACC - Vector Field guidance for three-dimensional curved path following with fixed-wing UAVs
    2015 American Control Conference (ACC), 2015
    Co-Authors: Yueqian Liang, Yingmin Jia, Jun Zhang
    Abstract:

    This paper investigates the three-dimensional (3D) curved path following problem using fixed-wing unmanned aerial vehicles (UAVs) in the presence of constant wind disturbance. Vector Field based approaches are used as the solution. Two Vector Fields are first developed, one is the tangent Vector Field based on path tangent Vector and coordinate transformation, and the other is the combined Vector Field based on the combination of a conservative Vector Field and a solenoidal Vector Field. A unified jointly saturated course rate and saturated climb rate controller is designed based on the proposed Vector Fields. Simulations are conducted to demonstrate the effectiveness of the proposed approach.

Ming Cao - One of the best experts on this subject based on the ideXlab platform.

  • singularity free guiding Vector Field for robot navigation
    IEEE Transactions on Robotics, 2021
    Co-Authors: Weijia Yao, Hector Garcia De Marina, Bohuan Lin, Ming Cao
    Abstract:

    In robot navigation tasks, such as unmanned aerial vehicle (UAV) highway traffic monitoring, it is important for a mobile robot to follow a specified desired path. However, most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-intersected desired paths due to the existence of singular points where navigation algorithms return unreliable or even no solutions. One typical example arises in Vector-Field guided path-following (VF-PF) navigation algorithms. These algorithms are based on a Vector Field, and the singular points are exactly where the Vector Field diminishes. Conventional VF-PF algorithms generate a Vector Field of the same dimensions as those of the space where the desired path lives. In this article, we show that it is mathematically impossible for conventional VF-PF algorithms to achieve global convergence to desired paths that are self-intersected or even just simple closed (precisely, homeomorphic to the unit circle). Motivated by this new impossibility result, we propose a novel method to transform self-intersected or simple closed desired paths to nonself-intersected and unbounded (precisely, homeomorphic to the real line) counterparts in a higher dimensional space. Corresponding to this new desired path, we construct a singularity-free guiding Vector Field on a higher dimensional space. The integral curves of this new guiding Vector Field is thus exploited to enable global convergence to the higher dimensional desired path, and therefore the projection of the integral curves on a lower dimensional subspace converge to the physical (lower dimensional) desired path. Rigorous theoretical analysis is carried out for the theoretical results using dynamical systems theory. In addition, we show both by theoretical analysis and numerical simulations that our proposed method is an extension combining conventional VF-PF algorithms and trajectory tracking algorithms. Finally, to show the practical value of our proposed approach for complex engineering systems, we conduct outdoor experiments with a fixed-wing airplane in windy environment to follow both 2-D and 3-D desired paths.

  • singularity free guiding Vector Field for robot navigation
    arXiv: Robotics, 2020
    Co-Authors: Weijia Yao, Hector Garcia De Marina, Bohuan Lin, Ming Cao
    Abstract:

    Most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-intersected desired paths due to the existence of singular points where navigation algorithms return unreliable or even no solutions. One typical example arises in Vector-Field guided path-following (VF-PF) navigation algorithms. These algorithms are based on a Vector Field, and the singular points are exactly where the Vector Field diminishes. In this paper, we show that it is mathematically impossible for conventional VF-PF algorithms to achieve global convergence to desired paths that are self-intersected or even just simple closed (precisely, homeomorphic to the unit circle). Motivated by this new impossibility result, we propose a novel method to transform self-intersected or simple closed desired paths to non-self-intersected and unbounded (precisely, homeomorphic to the real line) counterparts in a higher-dimensional space. Corresponding to this new desired path, we construct a singularity-free guiding Vector Field on a higher-dimensional space. The integral curves of this new guiding Vector Field is thus exploited to enable global convergence to the higher-dimensional desired path, and therefore the projection of the integral curves on a lower-dimensional subspace converge to the physical (lower-dimensional) desired path. Rigorous theoretical analysis is carried out for the theoretical results using dynamical systems theory. In addition, we show both by theoretical analysis and numerical simulations that our proposed method is an extension combining conventional VF-PF algorithms and trajectory tracking algorithms. Finally, to show the practical value of our proposed approach for complex engineering systems, we conduct outdoor experiments with a fixed-wing airplane in windy environment to follow both 2D and 3D desired paths.

Yingmin Jia - One of the best experts on this subject based on the ideXlab platform.

  • combined Vector Field approach for planar curved path following with fixed wing uavs
    Advances in Computing and Communications, 2015
    Co-Authors: Yueqian Liang, Yingmin Jia, Zhuo Wang, Fumitoshi Matsuno
    Abstract:

    In this paper the problem of planar curved path following using fixed-wing unmanned aerial vehicles (UAVs) is studied. UAV input constraints and constant wind disturbance are considered. A combined Vector Field is proposed by trading off a conservative Vector Field and a solenoidal Vector Field. Accordingly a saturated course rate controller is designed, and its stability is discussed through the Lyapunov stability theory. Simulation examples show us the effectiveness of the approach.

  • Vector Field guidance for three dimensional curved path following with fixed wing uavs
    Advances in Computing and Communications, 2015
    Co-Authors: Yueqian Liang, Yingmin Jia, Jun Zhang
    Abstract:

    This paper investigates the three-dimensional (3D) curved path following problem using fixed-wing unmanned aerial vehicles (UAVs) in the presence of constant wind disturbance. Vector Field based approaches are used as the solution. Two Vector Fields are first developed, one is the tangent Vector Field based on path tangent Vector and coordinate transformation, and the other is the combined Vector Field based on the combination of a conservative Vector Field and a solenoidal Vector Field. A unified jointly saturated course rate and saturated climb rate controller is designed based on the proposed Vector Fields. Simulations are conducted to demonstrate the effectiveness of the proposed approach.

  • ACC - Combined Vector Field approach for planar curved path following with fixed-wing UAVs
    2015 American Control Conference (ACC), 2015
    Co-Authors: Yueqian Liang, Yingmin Jia, Zhuo Wang, Fumitoshi Matsuno
    Abstract:

    In this paper the problem of planar curved path following using fixed-wing unmanned aerial vehicles (UAVs) is studied. UAV input constraints and constant wind disturbance are considered. A combined Vector Field is proposed by trading off a conservative Vector Field and a solenoidal Vector Field. Accordingly a saturated course rate controller is designed, and its stability is discussed through the Lyapunov stability theory. Simulation examples show us the effectiveness of the approach.

  • ACC - Vector Field guidance for three-dimensional curved path following with fixed-wing UAVs
    2015 American Control Conference (ACC), 2015
    Co-Authors: Yueqian Liang, Yingmin Jia, Jun Zhang
    Abstract:

    This paper investigates the three-dimensional (3D) curved path following problem using fixed-wing unmanned aerial vehicles (UAVs) in the presence of constant wind disturbance. Vector Field based approaches are used as the solution. Two Vector Fields are first developed, one is the tangent Vector Field based on path tangent Vector and coordinate transformation, and the other is the combined Vector Field based on the combination of a conservative Vector Field and a solenoidal Vector Field. A unified jointly saturated course rate and saturated climb rate controller is designed based on the proposed Vector Fields. Simulations are conducted to demonstrate the effectiveness of the proposed approach.