Barycentric Coordinate

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Zhiyun Lin - One of the best experts on this subject based on the ideXlab platform.

  • a Barycentric Coordinate based approach to three dimensional distributed localization for wireless sensor networks
    International Conference on Control and Automation, 2017
    Co-Authors: Tingrui Han, Zhiyun Lin, Ronghao Zheng, Zhimin Han, Haitao Zhang
    Abstract:

    This paper introduces a new range-based distributed localization algorithm for wireless sensor networks in the three-dimensional space. To overcome the difficulty in computing the Barycentric Coordinates of a node with respect to its neighbors in 3D, a new scheme is developed for this purpose by using the fact that a congruent framework of the subnetwork consisting of the node and its neighbors has the same Barycentric Coordinates. A multidimensional scaling (MDS) method is used to calculate the Coordinates of the congruent framework, which can provide a solution for each subnetwork with not only exact range measurements but also noisy range measurements. Thus, a linear equation related to a signed Laplacian is obtained to describe the geometric constraints of the whole network. We then show a globally convergent and linear iterative algorithm called MDS-DILOC for each node to locate itself in the three-dimensional space by solving the linear equation. Simulation is carried out to demonstrate the validity of MDS-DILOC.

  • A Barycentric Coordinate-Based Approach to Formation Control Under Directed and Switching Sensing Graphs
    IEEE transactions on cybernetics, 2017
    Co-Authors: Tingrui Han, Zhiyun Lin, Ronghao Zheng
    Abstract:

    This paper investigates two formation control problems for a leader–follower network in 3-D. One is called the formation marching control problem, the objective of which is to steer the agents to maintain a target formation shape while moving with the synchronized velocity. The other one is called the formation rotating control problem, whose goal is to drive the agents to rotate around a common axis with a target formation. For the above two problems, we consider directed and switching sensing topologies while the communication is assumed to be bidirectional and switching. We develop approaches utilizing Barycentric Coordinates toward these two problems. Local control laws and graphical conditions are acquired to ensure global convergence in both scenarios.

  • ICCA - A Barycentric Coordinate based approach to three-dimensional distributed localization for wireless sensor networks
    2017 13th IEEE International Conference on Control & Automation (ICCA), 2017
    Co-Authors: Tingrui Han, Zhiyun Lin, Ronghao Zheng, Zhimin Han, Haitao Zhang
    Abstract:

    This paper introduces a new range-based distributed localization algorithm for wireless sensor networks in the three-dimensional space. To overcome the difficulty in computing the Barycentric Coordinates of a node with respect to its neighbors in 3D, a new scheme is developed for this purpose by using the fact that a congruent framework of the subnetwork consisting of the node and its neighbors has the same Barycentric Coordinates. A multidimensional scaling (MDS) method is used to calculate the Coordinates of the congruent framework, which can provide a solution for each subnetwork with not only exact range measurements but also noisy range measurements. Thus, a linear equation related to a signed Laplacian is obtained to describe the geometric constraints of the whole network. We then show a globally convergent and linear iterative algorithm called MDS-DILOC for each node to locate itself in the three-dimensional space by solving the linear equation. Simulation is carried out to demonstrate the validity of MDS-DILOC.

  • Distributed localization with mixed measurements under switching topologies
    Automatica, 2017
    Co-Authors: Zhiyun Lin, Tingrui Han, Ronghao Zheng
    Abstract:

    Abstract This paper investigates the distributed localization problem of sensor networks with mixed measurements. Each node holds a local Coordinate system without a common orientation and is capable of measuring only one type of information (either distance, bearing, or relative position) to near-by nodes. Thus, three types of measurements are mixed in the sensor networks. Moreover, the communication topologies in the sensor networks may be time-varying due to unreliable communications. This paper develops a fully distributed algorithm called BCDL (Barycentric Coordinate based Distributed Localization) where each node starts from a random initial guess about its true Coordinate and converges to the true Coordinate via only local node interactions. The key idea in BCDL is to establish a unified linear equation constraints for the sensor Coordinates by using the Barycentric Coordinates of each node with respect to its neighbors though the sensor nodes may have different types of measurements. Then a distributed iterative algorithm is proposed to solve the linear equations under time-varying communication networks. A necessary and sufficient graphical condition is obtained to ensure global convergence of the distributed algorithm.

  • A single-mobile-anchor based distributed localization scheme for sensor networks
    2016 35th Chinese Control Conference (CCC), 2016
    Co-Authors: Peng Cheng, Ronghao Zheng, Tingrui Han, Xi Zhang, Zhiyun Lin
    Abstract:

    This paper investigates the distributed localization problem for a sensor network in the plane. It is assumed that one mobile robot wandering in the area acts as a mobile anchor. A distributed scheme is devised such that each node can localize itself using only its locally available distance measurements about its (possibly changing) neighbors. The key idea is based on a new way of calculating the Barycentric Coordinate of each node about its neighbors, which has the advantage that it is capable of handling distance measurement errors. A necessary and sufficient condition is obtained for the global convergence of the proposed distributed algorithm. Both simulation and experiment using ZigBee devices are carried out to validate the proposed distributed localization scheme.

Ronghao Zheng - One of the best experts on this subject based on the ideXlab platform.

  • a Barycentric Coordinate based approach to three dimensional distributed localization for wireless sensor networks
    International Conference on Control and Automation, 2017
    Co-Authors: Tingrui Han, Zhiyun Lin, Ronghao Zheng, Zhimin Han, Haitao Zhang
    Abstract:

    This paper introduces a new range-based distributed localization algorithm for wireless sensor networks in the three-dimensional space. To overcome the difficulty in computing the Barycentric Coordinates of a node with respect to its neighbors in 3D, a new scheme is developed for this purpose by using the fact that a congruent framework of the subnetwork consisting of the node and its neighbors has the same Barycentric Coordinates. A multidimensional scaling (MDS) method is used to calculate the Coordinates of the congruent framework, which can provide a solution for each subnetwork with not only exact range measurements but also noisy range measurements. Thus, a linear equation related to a signed Laplacian is obtained to describe the geometric constraints of the whole network. We then show a globally convergent and linear iterative algorithm called MDS-DILOC for each node to locate itself in the three-dimensional space by solving the linear equation. Simulation is carried out to demonstrate the validity of MDS-DILOC.

  • A Barycentric Coordinate-Based Approach to Formation Control Under Directed and Switching Sensing Graphs
    IEEE transactions on cybernetics, 2017
    Co-Authors: Tingrui Han, Zhiyun Lin, Ronghao Zheng
    Abstract:

    This paper investigates two formation control problems for a leader–follower network in 3-D. One is called the formation marching control problem, the objective of which is to steer the agents to maintain a target formation shape while moving with the synchronized velocity. The other one is called the formation rotating control problem, whose goal is to drive the agents to rotate around a common axis with a target formation. For the above two problems, we consider directed and switching sensing topologies while the communication is assumed to be bidirectional and switching. We develop approaches utilizing Barycentric Coordinates toward these two problems. Local control laws and graphical conditions are acquired to ensure global convergence in both scenarios.

  • ICCA - A Barycentric Coordinate based approach to three-dimensional distributed localization for wireless sensor networks
    2017 13th IEEE International Conference on Control & Automation (ICCA), 2017
    Co-Authors: Tingrui Han, Zhiyun Lin, Ronghao Zheng, Zhimin Han, Haitao Zhang
    Abstract:

    This paper introduces a new range-based distributed localization algorithm for wireless sensor networks in the three-dimensional space. To overcome the difficulty in computing the Barycentric Coordinates of a node with respect to its neighbors in 3D, a new scheme is developed for this purpose by using the fact that a congruent framework of the subnetwork consisting of the node and its neighbors has the same Barycentric Coordinates. A multidimensional scaling (MDS) method is used to calculate the Coordinates of the congruent framework, which can provide a solution for each subnetwork with not only exact range measurements but also noisy range measurements. Thus, a linear equation related to a signed Laplacian is obtained to describe the geometric constraints of the whole network. We then show a globally convergent and linear iterative algorithm called MDS-DILOC for each node to locate itself in the three-dimensional space by solving the linear equation. Simulation is carried out to demonstrate the validity of MDS-DILOC.

  • Distributed localization with mixed measurements under switching topologies
    Automatica, 2017
    Co-Authors: Zhiyun Lin, Tingrui Han, Ronghao Zheng
    Abstract:

    Abstract This paper investigates the distributed localization problem of sensor networks with mixed measurements. Each node holds a local Coordinate system without a common orientation and is capable of measuring only one type of information (either distance, bearing, or relative position) to near-by nodes. Thus, three types of measurements are mixed in the sensor networks. Moreover, the communication topologies in the sensor networks may be time-varying due to unreliable communications. This paper develops a fully distributed algorithm called BCDL (Barycentric Coordinate based Distributed Localization) where each node starts from a random initial guess about its true Coordinate and converges to the true Coordinate via only local node interactions. The key idea in BCDL is to establish a unified linear equation constraints for the sensor Coordinates by using the Barycentric Coordinates of each node with respect to its neighbors though the sensor nodes may have different types of measurements. Then a distributed iterative algorithm is proposed to solve the linear equations under time-varying communication networks. A necessary and sufficient graphical condition is obtained to ensure global convergence of the distributed algorithm.

  • A single-mobile-anchor based distributed localization scheme for sensor networks
    2016 35th Chinese Control Conference (CCC), 2016
    Co-Authors: Peng Cheng, Ronghao Zheng, Tingrui Han, Xi Zhang, Zhiyun Lin
    Abstract:

    This paper investigates the distributed localization problem for a sensor network in the plane. It is assumed that one mobile robot wandering in the area acts as a mobile anchor. A distributed scheme is devised such that each node can localize itself using only its locally available distance measurements about its (possibly changing) neighbors. The key idea is based on a new way of calculating the Barycentric Coordinate of each node about its neighbors, which has the advantage that it is capable of handling distance measurement errors. A necessary and sufficient condition is obtained for the global convergence of the proposed distributed algorithm. Both simulation and experiment using ZigBee devices are carried out to validate the proposed distributed localization scheme.

Tingrui Han - One of the best experts on this subject based on the ideXlab platform.

  • a Barycentric Coordinate based approach to three dimensional distributed localization for wireless sensor networks
    International Conference on Control and Automation, 2017
    Co-Authors: Tingrui Han, Zhiyun Lin, Ronghao Zheng, Zhimin Han, Haitao Zhang
    Abstract:

    This paper introduces a new range-based distributed localization algorithm for wireless sensor networks in the three-dimensional space. To overcome the difficulty in computing the Barycentric Coordinates of a node with respect to its neighbors in 3D, a new scheme is developed for this purpose by using the fact that a congruent framework of the subnetwork consisting of the node and its neighbors has the same Barycentric Coordinates. A multidimensional scaling (MDS) method is used to calculate the Coordinates of the congruent framework, which can provide a solution for each subnetwork with not only exact range measurements but also noisy range measurements. Thus, a linear equation related to a signed Laplacian is obtained to describe the geometric constraints of the whole network. We then show a globally convergent and linear iterative algorithm called MDS-DILOC for each node to locate itself in the three-dimensional space by solving the linear equation. Simulation is carried out to demonstrate the validity of MDS-DILOC.

  • A Barycentric Coordinate-Based Approach to Formation Control Under Directed and Switching Sensing Graphs
    IEEE transactions on cybernetics, 2017
    Co-Authors: Tingrui Han, Zhiyun Lin, Ronghao Zheng
    Abstract:

    This paper investigates two formation control problems for a leader–follower network in 3-D. One is called the formation marching control problem, the objective of which is to steer the agents to maintain a target formation shape while moving with the synchronized velocity. The other one is called the formation rotating control problem, whose goal is to drive the agents to rotate around a common axis with a target formation. For the above two problems, we consider directed and switching sensing topologies while the communication is assumed to be bidirectional and switching. We develop approaches utilizing Barycentric Coordinates toward these two problems. Local control laws and graphical conditions are acquired to ensure global convergence in both scenarios.

  • ICCA - A Barycentric Coordinate based approach to three-dimensional distributed localization for wireless sensor networks
    2017 13th IEEE International Conference on Control & Automation (ICCA), 2017
    Co-Authors: Tingrui Han, Zhiyun Lin, Ronghao Zheng, Zhimin Han, Haitao Zhang
    Abstract:

    This paper introduces a new range-based distributed localization algorithm for wireless sensor networks in the three-dimensional space. To overcome the difficulty in computing the Barycentric Coordinates of a node with respect to its neighbors in 3D, a new scheme is developed for this purpose by using the fact that a congruent framework of the subnetwork consisting of the node and its neighbors has the same Barycentric Coordinates. A multidimensional scaling (MDS) method is used to calculate the Coordinates of the congruent framework, which can provide a solution for each subnetwork with not only exact range measurements but also noisy range measurements. Thus, a linear equation related to a signed Laplacian is obtained to describe the geometric constraints of the whole network. We then show a globally convergent and linear iterative algorithm called MDS-DILOC for each node to locate itself in the three-dimensional space by solving the linear equation. Simulation is carried out to demonstrate the validity of MDS-DILOC.

  • Distributed localization with mixed measurements under switching topologies
    Automatica, 2017
    Co-Authors: Zhiyun Lin, Tingrui Han, Ronghao Zheng
    Abstract:

    Abstract This paper investigates the distributed localization problem of sensor networks with mixed measurements. Each node holds a local Coordinate system without a common orientation and is capable of measuring only one type of information (either distance, bearing, or relative position) to near-by nodes. Thus, three types of measurements are mixed in the sensor networks. Moreover, the communication topologies in the sensor networks may be time-varying due to unreliable communications. This paper develops a fully distributed algorithm called BCDL (Barycentric Coordinate based Distributed Localization) where each node starts from a random initial guess about its true Coordinate and converges to the true Coordinate via only local node interactions. The key idea in BCDL is to establish a unified linear equation constraints for the sensor Coordinates by using the Barycentric Coordinates of each node with respect to its neighbors though the sensor nodes may have different types of measurements. Then a distributed iterative algorithm is proposed to solve the linear equations under time-varying communication networks. A necessary and sufficient graphical condition is obtained to ensure global convergence of the distributed algorithm.

  • A single-mobile-anchor based distributed localization scheme for sensor networks
    2016 35th Chinese Control Conference (CCC), 2016
    Co-Authors: Peng Cheng, Ronghao Zheng, Tingrui Han, Xi Zhang, Zhiyun Lin
    Abstract:

    This paper investigates the distributed localization problem for a sensor network in the plane. It is assumed that one mobile robot wandering in the area acts as a mobile anchor. A distributed scheme is devised such that each node can localize itself using only its locally available distance measurements about its (possibly changing) neighbors. The key idea is based on a new way of calculating the Barycentric Coordinate of each node about its neighbors, which has the advantage that it is capable of handling distance measurement errors. A necessary and sufficient condition is obtained for the global convergence of the proposed distributed algorithm. Both simulation and experiment using ZigBee devices are carried out to validate the proposed distributed localization scheme.

Dmitry Sokolov - One of the best experts on this subject based on the ideXlab platform.

  • Robust Polylines Tracing for N-Symmetry Direction Field on Triangulated Surfaces
    ACM Transactions on Graphics, 2014
    Co-Authors: Nicolas Ray, Dmitry Sokolov
    Abstract:

    We are proposing an algorithm for tracing polylines that are oriented by a direction field defined on a triangle mesh. The challenge is to ensure that two such polylines cannot cross or merge. This property is fundamental for mesh segmentation and is impossible to enforce with existing algorithms. The core of our contribution is to determine how polylines cross each triangle. Our solution is inspired by EdgeMaps where each triangle boundary is decomposed into inflow and outflow intervals such that each inflow interval is mapped onto an outflow interval. To cross a triangle, we find the inflow interval that contains the entry point, and link it to the corresponding outflow interval, with the same Barycentric Coordinate. To ensure that polylines cannot merge or cross, we introduce a new direction field representation, we resolve the inflow/outflow interval pairing with a guaranteed combinatorial algorithm, and propagate the Barycentric positions with arbitrary precision number representation. Using these techniques, two streamlines crossing the same triangle cannot merge or cross, but only locally overlap when all streamline extremities are located on the same edge. Cross-free and merge-free polylines can be traced on the mesh by iteratively crossing triangles. Vector field singularities and polyline/vertex crossing are characterized and consistently handled.

Yuhua Cheng - One of the best experts on this subject based on the ideXlab platform.

  • Distributed Localization in Wireless Sensor Networks Under Denial-of-Service Attacks
    IEEE Control Systems Letters, 1
    Co-Authors: Lei Shi, Qingchen Liu, Jinliang Shao, Yuhua Cheng
    Abstract:

    In this letter, we study the problem of localizing the sensors’ positions in presence of denial-of-service (DoS) attacks. We consider a general attack model, in which the attacker action is only constrained through the frequency and duration of DoS attacks. We propose a distributed iterative localization algorithm with an abandonment strategy based on the Barycentric Coordinate of a sensor with respect to its neighbors, which is computed through relative distance measurements. In particular, if a sensor’s communication links for receiving its neighbors’ information lose packets due to DoS attacks, then the sensor abandons the location estimation. When the attacker launches DoS attacks, the AS-DILOC algorithm is proved theoretically to be able to accurately locate the sensors regardless of the attack strategy at each time. The effectiveness of the proposed algorithm is demonstrated through simulation examples.