Guidance using bearing-only measurements with three beacons in the plane

Trinh, Minh Hoang; Ko, Gwihan; Pham, Viet Hoang; Oh, Kwang‐Kyo; Ahn, Hyo‐Sung

doi:10.1016/j.conengprac.2016.03.013

Cited by 21 publications

(9 citation statements)

References 27 publications

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“…The set  3 contains all equilibria of Equation 11 and can be partitioned into  3 that contains all desired formations and  3 containing the undesired ones. Figure 4 depicts an example of 2 different triangular formations in  3 .…”

Section: The Three-agent Formationsmentioning

confidence: 99%

“…In bearing‐based formation control problems, a group of autonomous agents is required to achieve a target formation shape defined by some bearing variables. These variables are known as the subtended bearing angles or the relative bearing vectors . In previous works,() formation stabilization control laws, using only the bearing angles, were proposed for 3‐ and 4‐agent systems.…”

Section: Introductionmentioning

confidence: 99%

“…These variables are known as the subtended bearing angles or the relative bearing vectors. 11 In previous works, 7,8,12 formation stabilization control laws, using only the bearing angles, were proposed for 3-and 4-agent systems. In the work of Zhao et al, 13 an n-agent formation with an undirected cycle graph was investigated by controlling the subtended bearings.…”

Section: Introductionmentioning

confidence: 99%

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Formations on directed cycles with bearing‐only measurements

Trinh

Mukherjee

Zelazo

et al. 2017

Intl J Robust & Nonlinear

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Summary This paper studies a bearing‐only–based formation control problem for a group of single‐integrator agents with directed cycle sensing topology. In a 2‐dimensional space, a necessary and sufficient condition for the set of desired bearing vectors to be feasible is derived. Then, we propose a bearing‐only control law for every agent and prove that the formation asymptotically converges to a formation specified by a set of feasible desired bearing vectors. Analysis of the equilibrium formations in the plane for a 3‐agent system and subsequent extension to an n‐agent system is provided. We further extend the analysis on directed triangular formation into a 3‐dimensional space. Finally, simulations validate the theoretical results.

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Section: The Three-agent Formationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Formations on directed cycles with bearing‐only measurements

Trinh

Mukherjee

Zelazo

et al. 2017

Intl J Robust & Nonlinear

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“…While distance-based formation control was extensively studied [3]- [7], bearing-based formation control has recently attracted much research interest due to the emergent technology of small UAVs equipped with vision sensors [8], [9]. In bearing-based formation control problems, a group of autonomous agents (mobile robots, UAVs) has to achieve a target formation specified by some bearing information (bearing vectors and/or subtended bearing angles) [10].…”

Section: Introductionmentioning

confidence: 99%

Bearing-Based Formation Control of A Group of Agents with Leader-First Follower Structure

Trinh

Zhao

Sun

et al. 2018

IEEE Trans. Automat. Contr.

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101

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“…Nevertheless, the formation control strategies provided for SE(2) frameworks still require additional sensing [80], and a complete theory for bearing-only formation control is still unsolved. In addition to network localization and formation control, many other tasks may also be achieved with bearing-only measurements such as bearing-only rendezvous [84]- [88], and bearing-only target tracking [16]- [18], [89]- [91] though the analysis of these tasks may not rely on the bearing rigidity theory.…”

Section: Discussionmentioning

confidence: 99%

Bearing Rigidity Theory and Its Applications for Control and Estimation of Network Systems: Life Beyond Distance Rigidity

2019

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Distributed control and estimation of multi-agent systems has received tremendous research attention in recent years due to their potential across many application domains [1], [2]. Here, the term "agent" can represent a sensor, an autonomous vehicle, or any general dynamical system. These multi-agent systems are becoming increasingly attractive because of their robustness against system failure, their ability to adapt to dynamic and uncertain environments, and their economic advantages compared to the implementation of more expensive monolithic systems.Formation control and network localization are two fundamental tasks for multi-agent systems that enable them to perform complex missions. The goal of formation control is to control each agent using local information from neighboring agents so that the entire team forms a desired spatial geometric pattern (see [2] for a recent survey on formation control). While the notion of a formation as a geometric pattern has a natural meaning for robotic systems, it may also correspond to more abstract configurations for the system state of a team of agents. The goal of network localization is to estimate the location of each agent in a network using locally sensed or communicated information from neighboring agents [3]-[6]. Network localization is usually the first step that must be completed before a sensor network provides other services like positioning mobile robots or monitoring areas of interest.For a formation control or network localization task, the type of information available to each agent is an important factor that determines the design of the corresponding control or estimation algorithms. Most of the existing approaches for formation control assume that each agent can obtain the relative positions of their nearest neighbors. In order to obtain relative positions in practice, each agent can measure their absolute positions using, for example, GPS, and then share their positions with their neighbors via wireless communications. This method is, however, not applicable when operating in GPS-denied environments such as indoors, underwater, or in deep space. Furthermore, the absolute accuracy of the GPS may not meet the requirements of high-accuracy formation control tasks. Rather than relying on external positioning systems such as GPS, each agent can use onboard sensors to sense their neighbors.Optical cameras are widely used onboard sensors for ground and aerial vehicles to achieve various sensing tasks due to their characteristics of being low-cost, light-weight, and low-power. It is notable that optical cameras are inherently bearing-only sensors. Specifically, once a target has been recognized in an image, its bearing relative to the camera can be calculated immediately from its pixel coordinate based on the pin-hole camera model [7, Section 3.3]. As a comparison, the range from the target to the camera is more complicated to obtain because it requires additional geometric information of the target and extra estimation algorithms, which may significantly in...

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Guidance using bearing-only measurements with three beacons in the plane

Cited by 21 publications

References 27 publications

Formations on directed cycles with bearing‐only measurements

Formations on directed cycles with bearing‐only measurements

Bearing-Based Formation Control of A Group of Agents with Leader-First Follower Structure

Bearing Rigidity Theory and Its Applications for Control and Estimation of Network Systems: Life Beyond Distance Rigidity

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