A cooperative target-fencing protocol of multiple vehicles

doi:10.1016/j.automatica.2019.05.034

Automatica

Volume 107, September 2019, Pages 591-594

https://doi.org/10.1016/j.automatica.2019.05.034 Get rights and content

Abstract

A class of cooperative controllers is designed for a group of autonomous vehicles, using the relative positions between geographical neighbors and a specified target. The controller is equipped with three components: attractive component that drives each vehicle towards the target, repulsive component between adjacent vehicles, and rotation component for neighbored vehicles aligned with the target in a straight line. It is proved that the vehicles with the proposed autonomous controller can asymptotically fence a specified target to their convex hull. Meanwhile, the vehicles do not collide and they are not stuck in a singleton formation.

Introduction

The cooperative target-fencing problem studied in this paper aims at a class of autonomous controllers that can drive a group of vehicles to asymptotically fence a specified target to their convex hull. It is technically relevant to various cooperative formation control problems, for example, the circular motion in Ceccarelli et al., 2008, Chen and Zhang, 2011 and Sepulchre, Paley, and Leonard (2008). These circular formation control formulations do not essentially involve a physical target. The other class of relevant research was formulated as a target-enclosing or target-capturing problem. For instance, a cyclic pursuit strategy was used in Kim and Sugie (2007) to drive agents to enclose the target object, called target-capturing. The technique of enclosing a target by holonomic or nonholonomic mobile vehicles was reported in Guo, Yan, and Lin (2010) and Zheng, Liu, and Sun (2015), where vehicles eventually move on a circle centered at the target with a predefined stand-off distance.

In the aforementioned results, the group of agents aim to enclose a target within their moving trajectories. The agents do not necessarily enclose a target at every moment, even when the desired behavior is achieved. However, the target-fencing protocol studied in this paper aims to drive a group of vehicles to asymptotically approach some desired trajectories that fence a specified target to their convex hull, at every moment. A dual problem of target-fencing is the so-called containment control studied in, e.g., Ji, Ferrari-Trecate, Egerstedt, and Buffa (2008), that aims to drive a group of agents to be contained in an area fenced by another group of targets. The target-fencing problem is also called surrounding control in, e.g., Chen, Ren, and Cao (2010) and Lou and Hong (2015). A control approach was proposed in Chen et al. (2010) by assuming that the vehicles are initially placed within a circle and/or using a predefined stand-off distance between the vehicles and the target. In Lou and Hong (2015), the surrounding formation is specified by a complex-value adjacency matrix. A predefined distance was also used in the aforementioned target-enclosing or target-capturing problem such as Guo et al. (2010) and Zheng et al. (2015).

The main objective of this paper is to develop a novel class of cooperative target-fencing controllers for a group of autonomous vehicles, without a specified stand-off distance or formation. In other words, the distance between the vehicles and the target is autonomously maintained. Each controller uses only the relative positions between geographical neighbors and the target. The novelty of the controller is that it is equipped with three fundamental functionalities: attractive component that drives each vehicle towards the target, repulsive component between adjacent vehicles, and rotation component for neighbored vehicles aligned with the target in a straight line. It is proved that the group of vehicles with the controller can asymptotically fence a specified target to their convex hull. Meanwhile, the vehicles do not collide and they are not stuck in a singleton formation. It is worth mentioning that collision avoidance has its independent theoretical interest and practical importance and it has been extensively studied for various scenarios in, e.g., Chen and Zhang (2017) and Mylvaganam, Sassano, and Astolfi (2017). It is novel to include collision avoidance in the proposed target-fencing scenario.

Section snippets

Main results

Let $N = {1, 2, \dots, N}$ . Denote the complete position distribution of a multi-agent system by $x = {[x_{1}^{T}, \dots, x_{N}^{T}]}^{T}$ , where $x_{i} = {[x_{1, i}, x_{2, i}]}^{T} \in R^{2}$ , $i \in N$ , represents the Cartesian coordinates of the $i$ th vehicle. The kinematics model of each vehicle is represented by a continuous-time equation ${\dot{x}}_{i} (t) = u_{i} (t), i \in N$ with the input $u_{i}$ to be designed. Throughout the paper, the time argument $(t)$ is ignored for neatness when no confusion is caused. Denote the convex hull of $x_{1}$ , $\dots$ , $x_{N}$ by $co (x)$ , that is, $co (x) = \{\sum_{i = 1}^{N} λ_{i} x_{i} : λ_{i} \geq 0, \forall i and\}$

Simulation

The simulation is conducted for five vehicles equipped with the controller $u_{i} = u_{i}^{o}$ defined in (2) for $α (s) = \{\begin{matrix} {(s - d)}^{- 1} - {(μ - d)}^{- 1}, & s \in (d, μ) \\ 0, & s \in [μ, \infty), \end{matrix}$ $μ = 3$ , $d = 1$ , $ϵ = 0.05$ , $δ = 1 0^{\circ}$ , and $k = 1$ . The first result, plotted in the top graph of Fig. 1, shows the target-fencing trajectories with the initial positions of the five vehicles arbitrarily selected. In particular, the target at $x_{o} = {[3, 10]}^{T}$ is asymptotically fenced by the convex hull of the five vehicles, as expected by the property (P1). During the

Conclusion

The target-fencing problem has been solved in this paper by a novel autonomous controller equipped with three fundamental functionalities: attraction, repulsion, and rotation. The result holds subject to exponentially vanishing disturbance. The disturbance may also represent the error from an inner velocity regulation controller when vehicle dynamics are considered. It requires further investigation in the future research.

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There are more references available in the full text version of this article.

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This study addresses the moving target fencing (MTF) control problem of multiple underactuated marine surface vehicles (MSVs) with varying intermittent communication under a directed graph. A distributed internal model observer (DIMO) was proposed to estimate the target trajectory for each vehicle with intermittent communication. Combined with this observer, an MTF control scheme was developed to cooperatively fence a moving target in a convex hull that quasi-asymptotically rotates equally around the target at the centre. Collision avoidance was guaranteed simultaneously. Furthermore, the stability of the proposed control scheme was analysed using the Lyapunov theory. Finally, numerical examples and experiments are conducted to demonstrate the validity and stability of the proposed control approach.
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Citation Excerpt :
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^☆: The work was substantially supported by the National Natural Science Foundation of China under Grant No. 51729501. The material in this paper was presented at None. This paper was recommended for publication in revised form by Associate Editor Dimos V. Dimarogonas under the direction of Editor André L. Tits.

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Technical communiqueA cooperative target-fencing protocol of multiple vehicles☆

Abstract

Introduction

Section snippets

Main results

Simulation

Conclusion

Automatica

Systems & Control Letters

Automatica

Systems & Control Letters

Automatica

Technical communique
A cooperative target-fencing protocol of multiple vehicles☆