Dynamic Formation Control Over Directed Networks Using Graphical Laplacian Approach

The focus of this study is a joint analysis of the stability of formation control and the capacity of wireless communications between agents moving in a formation. The main results derived in this study show a connection between the second moment stability/convergence of formation control and the expected capacity of the data communications for multiagent systems in which the collective behavior of the multiple agents is dominated by formation control with random errors. More specifically, by developing a joint control-communication framework for the performance analysis, we investigate whether random errors in the formation control have a destructive influence on the data communications between agents. We prove that the expected capacity of the multiagent data communication link has a nonvanishing lower bound that can be evaluated through second moment performance analysis. The results from simulations indicate that the theoretical analysis provides reasonable lower bounds for different system parameters.

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“…with φ re (λ) defined in (13) ] < ∞, ∥E [ξ(t)]∥ 2 < ∞, and L i,j (t) < ∞, such that C ergL ( L i,j (t) ) > 0, and…”

Section: Define ξ(T)mentioning

confidence: 99%

Formation-Control Stability and Communication Capacity of Multiagent Systems: A Joint Analysis

Qian

Duan

et al. 2021

IEEE Trans. Control Netw. Syst.

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“…In fact, several tasks may benefit from solutions of formation control, such as load transportation with cooperative robots to move flexible payloads [10]. Different formation control scenarios have been investigated such as the ones incorporating, but not limited to, time-varying formations [11,12,13,14], formations with multiple leaders [15,16,17], switching network topologies [18,19,20], time-delays [21,22], etc. Stochastic switching topologies with time-varying delays have also been considered in [23].…”

Section: Introductionmentioning

confidence: 99%

Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators

Savino

Pimenta

Shah

et al. 2020

Journal of the Franklin Institute

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This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies. The dual quaternion algebra is used to model the agents' poses and also in the distributed control laws, making the proposed technique easily applicable to time-varying formation control of general robotic systems. The proposed pose consensus protocol has guaranteed convergence when the interaction among the agents is represented by directed graphs with directed spanning trees, which is a more general result when compared to the literature on formation control. In order to illustrate the proposed pose consensus protocol and its extension to the problem of formation control, we present a numerical simulation with a large number of free-flying agents and also an application of cooperative manipulation by using real mobile manipulators.the multi-agent system asymptotically achieves formation if and only if the graph G describing the network topology has a directed spanning tree and vec 8 u x,i is in the range space of J w,i . 2Proof. First we prove that vec 8 u x,i is in the range space of J w,i if and only if vec 8 uConversely, if J w,i J † w,i vec 8 u x,i = vec 8 u x,i then ∃v J † w,i vec 8 u x,i such that J w,i v = vec 8 u x,i , which implies that vec 8 u x,i ∈ range J w,i . Hence,

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“…As part of the design process of multi-robot formation control algorithm, many problems need to be considered, including robot model, external environmental interference, sensor measurement noise, algorithm control precision, and the controllability of different formations [3]. The existing formation control algorithms for multi-robots mainly include the leader-follower algorithm [4], the behavior-based algorithm [5], the graph theory-based method [6], the virtual structure method [7], and the artificial potential field method. The leader-follower algorithm has flexible motion strategy and scalability, but the algorithm cannot form stable and reliable feedback between the follower and the leader.…”

Section: Introductionmentioning

confidence: 99%

Consensus Algorithms Based Multi-Robot Formation Control under Noise and Time Delay Conditions

Wei¹,

Lv²,

Duo³

et al. 2019

Applied Sciences

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In recent years, the formation control of multi-mobile robots has been widely investigated by researchers. With increasing numbers of robots in the formation, distributed formation control has become the development trend of multi-mobile robot formation control, and the consensus problem is the most basic problem in the distributed multi-mobile robot control algorithm. Therefore, it is very important to analyze the consensus of multi-mobile robot systems. There are already mature and sophisticated strategies solving the consensus problem in ideal environments. However, in practical applications, uncertain factors like communication noise, communication delay and measurement errors will still lead to many problems in multi-robot formation control. In this paper, the consensus problem of second-order multi-robot systems with multiple time delays and noises is analyzed. The characteristic equation of the system is transformed into a quadratic polynomial of pure imaginary eigenvalues using the frequency domain analysis method, and then the critical stability state of the maximum time delay under noisy conditions is obtained. When all robot delays are less than the maximum time delay, the system can be stabilized and achieve consensus. Compared with the traditional Lyapunov method, this algorithm has lower conservativeness, and it is easier to extend the results to higher-order multi-robot systems. Finally, the results are verified by numerical simulation using MATLAB/Simulink. At the same time, a multi-mobile robot platform is built, and the proposed algorithm is applied to an actual multi-robot system. The experimental results show that the proposed algorithm is finally able to achieve the consensus of the second-order multi-robot system under delay and noise interference.

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Dynamic Formation Control Over Directed Networks Using Graphical Laplacian Approach

Cited by 38 publications

References 46 publications

Formation-Control Stability and Communication Capacity of Multiagent Systems: A Joint Analysis

Formation-Control Stability and Communication Capacity of Multiagent Systems: A Joint Analysis

Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators

Consensus Algorithms Based Multi-Robot Formation Control under Noise and Time Delay Conditions

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