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Optimal Formation Control of Multiple Quadrotors Based on Particle Swarm Optimization

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Modeling, Design and Simulation of Systems (AsiaSim 2017)

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Abstract

This paper presents the optimal formation control for a group of quadrotors based on particle swarm optimization (PSO) algorithm. This is motivated by the conventional approaches that still involve a certain degree of trial and error approach which may not give the optimal performance. The parameter optimization using PSO utilizes the linear quadrotor model obtained from feedback linearization technique. Simulations are conducted on the parameter optimization, followed by implementation of the optimal parameters for formation control of multiple quadrotors. The results show the effectiveness of the proposed technique.

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Acknowledgments

The first author would like to thank the Ministry of Higher Education (MOHE) and Universiti Sains Islam Malaysia (USIM) for their financial support under SLAB scheme, and all the authors acknowledge the support by Universiti Teknologi Malaysia in term of lab facilities. The project is supported under the Research University Grant No. Q.J130000.2608.14J62, Universiti Teknologi Malaysia.

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Correspondence to Abdul Rashid Husain .

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Appendix: Graph Theory

Appendix: Graph Theory

The interaction topology in multi-agent system can be modeled using directed graph \( G \), with the set of agents denoted as \( V = \left\{ {V_{1} , V_{2} , \cdots , V_{n} } \right\} \) and \( {\mathcal{E}} \) is the set of edges \( E_{ij} \) connecting two neighboring agents. If agent \( i \) receives information from agent \( j \), there will be an edge \( E_{ij} \) in \( {\mathcal{E}} \). The set of neighbors of agent \( i \) which it can communicates to excluding itself is denoted by \( {\mathcal{N}}_{i} \). The adjacency matrix \( {\mathcal{A}} = \left[ {a_{ij} } \right] \in {\mathbb{R}}^{{n{\text{x}}n}} \) is defined such that \( a_{ij} > 0 \) if \( E_{ij} \in {\mathcal{E}} \), and \( a_{ij} = 0 \) otherwise. Meanwhile the degree matrix is \( \varepsilon = diag\left( {d_{1} , \cdots ,d_{N} } \right) \) with \( d_{i} \) is the in-degree of the \( i \)-th agent. In multi-agent system, the frequently used matrix to represent the interaction topology is Laplacian matrix \( L = \Delta - {\mathcal{A}} \). For example, consider the interaction topology given in Fig. 9.

Fig. 9.
figure 9

An example of interaction topology.

The unweighted Laplacian matrix of the interaction is given as follows:

$$ \begin{aligned} L = \Delta - {\mathcal{A}} & = \left[ {\begin{array}{*{20}c} 2 & 0 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 0 & 2 \\ \end{array} } \right] - \left[ {\begin{array}{*{20}c} 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 \\ 1 & 0 & 0 & 1 & 0 \\ \end{array} } \right] \\ & = \left[ {\begin{array}{*{20}c} 2 & { - 1} & { - 1} & 0 & 0 \\ { - 1} & 2 & { - 1} & 0 & 0 \\ 0 & { - 1} & 2 & { - 1} & 0 \\ 0 & 0 & { - 1} & 2 & { - 1} \\ { - 1} & 0 & 0 & { - 1} & 2 \\ \end{array} } \right] \\ \end{aligned} $$
(25)

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Lazim, I.M., Husain, A.R., Mohd Subha, N.A., Mohamed, Z., Mohd Basri, M.A. (2017). Optimal Formation Control of Multiple Quadrotors Based on Particle Swarm Optimization. In: Mohamed Ali, M., Wahid, H., Mohd Subha, N., Sahlan, S., Md. Yunus, M., Wahap, A. (eds) Modeling, Design and Simulation of Systems. AsiaSim 2017. Communications in Computer and Information Science, vol 751. Springer, Singapore. https://doi.org/10.1007/978-981-10-6463-0_11

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  • DOI: https://doi.org/10.1007/978-981-10-6463-0_11

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