# An Evolutionary Algorithm to Optimise a Distributed UAV Swarm Formation System
###### Abstract  
In this article, we present a distributed robot 3D formation system optimally parameterised by a hybrid evolutionary algorithm (EA) in order to improve its efficiency and robustness. To achieve that, we first describe the novel distributed formation algorithm3 (DFA3), the proposed EA, and the two crossover operators to be tested. The EA hyperparametersisation is performed by using the irace package and the evaluation of the three case studies featuring three, five, and ten unmanned aerial vehicles (UAVs) is performed through realistic simulations by using ARGoS and ten scenarios evaluated in parallel to improve the robustness of the configurations calculated. The optimisation results, reported with statistical significance, and the validation performed on 270 unseen scenarios show that the use of a metaheuristic is imperative for such a complex problem despite some overfitting observed under certain circumstances. All in all, the UAV swarm self-organised itself to achieve stable formations in 95% of the scenarios studied with a plus/minus ten percent tolerance.  
Footnote 3: footnotemark:  
evolutionary algorithm; crossover operator; UAV; swarm robotics; argos simulator; formation control +
Footnote †: journal: Applied Sciences  
formation, surrounding an object such as a rogue drone in a sphere-like shape. It is part of a swarm-based counter UAS (C-UAS) system. We do not use a global coordinate system nor a different, intelligent node in the swarm. We just let the UAVs make their own local decisions based on local information. There is an exclusion zone (sphere) around the central point of the formation to avoid collisions with the rogue drone while the formation algorithm itself avoids collisions between the swarm members. Other applications can be derived from our proposal, such as asteroid observation, provided that the number of robots (probes) is high enough and the desired formation radius is achievable. Our proposal is tested on three case studies comprising swarms of three, five, and 10 UAVs. We proposed four individual UAV parameters and designed a hybrid EA to optimise them in order to achieve proper formations in all the 300 scenarios studied. The main contributions of this paper are as follows.  
1. A distributed robot 3D formation system able to surround and escort an object of interest is given.
2. A hybrid EA to optimise the parameters of the formation system providing efficiency and robustness is given.
3. A study of the EA parameters and an analysis of the proposed genetic operators is presented.
4. A simulation approach using a multi-physics robot simulator to evaluate the different configurations calculated by the EA is given.  
The rest of this paper is organised as follows. In the next section, we review the state of the art related to our proposal. In Section 3 our robot-formation system is presented. The optimisation approach is discussed in Section 4, wherein the optimisation algorithm and its parameterisation is described. The experimental results are in Section 5 and finally, Section 6 gives our conclusions and future work.