Optimal formation of robots by convex hull and particle swarm optimization

Formation control problem has been extensively investigated in the literature of multi-agent systems, robotics, and control, etc. Our previous work mainly concentrated on the theoretic study of line formation with three robots, however, it is hard to handle with the formation problem whose number of robots is strictly larger than 3. In order to effectively overcome this problem, this paper incorporates convex hull and the standard PSO algorithm to design the typical formation of several robots. Firstly, on the basis of convex hull of robots, objective function, corresponding to several constraints, is given by the new convex hull method. Secondly, the standard PSO algorithm is adopted to search for the desired positions of several robots to minimize the objective function and satisfy the formation constraints. To demonstrate the effectiveness of the proposed algorithm, numerical results, regarding the formation of several ships in the realistic ocean, mainly concentrate on triangle formation, diamond formation and regular polygon formation.