Design of a new algorithm for two dimensional movement of swarm robots according to collision avoidance with obstacles based on the Lagrange equations

In this paper, a new algorithm is presented for the swarm behavior of robots in order to initially aggregate the swarm in its center and subsequently move toward a given target point. Since the equation representing the swarm movement is based on Lagrange equations, the member of the swarm take the shortest distance to reach their destination providing that the amount of energy found in above-mentioned algorithm is minimized. In addition, assuming that there are obstacles on the path of the swarm movement, the algorithm applies a linear repulsive force, activated by a switch, to avoid the contact between the members and obstacles. Finally, the presented equations are simulated and validated through MATLAB software. The results obtained from the swarm behavior of robots are simulated on the basis of the algorithm, and the optimized behavior of the algorithm is shown when the amount of energy is minimized and there is no contact with the obstacle.