Designing an Optimal Stable Algorithm for Robot Swarm Motion toward a Target

In this paper, an optimal stable algorithm is presented for members of a robots swarm moving toward a target. Equations of motion of the swarm are based on Lagrangian energy equations. Regarding of similar research On the design of swarm motion algorithm, an equation of motion considered constraints to guarantee no collision between the members and the members and obstacles along the motion path is presented. In order to optimize the swarm motion stability algorithm, the required constraints are introduced into the equations of motion in the form of a potential function. Considering Points of various coordinates on a target and applied potential function, each member is guided to the closest point using their coordinates while communicating with others from the beginning of the swarm motion. As a result, the need for having the members gathered within an area close to the center of the swarm observed in previously designed algorithms is eliminated. The designed optimal stability algorithm is simulated in MATLAB Software for a swarm composed of two robots under different sets of conditions. Simulation results of swarm member behavior were indicative of reducing mission time with increasing motion space for the swarm members while optimizing the behavior of the swarm moving toward the target. Finally, some experimental results related to designed algorithm are presented.