In this paper, an optimal stable algorithm is presented for members of swarm robots to move toward a target. Firstly, equations of motion of the swarm are considered according to Lagrangian energy equations. Results of similar research wherein constraints are considered to guarantee no collision between the members and the members and obstacles. 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. Points of various coordinates are considered on a target, and the applied potential function acts in such a way that, from the beginning of the swarm motion, each of the members is guided to the closet point based on the knowledge of the coordinates of these points while communicating with other members. As a result, the need for having the members gathered within an area close to the center of the swarm (as has been 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. Results were indicative of reduced mission time along with increased maneuver space for the swarm members toward the target.