Stability is one of the most important issues in swarm movement. Stability in swarm movement is composed of features such as collision avoidance between members of the swarm with each other and also obstacle avoidance along the path of movement. This paper presents a new algorithm in the form of a dynamic equation based on Lagrange equations for stable movement of the swarm robot. One of the objective of presenting this algorithm is to enable aggregation at the target point. The new algorithm will be extended in two cases; first, when the members of the swarm have the tendency for aggregation from the beginning of the movement, and second, members of the swarm don’t have the tendency for aggregation along the path. At the end, the presented algorithms will be simulated and evaluated. The simulation results show successful obstacle avoidance along the path and aggregation at the target point. The results show that in the second case—when there is no aggregation along the path—the members of the swarm cover more area along the path. Covering more area along the path empowers the application of the proposed algorithm in cases such as identification, exploration, environmental monitoring and mapping along the path