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This paper presents an algorithm called augmented Lagrangian particle swarm optimization with velocity limits (VL-ALPSO). It uses a particle swarm optimization (PSO) based algorithm to optimize the motion planning for swarm mobile robots. Considering problems with engineering constraints and obstacles in the environment, the algorithm combines the method of augmented Lagrangian multipliers and strategies of velocity limits and virtual detectors so as to ensure enforcement of constraints, obstacle avoidance and mutual avoidance. All the strategies together with basic PSO are corresponding to real situations of swarm mobile robots in coordinated movements. This work also builds a swarm motion model based on Euler forward time integration that involves some mechanical properties such as masses, inertias or external forces to the swarm robotic system. Simulations show that the robots moving in the environment display the desired behavior. Each robot has the ability to do target searching, obstacle avoidance, random wonder, acceleration or deceleration and escape entrapment. So, in summary due to the characteristic features of the VL-ALPSO algorithm, after some engineering adaptation, it can work well for the planning of coordinated movements of swarm robotic systems.