Lately, robot swarm has widely employed in many applications like search and rescue missions, fire forest detection and navigation in hazard environments. Each robot in a swarm is supposed to move without collision and avoid obstacles while performing the assigned job. Therefore, a formation control is required to achieve the robot swarm three tasks. In this article, we introduce a decentralized formation control algorithm based on the potential field method for robot swarm. Our formation control algorithm is proposed to achieve the three tasks: avoid obstacles in the environment, keep a fixed distance among robots to maintain a formation and perform an assigned task. An artificial neural network is engaged in the online optimization of the parameters of the potential force. Then, real-time experiments are conducted to confirm the reliability and applicability of our proposed decentralized formation control algorithm. The real-time experiment results prove that the proposed decentralized formation control algorithm enables the swarm to avoid obstacles and maintain formation while performing a certain task. The swarm manages to reach a certain goal and tracks a given trajectory. Moreover, the proposed decentralized formation control algorithm enables the swarm to escape from local minima, to pass through two narrow placed obstacles without oscillation near them. From a comparison between the proposed decentralized formation control algorithm and the traditional PFM, we obtained that NN-swarm successes to reach its goal with average accuracy 0.14 m compared to 0.22 m for the T-swarm. The NN-swarm also keeps a fixed distance between robots with a higher swarming error reaches 34.83%, while the T-swarm reaches 23.59%. Also, the NN-swarm is more accurate in tracking a trajectory with a higher tracking error reaches 0.0086 m compared to min. error of T-swarm equals to 0.01 m. Besides, the NN-swarm maintains formation much longer than T-swarm while tracking trajectory reaches 94.31% while the T-swarm reaches 81.07% from the execution time, in environments with different numbers of obstacles.
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