In this paper, a new multi-robot task allocation (MRTA) algorithm inspired by the Newtonian law of gravity is proposed. In the proposed method, targets and robots are considered as fixed objects and movable objects, respectively. For each target, a constant mass is assigned, which corresponds to its quality. The fixed objects (which refer to targets) apply a gravitational force to the movable objects (which are considered as robots) and change their positions in the feasible search space and therefore, the best target allocation of robots is determined by employing the law of gravity. In the proposed scenario, task allocation consists of assigning the robots to the found targets in a 2-D feasible area. The expected distribution is obtained from the targets’ qualities that are represented as scalar values. Decision-making is a distributed mechanism and robots choose their assignments, taking into account targets’ qualities and distances. Moreover, a control parameter is planned to make a remarkable balance between exploration and exploitation ability of the proposed algorithm. A self-adaptive mechanism is proposed to adjust the value of the exploration parameter automatically, aiming to maintain the balance between exploration and exploitation ability of robots. Furthermore, in order to decrease the time of reaching the target and accelerate computation, a selection memory is designed. In the experiments, we examine the scalability of the proposed method in terms of the number of robots and the number of targets and speed of algorithm to deliver robots to the desired targets with comparison to other competitors. The simulation results show the scalability of the algorithm, comparing the existing methods. Moreover, some non-parametric statistical tests are utilized to compare the results obtained in experiments. The statistical comparisons confirm the superiority of the proposed method compared over the existing methods.

本文提出了一种新的受牛顿重力定律启发的多机器人任务分配算法。在提出的方法中，目标和机器人分别被视为固定对象和可移动对象。为每个目标分配一个恒定质量，该质量与其质量相对应。固定物体（指目标）向可移动物体（被视为机器人）施加重力，并改变它们在可行搜索空间中的位置，因此，通过利用重力定律确定最佳的机器人目标分配。在提出的方案中，任务分配包括将机器人分配给二维可行区域中找到的目标。从标量值表示的目标质量获得预期分布。决策是一种分布式机制，机器人会根据目标的质量和距离来选择任务。此外，计划控制参数以在所提出算法的探索和开发能力之间取得显着平衡。提出了一种自适应机制，可以自动调整探索参数的值，以保持机器人的探索与开发能力之间的平衡。此外，为了减少到达目标的时间并加速计算，设计了选择存储器。在实验中，我们与其他竞争者相比，从机器人数量和目标数量以及将机器人交付到所需目标的算法速度方面，研究了所提出方法的可扩展性。仿真结果表明了该算法的可扩展性，与现有方法进行了比较。此外，一些非参数统计检验用于比较实验中获得的结果。统计比较证实了所提出的方法与现有方法相比的优越性。