Multi-robot task allocation (MRTA) is the basis of a multi-robot system to perform tasks automatically, which directly affects the execution efficiency of the whole system. A distributed cooperative task allocation strategy based on the algorithm of the improved Grey Wolf Optimizer (IGWO) was proposed to quickly and effectively plan the cooperative task path with a large number of working task points. The MRTA problem was transformed into multiple traveling salesman problems (MTSPs), and the task target points were clustered by the K-means clustering algorithm and divided into several traveling salesman problems (TSPs). The Grey Wolf Optimizer (GWO) was improved by the Kent chaotic algorithm to initialize the population and enhance the diversity of the population. Furthermore, an adaptive adjustment strategy of the control parameter $$\vec {a}$$ was proposed to balance exploration and exploitation. The individual speed and position updates in PSO were introduced to enable the gray wolf individual to preserve its optimal location information and accelerate the convergence speed. The IGWO was used to solve the optimal solutions to multiple TSP problems. Finally, the optimal solution space was integrated to get the optimal solution of MTSP, and 16 international classical test functions simulated the IGWO. The results showed that the IGWO algorithm has faster convergence speed and higher accuracy. The task allocation strategy is reasonable, with roughly equal path length, small planning cost, fast convergence speed, and excellent stability.
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