This study focuses on exploring the solution to coordination in multirobot systems faced with competitive states, where the competition behavior can be described as a$k$-winner-take-all ($k$WTA) operation. To address the$k$WTA problem, a fuzzy$k$WTA (F-$k$WTA) network is proposed, which incorporates a fuzzy mechanism into the network that adapts the convergence rate of the F-$k$WTA network based on the error, leading to exceptional convergence behavior. In addition, a set of activation functions are provided to further enhance the capabilities of the F-$k$WTA network. In addition, the proposed network demonstrates remarkable convergence performance, as illustrated through both theorems and simulations. Finally, the practical application value of the F-$k$WTA network is demonstrated on a multirobot system.

Enlightened by competitive and collaborative coordination behaviors widely observed in natural swarm systems, this work emphasizes these coordinating modes in multirobot systems and optimizes system stability along with resource utilization. Then, schemes are constructed to describe and model these two modes, where a$k$-winner-take-all concept is introduced as the driving principle of multirobot competition. In addition, a distributed coordination approach is established to effectively handle the above schemes aided with optimality theory, which is developed by a fusion of a recurrent neural dynamics solver and a distributed solver. The former is a single-layer neural dynamics model with a simple structure, and the latter transforms the involved global information to a distributed type via consensus. Both of them are carried out in the discrete-time domain to fit the actual application. Finally, the convergence and stability of the proposed coordination approach are proved via theoretical analysis and further demonstrated through simulations and experiments.