Distributed and Time-Delayed -Winner-Take-All Network for Competitive Coordination of Multiple Robots

In this article, a distributed and time-delayed <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-winner-take-all (DT-<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>WTA) network is established and analyzed for competitively coordinated task assignment of a multirobot system. It is considered and designed from the following three aspects. First, a network is built based on a <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-winner-take-all (<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>WTA) competitive algorithm that selects <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> maximum values from the inputs. Second, a distributed control strategy is used to improve the network in terms of communication load and computational burden. Third, the time-delayed problem prevalent in arbitrary causal systems (especially, in networks) is taken into account in the proposed network. This work combines distributed <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>WTA competition network with time delay for the first time, thus enabling it to better handle realistic applications than previous work. In addition, it theoretically derives the maximum delay allowed by the network and proves the convergence and robustness of the network. The results are applied to a multirobot system to conduct its robots’ competitive coordination to complete the given task.