An Event-Triggered $\boldsymbol{k}$-WTA Model With Experimental Verification on Multirobot System

Abstract

A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{k}$</tex-math></inline-formula>-winners-take-all (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{k}$</tex-math></inline-formula>-WTA) model is capable of selecting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{k}$</tex-math></inline-formula> winners from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula> participants via competitive operations for dynamic task allocation in a multirobot system (MRS). In this article, an event-triggered <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{k}$</tex-math></inline-formula>-WTA (ET-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{k}$</tex-math></inline-formula>WTA) model is proposed to improve communication efficiency and alleviate the computational burden of competitive coordination in an MRS. By detecting the rate of change on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{k}$</tex-math></inline-formula>-WTA outputs of each robot, an ET condition based on Lyapunov stability is derived. Through the ET condition, different communication and computation frequencies are selected so that the computational performance and communication frequency are equilibrated. Thus, communication interactions and the computational burden of the MRS are subtly reduced. Theoretical analyses are provided to guarantee the convergence and robustness of the proposed ET-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{k}$</tex-math></inline-formula>WTA model. Furthermore, comparative simulations and experiments are conducted to illustrate the effectiveness and superiority of the proposed ET-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{k}$</tex-math></inline-formula>WTA model.