Predetermined Time Optimal Multi-Robot Formation: A Zeroing Neural Dynamics Approach

摘要

With the rapid development of the multi-robot systems, formation control has become a fundamental challenge. Traditional approaches focus mainly on the design of control algorithms to realize specific formation patterns, while neglecting how to determine the desired formation. In this paper, the optimal formation problem based on shape theory is reformulated as a convex optimization problem. A predetermined time convergent zeroing neural dynamics (PDTZND) approach, derived from zeroing neural networks (ZNN), is proposed to efficiently solve this problem. The PDTZND approach ensures that the system error converges in a strict and predetermined time, which provides an efficient, accurate solution for optimal formation. In addition, the convergence of the proposed approach is rigorously analyzed by means of Lyapunov theory, and its validity and superiority are verified by numerical simulations and physical experiments.