Optimization-Based Finite-Time Multi-Robot Formation: A Zeroing Neurodynamics Method

The problem of multi-robot formation is prevalent in scientific and engineering applications, where robots must adapt to uncertain and dynamic behaviors due to real-time environmental or task changes. Traditional methods struggle to meet the demand for high-precision solutions within finite time frames. Zeroing Neural Networks (ZNNs), which utilize the time derivatives of time-varying coefficients, outperform other networks in handling dynamic system behaviors. This paper marks the first attempt to extend the ZNN approach to address finite-time multi-robot through optimization modeling. We introduce an innovative strategy that employs complex number structures to map robot coordinates, simplifying the computation needed for dynamic formation tasks. Additionally, we present a multi-robot formation strategy that minimizes the distance between neighboring robots while adhering to bias-type center constraint. This is effectively reformulated as a complex-valued time-varying matrix equation. Based on this, two complex-type Finite-Time Zeroing Dynamic Controllers (FTZDC) are designed, with their stability and convergence time bounds rigorously analyzed. Finally, in two specific formation tasks, the proposed strategy and FTZDC models achieve precise multi-robot formation, independent of the robots’ initial positions, all within finite time.