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.

Neural dynamics is a powerful tool to solve online optimization problems and has been used in many applications. However, some problems cannot be modelled as a single objective optimization and neural dynamics method does not apply. This paper proposes the first neural dynamics model to solve bi-objective constrained quadratic program, which opens the avenue to extend the power of neural dynamics to multi-objective optimization. We rigorously prove that the designed neural dynamics is globally convergent and it converges to the optimal solution of the bi-objective optimization in Pareto sense. Illustrative examples on bi-objective geometric optimization are used to verify the correctness of the proposed method. The developed model is also tested in scientific computing with data from real industrial data with demonstrated superior to rival schemes.