A New Neural Network approach for Torus Super Structured Quadrilateral Dynamic Resistor Networks and its applications

In recent years, resistor networks have found wide applications. However, existing methods for dynamic problems often suffer from slow convergence and low computational efficiency. The torus structure, characterized by periodic closure, is a super structured quadrilateral mesh ubiquitous in engineering and scientific systems and increasingly relevant to robot path planning. To address these issues, a New Neural Network (NNN) algorithm is proposed to solve the node potential of the Torus Super Structured Quadrilateral (TSSQ) Dynamic Resistor Networks. First, a model is constructed to solve the voltage–current relationship in torus resistor networks. By exploiting the structural properties of the Laplacian matrix, an optimized computational scheme is developed, significantly improving computational efficiency. Second, integrating the inherent natural decline characteristic of the node potential of the resistor network into the core layer of the design for the intelligent robot’s path-finding algorithm, an innovative and effective algorithm for the path planning of the intelligent robot has been presented. The algorithm efficiently generates collision-free paths in static environments and demonstrates superior efficiency compared with classical methods, while also exhibiting robust performance in dynamic environments. Finally, a conjecture is presented that the natural descent of electric potential corresponds to the fastest path.