A Spiking Cerebellar Model Enhanced Gradient Neural Solution to Time-Varying Linear Equations With Application to Robot Motion Planning

Time-varying linear equations (TVLEs) are prevalent in science and engineering, especially in artificial intelligence and robotics. When solving TVLEs, the existing recurrent neural networks (RNNs) either suffer from non-vanishing errors, iterative computations at each time step, or the involvement of matrix inversion and time derivatives of coefficients. Inspired by the human cerebellum's role in fine-tuning and coordinating motor commands, this paper presents a spiking cerebellar model enhanced gradient neural network (SCM-GNN), where the GNN and the SCM generate an approximate solution and a corrective signal, respectively. The SCM-GNN model embraces spiking neural networks' potential merits including biological plausibility, and it is a non-iterative solution that performs only one iteration of computations at each time step with no matrix inversion and time derivatives of coefficients involved. For performance validations, the SCM-GNN is successfully applied to a numerical example and a cyclical motion planning scheme of a robot tracking a user-specified path, validating its effectiveness and practicality.