A Cerebellum Model Enhanced Gradient Neural Network for Solving Time-Variant Linear Equations Applied to Robot Control

Abstract

Recurrent neural networks (RNNs) are powerful alternatives to solving time-variant linear equations (TVLEs) arising in science and engineering. However, existing RNN solutions to time-variant problems including TVLEs remain less satis-factory. For instance, gradient neural networks (GNNs) inevitably exhibit non-vanishing errors, and both Getz-Marsden dynamic inverters (GMDIs) and zeroing neural networks (ZNNs) involve matrix inversion and time-derivative information of coefficients. To tackle this situation, this paper proposes a cerebellum model enhanced GNN (CM-GNN) solver by borrowing inspirations from the design principle of GMDIs and the biological function of the human cerebellum. The CM-GNN solver consists of a conventional GNN and a cerebellum model for error compensation, with no matrix inversion and time derivatives of coefficients involved. This paper first details the design of the CM-GNN solver. After that, the proposed CM-GNN solver and a conventional GNN solver are comparatively applied to i) a same TVLE as a numerical example, and ii) a same path-tracking task of a Franka Emika Panda robot. Both numerical and experimental results demonstrate that the proposed CM-GNN solver outperforms the conventional GNN solver in terms of the solution accuracy and the path-tracking accuracy.