A Fractional-Order Gradient Neural Solution to Time-Variant Quadratic Programming With Application to Robot Motion Planning

This article proposes the fractional-order gradient neural network (FO-GNN) model for time-variant quadratic programming (TVQP) problems, marking the first integration of fractional calculus into neural solver design for cyclic motion planning in robotics. The FO-GNN evolves from traditional GNNs by employing fractional gradient operators, thus bypassing the differentiation typically required in zeroing neural networks (ZNNs). This innovation leads to a streamlined computational approach and convergence that does not rely on the convexity of the energy function. Compared to ZNN, standard GNN, and MATLAB's quadprog, the FO-GNN offers enhanced precision and expedited convergence for both time-invariant and TVQP challenges. Empirical tests, including simulations and experiments with the Flexiv Rizon robotic arm, confirm the FO-GNN's precise tracking and computational efficiency, underlining its robustness for kinematic control and its adept handling of nonsmooth dynamic constraints.