A Fractional-Order Recurrent Neural Network Model for Time-Variant Quadratic Programming in Robot Motion Planning

Abstract

This paper develops the Fractional-Order Zeroing Neural Network (FO-ZNN) model for addressing time-variant quadratic programming (TVQP) problems, marking an inaugural application of fractional calculus in neural models for robotic motion planning. Diverging from standard ZNN model, the FO-ZNN model incorporates a conformable fractional derivative definition that adheres to the Leibniz rule, which is commonly violated by other traditional fractional derivative definitions. In comparative analyses with the traditional ZNN model, the FO-ZNN model, parameterized with $0\lt \alpha\gt 1$, achieves significantly accelerated convergence rates in TVQP scenarios, albeit with a marginal trade-off in accuracy. Conversely, when $\alpha$ is greater than 1, the FO-ZNN model not only enhances its accuracy but also exhibits augmented convergence speeds, outperforming in both time-invariant and time-variant QP challenges. In addition, the FO-ZNN model with differentiation perturbations demonstrates notable convergence attributes, showcasing its robustness to maintain bounded steady-state residual errors and to achieve convergence with increased $\gamma$ value. Rigorous and empirical evaluations, including both simulations and physical experiments with a Flexiv Rizon robotic arm, validate the FO-ZNN’s capability for accurate trajectory tracking and computational efficiency, highlighting its robustness in kinematic control.