Adaptive fractional PID control of biped robots with time-delayed feedback

This paper presents the application of Fractional Order Time- Delay adaptive neural networks to the trajectory tracking for chaos synchronization between Fractional Order delayed plant, reference and Fractional Order Time-Delay adaptive neural networks. The proposed new control scheme is applied via simulations to control of a 4-DOF Biped Robot [1]. The main methodologies, on which the approach is based, are Fractional Order PID the Fractional Order Lyapunov-Krasovskii functions methodology. The structure of the biped robot is designed with two degrees of freedom per leg, corresponding to the knee and hip joints. Since torso and ankle are not considered, it is obtained a 4-DOF system, and each leg, we try to force this biped robot to track a reference signal given by undamped Duffing equation. The tracking error is globally asymptotically stabilized by two control laws derived based on a Lyapunov-Krasovski functional