Trajectory Tracking Using Adaptive Fractional PID Control of Biped Robots with Time-Delay Feedback

Abstract

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. For this purpose, we obtained two control laws and laws of adaptive weights online, obtained using the fractional order Lyapunov-Krasovskii stability analysis methodology. The main methodologies, on which the approach is based, are fractional order PID the fractional order Lyapunov-Krasovskii functions methodology, although the results we obtain are applied to a wide class of non-linear systems, we will apply it in this chapter to a bipedal robot. 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. To verify the analytical results, an example of dynamical network is simulated, and two theorems are proposed to ensure the tracking of the nonlinear system. The tracking error is globally asymptotically stabilized by two control laws derived based on a Lyapunov-Krasovskii functional.

FPGA Realization and Lyapunov–Krasovskii Analysis for a Master-Slave Synchronization Scheme Involving Chaotic Systems and Time-Delay Neural Networks

“…e Genesio-Tesi and Liu systems are considered. Although the proposed scheme could be useful to follow other nonlinear systems, we decide to restrict this work using only these two chaotic systems because their tracking can be more challenging than other tracking problems such as the reproduction of the gait cycle in humanoids [25] or the trajectory tracking in different mechanical systems [26] and complex systems [27]. In all the former cases, the movement may be softer and periodic.…”