Finite-Time Output Feedback Robust Controller Based on Tangent Barrier Lyapunov Function for Restricted State Space for Biped Robot

Abstract

This study has the aim of introducing a new type of trajectory tracking robust controllers for a class of rehabilitation robotic system considering the articulations restrictions. The robotic device consists of a suspended biped configuration. The suggested robust control considers the application of state depending gains which provide finite-time convergence for the tracking deviation. The state restrictions are fulfilled by the implementation of controller gains estimated by a class of the controlled tangent barrier Lyapunov function. Stability analysis for the tracking error yields the explicit design of the state dependent gains. The rate of convergence for the controller design is enhanced using a matrix inequality convex optimization method. Based on the forward complete characteristic of the suggested rehabilitation device, it is allowed using a finite-time convergent super-twisting-based differentiator to concrete an output feedback realization of the proposed controller. A computerized model of the tendered rehabilitation robot provides a reliable testing platform to the suggested roust controller. Numerical evaluations appear to serve as an indirect confirmation for the tracking error convergence, satisfying the articulation restrictions, and the effect of the gain optimization design. For comparison purposes, the regular state feedback control design is considered as benchmark. The faster convergence of the mean square estimation of the tracking error justifies the design of the proposed control design as well as the state feedback structure justifies the origin is a fixed-time stable equilibrium point for the space of tracking error at the same time that state space restrictions remain satisfied. The experimental evaluations of the proposed controller justifies the barrier controller which, in spite of the modeling uncertainties and the implementation issues, tracked the reference trajectories.