A Generalized <italic>Supertwisting</italic> Algorithm Based on Terminal Sliding Manifold Control of Perturbed Unicycle Mobile Robots

Abstract

This paper addresses the topic of stabilizing a class of nonholonomic systems in chained form impacted by matched uncertainties and time-varying perturbations. To design efficient stabilizing control law, the whole problem is divided into two sub-problems. The first sub-problem considers a system with perturbation stabilized using a fixed-time controller. The second sub-problem consists of the design of a controller for a second system operating under perturbations and uncertainties. To control this second system, firstly a terminal sliding mode manifold is proposed to achieve a fixed-time stability. As opposed to the traditional supertwisting algorithm (STA), the present work proposes a generalized STA (GSTA). The proposed method’s most striking feature is the substitution of a fractional power term for the standard STA’s discontinuous term, which can significantly boost the former’s performance. It is demonstrated that the GSTA will reduce to the traditional STA if the fractional power in the nonsmooth term equals −1/2. The ability of the sliding variables to finite-time converge to an arbitrary tiny region in the vicinity of the origin by adjusting the gains and the fractional power will be thoroughly proven under the GSTA by utilizing strict Lyapunov analysis. The effectiveness of the proposed control method is shown through extensive simulations.

Keywords

• Perturbed unicycle mobile robots
• nonholonomic systems
• fixed-time/finite stabilization
• Lyapunov methods
• high order sliding mode
• perturbations