Derivative-Free Generalized Multivariable Super-Twisting Control for Constrained Euler-Lagrange Systems

Abstract

Robotic manipulators performing payload lift-and-transfer must track prescribed trajectories under abrupt load changes, with limited actuation and inaccurate plant knowledge. Such plants are inherently described by multivariable Euler--Lagrange~(EL) dynamics with cross-coupling established through inertial and Coriolis terms. The super-twisting algorithm~(STA) is the standard approach to regulating a first-order sliding mode~(FOSM) in such settings, yet existing designs are largely restricted to scalar sliding variables, and rest on a disturbance-derivative assumption that EL systems violate. In particular, the FOSM dynamics depend on the disturbance and become discontinuous under the step changes in load produced by payload engagement and release, rendering that derivative ill-defined. This study resolves both with a derivative-free generalized multivariable super-twisting framework. The discontinuous sign-function integral term is replaced with a continuous fractional-power term whose dynamics are independent of the disturbance derivative, while the known state-dependent scaling of the perturbation is incorporated into both the control law and the adaptive gain update. A time-shifting barrier function guarantees prescribed-time convergence to a user-specified bound independently of initial conditions, with the design relying only on mass-matrix norm bounds. Simulation and experimental results on a 7-DoF manipulator under actuator saturation are used to validate the proposed scheme.