Adaptive sliding-mode control with integral compensation for robotic devices with state constraints

The aim of this study was to design a discontinuous controller with adaptive gains, based on the sliding-mode theory. The adaptive controller solved the trajectory tracking problem for a class of systems with state constraints, specifically for a class of multi-articulated robot manipulator with a constraint work-space. The controller implemented a state dependent adaptive gain that grows in value when the trajectories approach the boundary of the set that characterized the states constraints. The design of the adaptive gain guaranteed the existence of a finite-time stable equilibrium point for a special sliding surface depending on the tracking trajectory error. The specific law used to adjust the gain was obtained by a Lyapunov-based stability analysis. Some numerical simulations proved that the sliding-mode controller showed a superior performance, measured by the mean square value of the tracking result, compared to the non-adaptive gain first order sliding-mode controller.