Model-free adaptive task-space sliding mode control of a Delta robot using a novel reaching law

This paper presents a model-free adaptive sliding mode control for the Delta robot with a novel reaching law for achieving a less conservative sign-function gain and protecting the Delta robot against overloads. A desired closed-loop system with asymptotic stability based on the Lyapunov theorem is proposed to derive the control law. The proposed control system can overcome uncertainties without prior knowledge of the bounding functions. The reaching time is adjusted adaptively to achieve a smooth convergence to the sliding surface, resulting in chattering attenuation. The gradient descent algorithm is utilized for the first time with a novel adaptation rule to estimate the Delta robot inverse Jacobian matrix. Instead of employing a numerical dynamic model, an analytical model is used for the proposed control law, stability analysis, and simulations. A simple, straightforward inverse-kinematics solution based on a geometrical approach is presented. Simulation results demonstrate a superior performance of the proposed reaching law through comparisons.