Cueing end‐effector acceleration of a two‐link robotic arm by dynamic averaged sub‐gradient integral sliding mode control

Abstract

AbstractThe primary objective of this research is to determine if the dynamic version of an averaged sub‐gradient (ASG) integral siding mode (ISM) controller can effectively handle the end‐effector acceleration tracking problem for a two‐link robotic arm avoiding singularity conditions. The proposed scheme solves a nonlinear extremum seeking problem that minimizes a non‐strictly convex function that depends on the acceleration tracking error defined by the difference between the desired acceleration trajectory and the cueing end‐effector acceleration of a two‐link robotic arm in a 2D‐plane. A second‐order differential equation drives the proposed dynamic ASG with nonlinear coefficients and a discontinuous right‐hand side term, which allows for the achievement of the necessary ISM regime in the presence of considerable errors in the mathematical model description. A special switch between modes allows the controller to track accelerations even in extreme positions (near to the active boundaries of the joint articulations) effectively.