Averaged sub-gradient integral sliding mode control design for cueing end-effector acceleration of a two-link robotic arm

Acceleration tracking is a significant problem in aeronautics, automotive, and biomedical technical areas because its solution may yield effective simulation of motion cues. In the case of aeronautics, the proper solution for the tracking problem improves the in-flight simulations for the training of plane pilots. These simulators can be set up using robotic devices that develop controlled motions with the end-effector following the required three-dimensional reference accelerations robustly. Hence, the primary goal of this study is the effective application of the integral sliding mode controller to solve the acceleration tracking problem for the end-effector of a two-link robotic arm. The control design problem is formulated as an optimization of a convex (non-strict) performance functional depending on the difference between the acceleration of the robotic arm and the desired acceleration using the averaged sub-gradient (ASG) descendant method. A novel sliding surface considers the sensitiveness threshold for acceleration dynamics, inspired by the limit of detection in the pilot vestibular apparatus. The proposed controller was analyzed in terms of the finite-time convergence of the sliding surface and the practical stability analysis for the tracking error dynamics. Our main contribution is the design of the online averaged sub-gradient optimization controller based on integral SMCs. The controller solves the end-effector acceleration tracking for a two-link robotic arm, which implements a simplified version of a flight simulator that is considered to be operated under uncertain scenarios and assumes the presence of perturbations and modeling errors. The controller considers the case of incomplete knowledge of the robotic arm model, which adds an extra degree of robustness to the control design.