Adaptive Controller Based on Barrier Lyapunov Function for a Composite Cartesian-Delta Robotic Device for Precise Time-Varying Position Tracking

This paper describes the design of an adaptive controller based on a barrier Lyapunov function (CBLF) that solves the trajectory tracking problem of a hybrid robotic structure with an event-driven regulator. The selected robot is a fully actuated Cartesian-delta device composed of 5 Degrees of Freedom (DoFs); the first 2 DoFs correspond to the Cartesian robot, and the last 3 DoFs for the delta device. This adaptive controller considers the state restrictions for the end-effector position and the set of joints. The activation function of the adaptive event-driven controller is defined according to a convergence quality indicator, and its adjustment laws for the control gains were derived using a control barrier Lyapunov function. An experimental test is presented to prove the algorithm performance. The robot tracked the reference trajectories considering that the robot works in two stages; one for the serial and the other for the parallel one. The adaptive scheme a better performance than the proportional- integral-derivative (PID) control.