Passivity-based adaptive trajectory control of an underactuated 3-DOF overhead crane

This paper presents a robust passivity-based adaptive control method for payload trajectory tracking of a three degree-of-freedom overhead crane with a varying-length rigid hoist cable. A reformulation of the overhead crane's equations of motion is used and an adaptive control law is developed to ensure the system has an output strictly passive (OSP) input-output mapping. The Passivity Theorem is used to prove that the closed loop system is input-output stable when an OSP negative feedback controller is implemented. Convergence and boundedness of the payload trajectory tracking error is proven with two candidate OSP feedback controllers, including a constant gain and a strictly positive real (SPR) controller. Numerical simulations and experiments are performed with the proposed control method and two state-of-the-art control laws from the literature. The results demonstrate the practicality of the proposed control method and the improved performance of the proposed SPR controller in the experiments compared to the controllers from the literature.