Modeling and Tracking Control of Underactuated Systems: A 5-DOF Robotic Crane Case Study

The modeling and control of underactuated robotic systems with multiple degrees of freedom (DOF) have been open problems. Using a 5-DOF underactuated shipboard crane as a case study, this article addresses the modeling and tracking control problem in noninertial reference frame. Although considerable progress has been made, most studies establish the dynamic model and designed the control method in the inertia reference frame. However, in certain operating scenarios, some state variables in the inertial reference frame are difficult to measure directly and converting them between the ship-fixed (noninertial reference frame) and the inertial frames may lead to singularity problems. Aiming at these open problems, by using the Lagrange equation of the second kind and the virtual work theory, the dynamic model of a 5-DOF shipboard rotary crane is established in thenoninertial reference framein consideration of ship 6-DOF movements and the offset between the crane mounting position and the ship’s center of gravity. After that, an adaptive neural network (NN)-based nonlinear feedback tracking control method is designed to track the desired trajectory and suppress the cargo swing simultaneously. The closed-loop stability is also analyzed. Finally, the performance of the control method is validated through experiments on a self-made experimental testbed.