A time optimal trajectory planning method for offshore cranes with ship roll motions

Abstract

With the fast development of the economy, marine activities are increasing. Due to the advantages of offshore cranes, they are widely used in marine production as effective transportation tools. As a matter of fact, the offshore crane works on the ship known as a typical noninnertial system, which is affected by the ship movement. To tackle this problem, we propose a time optimal trajectory planning method for the considered offshore crane. Specifically, to tackle the couplings between state variables, we show that the offshore crane system is differentially flat with the payload coordinates as the flat outputs. Based on this fact, the planning problems for the jib motion and the rope length are further converted into the planning problems for flat outputs. Then, in order to ensure the trackability of the planned trajectory and improve the safety, we consider a series of physical constraints including the jib luffing motion velocity and acceleration constraints, the rope length varying velocity and acceleration constraints, and the payload swing angle and angular velocity constraints, and then a time optimization problem is further formulated. By utilizing a bisection-based method, the optimal payload transportation time is obtained as well as the corresponding time optimal trajectories. As far as we know, it is the first time optimal trajectory planning method designed for offshore cranes to achieve the fast and accurate payload transportation as well as the payload swing elimination in earth-fixed frame. At last, the effectiveness of the proposed method is verified by simulation tests.