Minimum-Time Trajectory Planning for Underactuated Overhead Crane Systems With State and Control Constraints

In this paper, we propose a novel offline minimum-time trajectory planning (MTTP) approach for underactuated overhead cranes. To the best of our knowledge, it is the first optimal solution to the MTTP problem for overhead crane systems, which simultaneously takes into account various constraints, including the bounded swing angle for the payload, bounded velocity, acceleration, and even jerk for the trolley. Different from existing approaches, by means of system discretization and augmentation, the quasi-convex optimization technique is successfully adopted to find the minimum-time solution while satisfying all the aforementioned constraints. Extensive simulation and experiments with comparisons to previously published methods are conducted to show the superior performance of the proposed method. Note that the results derived in this paper also serve as promising guidance in engineering applications, since it provides a performance limit, namely, the possible highest efficiency for automatic or manual operation of overhead cranes.