Pseudospectral method based time optimal anti-swing trajectory planning for double pendulum crane systems

In practice, an overhead crane system may behave like a double pendulum, which has more unactuated states and is more difficult to be controlled properly. Motivated by this observation, we present a time optimal trajectory planning scheme for double pendulum crane systems, which can yield a global time-optimal swing-free trajectory. Specifically, to facilitate the optimization problem creation process, we first implement some basic transformations on the system kinematics. Then, various constraints, including upper and lower bounds of the two pendulum angles and upper bounds of the trolley velocity and acceleration, are taken into consideration to set up the optimization problem. After that, the Gauss-pseudospectral method (GPM) is utilized to convert the constrained optimization problem into a nonlinear programming problem, which can be solved more conveniently, while the trajectory constraints are also considered during the transformation. By solving the constructed nonlinear programming problem, a global time-optimal result is obtained, which is different from most existing methods. Finally, numerical simulation and experimental results are given to illustrate the satisfactory performance of the proposed method. Copyright © 2016 Acta Automatica Sinica. All rights reserved.