Efficient Trajectory Planning and Tracking Control for Underactuated Crane

The crane is a typical underactuated plant, which makes the trajectory planning and control to be challenging. To solve this problem, efficient trajectory planning and tracking control methods should be sought. The plant can be reduced in dimension by using reasonable linearization and the differential flatness (DF) method, wherein the state and control variables are represented directly through the flat output (FO). Combined with the pseudospectral method (PSM) wherein multiple constraints are taken into account, the FO reference can be parameterized by using a polynomial. By doing so, it can reduce the degree of freedom to be optimized. To eliminate the adverse effects from the high-order terms ignored in the linearization, the extended state observer is used for deviation estimation and compensation. The closedloop stability can be ensured by using the Lyapunov method. Both numerical simulations and hardware experiments are performed to demonstrate the feasibility and efficiency of the proposed method.