Abstract: Uncertain factors make the crane deviate from the predetermined trajectory, which leads to serious security accidents. In order to investigate the impact of uncertainty on the crane movement in the stage of trajectory planning, an uncertain method based on interval model is proposed. Firstly, uncertainty is described by interval model and an uncertain trajectory planning problem in the forms of interval is established.Then,a symplectic pseudospectral methodis used to sample and Chebyshev surrogate model method (CSMM) is proposed to approximate the original trajectory planning. The uncertain interval results are obtained by scanning surrogate model. In numerical examples, the intervals of crane movement trajectory are obtained by the proposed method and the impact of uncertain level on crane movement trajectory is analyzed.Compared with other methods, the proposed method has characteristic of low computational cost and satisfactory accuracy.The intervals of crane movement trajectory under uncertainty can be obtained via the proposed method, the impact of uncertainty on crane movement is intuitively expressed,which offer the reference for stability and robustness of the crane system.

Key words: crane, interval uncertainty, optimal control, surrogate model, trajectory planning