Interval estimation and optimization for motion trajectory of overhead crane under uncertainty

Abstract

The parameter uncertainty has an important effect on the motion planning of overhead cranes, especially in relation to its industrial safety of production activities. Thus, a novel uncertain estimation-and-optimization strategy is proposed for motion planning of overhead cranes with uncertainty in this paper. The main work of this paper includes the following aspects. First, the overhead crane is simplified as a double pendulum model and the corresponding motion planning is described as an optimal control problem with uncertainty. Second, uncertainties are expressed as interval parameters where only the upper and lower bounds are required without probability information and a bounds estimation problem for optimal control with uncertainty is established; the solution contains all possible values. Third, the bounds estimation problem is solved by a surrogate model-based method, the motion trajectory intervals of overhead cranes are obtained. Fourth, in order to reduce the influence of uncertainty on the motion planning of overhead cranes, an optimization method is introduced to reduce the sensitivity to uncertainty. Finally, the numerical examples show that high accurate interval estimation results are obtained with a reasonable computational cost, and the sensitivity of motion trajectory to uncertainty is reduced obviously with the help of optimization. The proposed strategy provides a guidance for uncertain analysis and online controller design of overhead cranes.