Peng Haijun, Zhao Haisong, Wang Xinwei, Li Yunpeng
Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, China.
Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, China.
ISA Trans. 2021 Apr;110:71-85. doi: 10.1016/j.isatra.2020.10.044. Epub 2020 Oct 15.
In this paper, we present a polynomial chaos-based framework for the trajectory optimization of an overhead crane system under uncertainty. The main research described in this paper is as follows. First, the deterministic trajectory optimization problem formulation of a two-dimensional overhead crane model is constructed. Based on this basic mathematical formulation, the uncertainty trajectory optimization problem is formed considering the uncertainty of initial state and system parameter. Then, to solve the uncertainty trajectory optimization problem efficiently, a robust trajectory optimization problem formulation is proposed. However, it is difficult to solve the robust trajectory optimization problem directly because it contains stochastic function terms, such as stochastic dynamic equations, constraint functions and objective functions. We consider both the system state and control input as functions of uncertainty and use polynomial chaos expansion to quantify these stochastic functions. An augmented deterministic trajectory optimization problem which can be solved directly is finally obtained. Based on the proposed robust trajectory optimization formation, the motion trajectory optimization of an overhead crane system under two different uncertainty types of is solved. All simulation results are compared with traditional sampling-based Monte Carlo simulations to demonstrate the feasibility and effectiveness of the proposed method.
在本文中，我们提出了一种基于多项式混沌的框架，用于不确定性下桥式起重机系统的轨迹优化。本文所描述的主要研究内容如下。首先，构建了二维桥式起重机模型的确定性轨迹优化问题公式。基于这个基本数学公式，考虑初始状态和系统参数的不确定性，形成了不确定性轨迹优化问题。然后，为了有效解决不确定性轨迹优化问题，提出了一个鲁棒轨迹优化问题公式。然而，直接求解鲁棒轨迹优化问题很困难，因为它包含随机函数项，如随机动力学方程、约束函数和目标函数。我们将系统状态和控制输入都视为不确定性的函数，并使用多项式混沌展开来量化这些随机函数。最终得到了一个可以直接求解的增强确定性轨迹优化问题。基于所提出的鲁棒轨迹优化公式，解决了桥式起重机系统在两种不同不确定性类型下的运动轨迹优化问题。所有仿真结果都与传统的基于采样的蒙特卡罗仿真进行了比较，以证明所提方法的可行性和有效性。
