平流层飞艇上升段轨迹优化的初值选取方法

Initial Value Selection Method of Ascent Minimum-time Trajectory Optimization for Stratospheric Airship

提出了一种平流层飞艇轨迹优化问题中的初值选取及优化求解方法。首先引入平流层飞艇的三自由度模型,综合考虑静浮力模型、气动力模型、附加质量、常值风场、地球自转、大气环境以及反作用力,并对参数处理后给出了归一化系统方程;其次采用直接配点法将轨迹优化问题转换为非线性规划问题,以最小时间为目标函数,加入初始和终端位置约束、飞行过程约束、状态变量上下界及控制率的约束,从而将具体的动力学问题转换为数学求解问题;然后对优化问题初值选取方法进行分析讨论,结合理论分析及工程经验给出了该优化问题的初值选取方法,保证了可行解的快速求解;最终求得时间最优场景的可行解,仿真结果表明平流层飞艇在几乎全程满功率运行的条件下快速完成上升段的放飞过程,该优化初值选取方法有效可行,且能推广至同类优化问题中,极具有理论和工程应用价值。

The initial value selection method of stratospheric airship trajectory optimization is presented.Firstly,three-dimensional dynamics model of stratospheric airship was introduced by the zero net buoyancy model,aerodynamic forces model,added mass,constant wind,rotation of the Earth,environmental model and reactive force,and then the variables were scaled to get a normalized system equation.Secondly,transform this optimization problem into a nonlinear programming problem by using direct collocation method,the minimumtime scene and constraints has been considered to transform this dynamic issue into mathematical issue.Thirdly,discussing and offering the initial value selection method to inform the feasible solution for this optimization.Eventually,the feasible solution was obtained,the results showed that airship finish this fast release under nearly max power condition during the ascent process.In addition,this method can be promoted in solving similar type issue and have a wide range of application prospects.