基于奇异摄动法的平流层飞艇水平面轨迹优化

摘要

As a low-velocity aircraft,the stratosphere airship has a high sensibility to wind disturbance,so it costs much energy for long distance cruising horizontally against the wind.Aiming at minimum energy con-sumption,a trajectory optimization method for stratosphere airship is proposed by using the singular perturba-tion method.Firstly,the wind field coordinate system is established for converting the process of airship crui-sing to desired destination into a similar optimal interception problem.According to the behaviors of state varia-bles of airship,and using proportional navigation guidance,three time-scale separations are established and the mathematical model of the singular perturbation is set up.Then,analytical solutions are derived by solving the corresponding three sub-problems.Finally,a numerical simulation is carried out.The result shows that the proposed trajectory optimization method is efficient for stratosphere airship and has some certain applications in engineering.%平流层飞艇作为一种低速飞行器对风场干扰具有很强的敏感性，它在水平面长距离逆风巡航时需要消耗较多的能量。针对此问题，提出了一种基于奇异摄动法的最小能量水平面轨迹优化方法。首先建立风场坐标系，将飞艇巡航到目标点的过程转化成类似的最优拦截问题；根据飞艇运动学、动力学状态变量变化的特点，引入比例导引法，将其进行3个快慢时间尺度的划分，建立基于奇异摄动法的数学模型；再分别求解3个不同时间尺度上的子问题，得到解析解；最后，给出了一个仿真算例，结果表明，所提方法是有效的，具有一定的工程应用前景。