基于Hamilton-Jacobi方程的飞行器机动动作可达集分析

Reachability Calculation for Aircraft Maneuver Using Hamilton-Jacobi Function

为了给驾驶员完成标准机动动作提供决策支持,提出一种使用哈密尔顿–雅克比(Hamilton-Jacobi)方程求解机动动作可行状态空间的研究方法.使用关键点将机动动作划分为不同阶段,将各关键点的标准状态约束作为目标集,逆时间求解目标集对应的可达集得到各阶段的边界状态范围,目标集和可达集均由零水平集表示.使用该方法得到斤斗动作三维度运动模型下各阶段的可达集及斤斗动作的可行状态空间,为了使运动模型的控制量与驾驶员实际操纵更为接近,构建了以迎角变化率为控制量的四维度运动模型,在此基础上对斤斗动作各阶段的可达集进行了分析.

To help the pilots make decisions for aircraft maneuvers, a reachability analysis method using Hamilton-Jacobi partial differential equation is proposed in this paper. The aircraft maneuver is divided into several phases based on the key points. The restricted set of aircraft states at each key point is seen as the target set, and then a reachable set can be obtained by solving the Hamilton-Jacobi partial differential equation. The target set and the reachable set are both described by zero level set. For the three dimensional dynamical model of the aircraft, the reachable set of each key point and the feasible state space of the whole loop maneuver have been achieved. In order to make the analysis results more easy to use in practice, a four dimensional dynamical model of the aircraft which takes the rate of the angle of attack as the control parameter is formulated. Based on the four dimensional dynamical model, the reachable set is analyzed by means of the proposed method.