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针对自由飞行条件下的飞行冲突解脱问题,提出了一种基于析取关系直接变换的联立求解方法(DDTSA)。首先在不引入额外辅助变量的情况下,将基于析取关系的安全边界条件变换成易于联立求解的约束条件,使问题的变量和方程个数大幅度减少,从而降低问题的求解难度。然后为保证求解的精度和稳定性,采用基于Radau配置点的拉格朗日插值多项式对微分代数方程组进行离散化处理,继而求解离散化得到的非线性规划问题。最后分别对2架、3架以及4架飞机的冲突解脱问题进行仿真,仿真结果表明与相关文献中的方法相比,该方法具有更高的计算效率并且能够得到更优的结果。
In order to solve the problem of flight conflict free flight, a simultaneous solution method (DDTSA) based on disjunctional direct transformation is proposed. First, without introducing additional auxiliary variables, the security boundary conditions based on the disjunction relations are transformed into the constraints that are easily solved by simultaneous equations. The number of variables and the equations of the problem are greatly reduced, which reduces the difficulty of solving the problem. Then, in order to ensure the accuracy and stability of the solution, Lagrange interpolation polynomials based on Radau configuration points are used to discretize the differential algebraic equations and then to solve the discretized nonlinear programming problem. Finally, the conflict release of two, three and four aircrafts is simulated respectively. The simulation results show that this method has higher computational efficiency and better results than those in the related literature.