多无人机编队保持轨迹的对偶优化设计

Dual Optimization Design for Multi-UAV Formation Keeping Trajectory

考虑多无人机编队保持优化模型的设计问题,联合多无人机的运动学方程、性能指标及其约束构成一个约束优化问题。通过对指标函数的某种线性变换达到解耦的效果,引入拉格朗日乘子矢量构造该约束优化问题的拉格朗日函数。对于对偶问题中出现的两类优化变量——基变量和对偶变量,将所有基变量和对偶变量全转化为某一个对偶变量的关系式。对于该对偶变量求解,采用凸算法中的梯度投影策略,通过简单的代入运算可得到其他优化变量的数值。最后用仿真算例验证了该方法的有效性。

To the problem of how to design a multi-UAV formation keeping optimization model,we combined the kinematic equation of multi-UAV,performance index and constrained condition together to construct a constrained optimization problem.After transformation was made to the performance function to decouple the optimization problem,we introduced the Lagrange multiplier vector to construct a Lagrange function.To the two classes of optimization variables,the basic and dual variables,we found that all the basic and dual variables could be formulated to the expressions of one dual variable.Then the gradient projection method from the convex optimization was proposed to solve this dual variable.And the other optimization variables could also be obtained through simple substitution.Finally,the effectiveness of the proposed strategy was confirmed by the simulation example results.