Dual optimization design in formation keeping trajectory of multi UAV

When considering the problem of how to design multi UAV formation keeping optimization model, we combine the kinematic equation of multi UAV, performance index and constrained condition to construct a constrained optimization problem. After some transformation is used in the performance function to decompose the optimization problem, we introduce the Lagrange multiplier vector to construct a Lagrange function of this constrained optimization problem. To obtain the two classes of optimization variables-primal variable and dual variable, we find that all primal variables and dual variables can be formulated to the expressions about one dual variable. Then the gradient projection method from the convex optimization theory is proposed to obtain this dual variable. When this dual variable is solved, all the other optimization variables can also be obtained through simple substitution Finally, the efficiency of the proposed strategy can be confirmed by the simulation results.