Trajectory optimization for guided bombs based on differential flatness

A trajectory optimization scheme is presented based on differential flatness theory. In this scheme, appropriate flat variables are introduced for original trajectory model, and the other states and control input can be expressed in terms of the flat variables and their derivatives. Although the dimensionality is not necessarily to decrease, the flat variables are generally parameterized as polynomials whose higher derivatives are easy to be obtained from lower derivatives and it needs less number of pieces due to flatness property. Hence, the trajectory model can be reformulated in reduced-dimension space. Furthermore, a numerical algorithm is proposed based on collocation method. Since most of differential constraints in dynamic model are transformed into algebraic constraints, less collocation points are required. Finally, both the reformulation deriving and the simulation results validate its efficiency and validity.