Maximum Range computation based on differential flatness for guided bombs

The paper presents an efficient computational method for Maximum Range of guided bombs based on differential flatness. Differential flatness theory is briefly described and original motion model of guided bomb is reformulated by introducing flat outputs. The original states and inputs can be defined in terms of the flat outputs and their derivatives, and all the boundary conditions and path constraints are also mapped into the flat output space. Any curve that satisfies the boundary conditions as well as path constraints is a solution trajectory of the original system. Therefore, maximum range trajectory is planned in the flat output space. Then, the dynamic optimization problem is translated into static optimization one by collocation method. Finally, the computation approach is proved to be feasible and optimal by an initial trajectory integral that the target is set at maximum range.