A homotopy method for guided bomb's optimal glide problem

Development of feasible and precise methods for calculating guided bomb's optimal trajectory has been a traditional and challenging task. The inherent difficulty arises from significant nonlinearity of trajectory model, limited control inputs and various constrained states. And most conventional direct and indirect methods are very sensitive to the initial guess that needs much experience. This paper presents a homotopy method to overcome initial guess problem by constructing a homotopy trajectory using maximum lift-drag ratio control. The method reaches smoothly the original optimal problem by regulating a continuation parameter. And the deriving process is described for homotopy trajectory which is easy to gain for any given initial states. Finally, the simulation results validated that the global optimization solution can be caught faster and the approach can be easily expanded in trajectory optimization.