Optimal trajectory for time-on-target of a guided projectile using direct collocation method

The problem of multi-phase trajectory optimization of a guided projectile is studied. The objective of this paper is to determine an optimal steering law for a low lift-to-drag ratio projectile. An optimization performance and path constraint are derived that attempt to control different projectiles which are launched successively impact the terminal target simultaneous. The whole trajectory of each projectile is divided into four phases and formulated as an optimal control problem which is transcribed to a nonlinear programming problem by using Gauss pseudospectral method. The time of flight is chosen as the strictly constraint. Finally, the results illustrate the key features of the optimal trajectory, and demonstrate the effectiveness of Gauss pseudospectral method to trajectory design.