Minimum-time optimal trajectories for the terminal bunt manoeuvre

This paper focuses on optimal trajectories of a generic cruise missile attacking a fixed target in minimum time. The target must be struck from above, subject to missile dynamics and path constraints. The generic shape of the optimal trajectory is: level flight, climbing, dive; this combination of the three flight phases is called the bunt manoeuvre. The resulting nonlinear optimal control problem is solved in two complementary ways. Firstly, a direct approach based on a collocation method is used to reveal the structure of the optimal solution which is composed of several arcs, each of which can be identified by the corresponding manoeuvre executed and constraints active. The DIRCOL package used in the direct approach produces approximate solutions for both states and costates. Secondly, the indirect approach is employed to derive optimality conditions based on Pontryagin's Minimum Principle. The resulting two-point boundary value problem is then solved via multiple shooting with the BNDSCO package. The DIRCOL results provide an initial guess for BNDSCO. The minimum-time trajectories are computed for several different terminal conditions in order to elucidate the character and quality of solutions.