Optimal trajectory synthesis for terrain-following flight

A methodology for optimal trajectory planning useful for the nap-of-the-Earth guidance of helicopters is presented. This approach employs an adjoint-control transformatio n together with a one-dimensional search scheme for generating the time-terrain masking optimal trajectories. The trajectory planning problem bears a striking resemblance to the classical Zermelo's problem in the calculus of variations. In addition to being useful for helicopter nap-of-the-Earth guidance, the trajectory planning solution is of interest in several other contexts, such as robotic vehicle guidance and terrain-following guidance for cruise missiles and aircraft. A distinguishing feature of the present research is that the terrain constraint and threat envelopes are incorporated into the vehicle equations of motion. Second-order necessary conditions for this problem are examined.