Optimal planar interception with terminal constraints

In this paper, planar interception laws for maneuvering targets with known trajectories are presented. Optimal interception problems are defined, which include constraints on the initial and final flight-path angles of the interceptor. For cases where the initial flight-path angle can be freely assigned, it is included in the optimization problem. Analytical solutions for the planar interception problems are derived. Numerical examples that demonstrate the optimal trajectories are presented showing also the effect of the interceptor initial flight-path angle on the interception characteristics. It is shown that when the interceptor initial conditions can be optimized superior performance is obtained.