Analytical Solution for Nonlinear Three-Dimensional Guidance With Impact Angle and Field-of-View Constraints

An analytical 3-D guidance law with impact angle and field-of-view (FOV) constraints considering nonlinear coupled dynamics is proposed. As a stepping stone, the guidance model is transformed to a set of nonlinear differential equations in terms of the relative range variable. To meet the desired impact angles in the pitch and yaw planes, two cubic polynomials including eight coefficients are developed with respect to the relative range for creating reference line-of-sight (LOS) profiles. The unknown coefficients are explicitly solved by initial and terminal conditions on the LOS angles and LOS rates in the mutually orthogonal planes. Then, the analytical 3-D impact angle guidance (IAG) law is derived via formulating the second-order LOS dynamics of the transformed model. Moreover, the relation between the seeker's look angle and the reference LOS profiles is developed, such that the achievable impact angle set can be obtained to handle the FOV limit. Numerical simulations with comparison study and a realistic model are conducted to verify effectiveness and robustness of the guidance law. Its feasibility is additionally validated by applying it to the guidance of unmanned aerial vehicles landing on surface moving carriers.