Polynomial-Shaping-Based Three-Dimensional Guidance with Terminal and Field-of-View Constraints

This paper proposes a three-dimensional nonlinear guidance strategy to intercept nonmaneuvering targets from a prespecified direction at a given time of impact. The proposed guidance strategy also ensures the confinement of the seeker’s look angle values within the given bounds throughout the engagement. The motion of the nonmaneuvering target is incorporated in the development of the guidance law using the concept of predicted interception point (PIP). A polynomial-shaping-based technique is employed to shape the line-of-sight (LOS) angles in both pitch and yaw planes between the interceptor and a virtual target at the PIP as a function of the relative range between them. Expressions relating the third-degree LOS polynomials with the given constraints of impact angle, impact time, and FOV bounds are derived. These expressions are then used to subject boundary conditions on LOS polynomials to obtain the desired coefficients. The reference LOS and lead angle values are obtained using these calculated coefficients. A nonlinear dynamic inversion (NDI)-based tracking controller is then designed to track the reference lead angle values, enabling the interceptor to achieve interception of nonmaneuvering targets at the desired impact angle and impact time while satisfying FOV constraints. The development of the proposed guidance strategy restrains the use of linearization or decoupling of coupled engagement dynamics to achieve enhanced performance. Moreover, switching logic and multiphase guidance structures are prohibited to achieve a smooth control profile. The effectiveness of the proposed guidance law is validated using numerical simulations, and a comparison study with an existing strategy is performed to establish its superiority.