Three-dimensional terminal guidance law with multiple constraints via high-order lead-angle shaping

To achieve prescribed impact angle or impact time under limited seeker field-of-view (FOV), a three-dimensional (3-D) multi-constraint terminal guidance law based on high-order lead-angle polynomial profile shaping is proposed. The reference profiles of the lead-angle components are modeled as high-order polynomials in the normalized relative-range variable. By imposing initial and terminal boundary conditions, the convergence process from the missile’s initial state to the reference profiles is eliminated and the profiles are reduced to a form with a single tunable parameter, from which the guidance commands driving the missile along the profile are derived. For various impact constraints, a closed-form tuning method for the remaining profile parameters is presented. By incorporating the FOV constraint, an analytical safe set of the shaping parameter and the corresponding reachable region of impact constraints are obtained. Unlike existing approaches, this work provides a general design methodology for arbitrary-order lead-angle profiles along with a theoretical analysis of the constrained reachable region. The proposed guidance law depends neither on model linearization nor discontinuous switching logic and is fully adaptive to varying-speed engagement models. The analytical solution obviates the need for iterative numerical searches and avoids blind initial parameter selection. Finally, extensive numerical simulations, Monte Carlo tests, and comparative studies confirm the effectiveness, robustness, and reduced control effort of the proposed guidance law.