Advanced Guidance Laws for Field-of-View and Impact Angle Constrained Engagements

Abstract

This thesis deals with the development of guidance laws for interceptors with seeker field-of-view (FOV) and impact angle constraints. Two classes of guidance problems, namely, field-of- view and impact angle constrained guidance; midcourse guidance of dual pulse interceptors with look angle constraints, are considered in this thesis. In the first problem, decision variables are lateral acceleration commands whereas the second problem has an additional decision variable of second thrust pulse firing time. For the first problem, three guidance laws are proposed using nonlinear control theory. These are (i) Backstepping control based guidance law (ii) Nonlinear mapping based guidance law for three dimensional engagements, and (iii) Partial integrated guidance and control based guidance law. For the second problem, singular perturbation technique is used to derive the guidance law.

First, backstepping control based guidance law is proposed for impact angle and field-of-view constrained engagements in a planar geometry. The kinematic equations governing the problem are modified to strict feedback form for deriving the guidance law using backstepping technique. The look-angle, which is virtual input to the backstepping structure, is designed such that it is within the feasible domain and achieves the desired impact angle. Barrier Lyapunov functionals are used to derive a guidance law to track the virtual input without violating the field-of-view constraints. Further, capturability of the proposed guidance law is analyzed in the relative velocity plane. Simulation results are presented using a constant speed as well as a realistic interceptor model to show the efficacy of the guidance law.

Next, backstepping control based guidance law is further extended to intercept targets in three dimensional space using nonlinear transformation. The interception geometry is controlled by defining impact angles in terms of flight path angles of interceptor and target. The impact angles are related to line-of-sight angles and the problem is converted to line-of-sight angle tracking problem. The state model for the control design is transformed into a new domain using tangent hyperbolic functions to handle the FOV constraints. The look angles which are constrained in the original domain are free from constraints in the transformed domain. Error surfaces are defined in the transformed domain and Lyapunov theory is used to derive the guidance law. Simulation studies performed using constant speed as well as realistic models of interceptor demonstrates the effectiveness of the proposed guidance law for three dimensional engagements.

Approximations considering kinematic look angle may degrade guidance law performance. A partial integrated guidance and control (PIGC) based guidance law is proposed considering look angle without any approximations. A three dimensional engagement geometry and six degree of freedom (6-DOF) model of interceptor are used in the guidance law design. The partial integrated guidance and control uses a two loop architecture, wherein the outer loop generates body rate commands and the inner loop tracks the desired body rates by deflecting the fins. Both the loops are designed using Lyapunov theory. The look angle constraints are accounted for in the outer loop by using barrier functionals in the error surfaces. The guidance law efficiently uses the available look angle freedom to intercept the target with the desired impact angle. Simulation results using the 6-DOF model demonstrate the effectiveness of the PIGC law. Finally, Monte-Carlo studies highlight the robustness of the proposed guidance law against uncertainties in aerodynamic coefficients.

In the last part of the thesis, the problem of midcourse guidance of dual pulse interceptors with look angle constraints is addressed using singular perturbation (SP) technique. This guidance law is applicable in the midcourse phase where the objective is to conserve the kinetic energy to maximize the range. This is achieved by choosing a combination of terminal velocity and flight time as a performance measure. In addition to seeker field-of-view limit, constraints in the optimization problem include minimum dynamic pressure limit arising due to aerodynamic controllability. Using the time scale separation between the state variables, the full order problem is reduced into lower order sub-problems and a closed-form solution for the guidance law is derived. It is shown that the performance of the interceptor is not very sensitive to perturbation of pulse firing time and an offline generated lookup table is used to time the second thrust pulse firing. The proposed guidance law is computationally efficient and its performance is benchmarked with that of pseudospectral based feedback guidance with much lower computational cost. Simulation studies with point mass and 6-DOF model are presented highlighting the accuracy and efficacy of the proposed guidance law.