Guidance Laws For Impact Angle Constraints And Exo-Atmospheric Engagements
This thesis deals with development of guidance laws for advanced applications. Two class of guidance problems, namely, impact angle constrained guidance and pulsed guidance for exo-atmospheric engagements, are considered here. Three impact angle constrained guidance schemes are developed using (i) Proportional navigation guidance (PNG), (ii) State Dependent Riccati Equation (SDRE) technique and (iii) geometric concepts, respectively. A collision course based pulsed guidance law is presented for exo-atmospheric interceptors. Proportional Navigation Guidance (PNG) law is the most widely used guidance law because of its ease of implementation and efficiency. However, in its original form, it achieves only a limited set of impact angles. A two stage PNG law is presented for achieving all impact angles against a stationary target. In the first phase of guidance, an orientation PNG command is used. The orientation navigation constant (N ) is a function of the initial engagement geometry and has a lower value (N less than 2). It is proved that following the orientation trajectory, the interceptor can switch to N = 2 and achieve the desired impact angle. Simulations, with a constant speed and with a realistic interceptor model, show successful interception of the target with all desired impact angles. Feedback implementation of the guidance law results in negligible errors in impact angle with uncompensated autopilot delays. The idea of a two-stage PNG law with impact angle constraint is further used to develop a guidance law for intercepting moving targets. Following the orientation trajectory, the interceptor can switch to N = 3 and achieve the desired impact angle. It is proved that the guidance achieves all impact angles in a surface-to-surface engagement scenario with receding and approaching targets, respectively. In a air-to-surface engagement scenario, it is proved that the guidance law achieves all impact angles in a deterministic set. Constant speed and realistic interceptor models are used for simulations. Results show negligible error in impact angle and miss distance for moving targets. The guidance law, in its feedback implementation form, achieves the desired impact angle for interceptors with delay and with a maneuvering target. The impact angle errors are low with negligible errors in miss distance. Next, the impact angle constrained guidance problem against a stationary target is solved as a non-linear regulator problem using the SDRE technique. The interceptor guidance problems are of finite time nature. As the main contribution of this part of the work, we solve a finite time interceptor guidance problem with infinite horizon SDRE formulation by choosing the state weighting matrix as a function of time-to-go. Numerical simulations are carried out both for a constant speed interceptor model and a realistic interceptor model. Simulations for both the models are carried out for various impact angles and firing angles. Robustness of the proposed guidance law with respect to autopilot lag is also verified by simulations. Results obtained show the efficiency of the SDRE approach for impact angle constrained missile guidance. A geometric guidance scheme is proposed for lateral interception of targets in a planar engagement scenario in the absence of line-of-sight rate information. A kill-band is defined for target initial positions capturable by an arc maneuver, followed by a straight line path by the interceptor. Guidance law for capturing targets inside the kill-band is presented and is further modified for targets outside the kill-band. Based on analytical studies on the kill-band, a guidance law is proposed for lateral interception of maneuvering targets. Simulations are carried with for typical low speed engagements. The concept of kill-band provides an inherent robustness to the proposed guidance law with respect to uncompensated system delays and target maneuver. As the final part of the work, an interceptor endgame pulsed guidance law for exoatmospheric engagements is derived by using the notion of collision heading. The proposed guidance law is derived in steps by (i) Obtaining the collision heading based on the collision triangle engagement geometry and then (ii) Computing the width of the pulse fired by the divert thruster to attain the collision heading. It is shown that this strategy is more effective than the existing zero effort miss (ZEM) based guidance laws for intercepting targets with higher heading angles off the nominal head-on collision course. A result on pulse firing sequence is also presented showing that firing pulses in quick succession results in minimum pulse widths and hence minimum control effort for a desired miss distance. Simulations are carried out for various engagement scenarios. Results show better miss-distance and divert thrust performance as compared to the existing ZEM based law.