Ph.D Student Tsalik Ronny Optimal Guidance and Control for Imposing Impact Angle and Time Department of Aerospace Engineering Professor Tal Shima Abstract

This research presents the derivations and investigation of new constrained impact-angle and impact-time guidance concepts. The main contribution of this research is the derivation of new geometric rules to impose impact-angle and impact-time. These

concepts are derived from basic circular and elliptic geometric principles. To implement these new geometric rules, new optimal and nonlinear robust guidance laws were derived.

Initially, we deepen the analysis on the inscribed-angle guidance concept for moving targets. A relation between inscribed angle guidance and parallel navigation is noticed, showing that a collision course can be obtained for a specific constant inscribed angle. The resulting impact angle for the inscribed angle guidance against moving targets is studied and compared to the stationary target case. Closed-form solutions for the intercept trajectories are obtained based on elliptic integrals.

Next, we derive a new linear optimal guidance law for impact angle interception.

The linearization of the non-linear equations of motion is performed around a nominal

circular trajectory, thus allowing the linearization to be valid far from the initial line-of-sight.

The proposed law can be viewed as a generalization of the optimal rendezvous

problem. Closed form expressions for the miss distance, the intercept angle error, and

the control effort are derived for the linear model.

Following, nonlinear robust guidance strategies, based on sliding mode control,

are proposed to impose a pre-specified impact angle against stationary targets. The

guidance strategies are based on the constant inscribed angle geometric rule, and vary

in the type of information needed for their implementation. The guidance design does

not require linearization thus enabling it to perform well in scenarios far

from the nominal ones. Effect of uncertainties on the control effort of guidance strategies is analyzed.

Then, a new guidance concept to impose a desired impact-time is presented and

investigated. The guidance concept is based on the geometrical principle that constraints the interceptor to follow a circular trajectory to the target. The concept is extended for moving targets, varying interceptor speed, and constrained field of view of the interceptor. Application of the guidance concept for stand-off tracking of stationary and moving targets is also demonstrated.

Finally, a new three-point guidance concept for imposing a launch angle, impact

angle, and intercept time against a stationary target is proposed. The guidance concept is based on defining geometric rule of an ellipse. This rule states that for every

point along an ellipse, the sum of the distances to the two focal points is constant. A

general method for finding the desired elliptical trajectory that achieves a desired launch angle, impact angle, and intercept time is presented. Once the elliptical trajectory is determined, the sum of the distances between the interceptor and the two foci is the only information required for implementation. The interceptor's equations of motion are linearized around the desired elliptical trajectory and a PID controller is used to implement the elliptical geometric rule.