Elliptic Guidance

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 the 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 proportional-integral-derivative controller is used to implement the elliptical geometric rule. Nonlinear simulations are performed for an interceptor imposing different impact angles with the same intercept time as well as different intercept times at the same impact angle, both against a stationary target. The effects of initial heading errors and first-order interceptor dynamics are also examined.