N-Point Polyelliptic Guidance

This work introduces a novel geometric-rule-based guidance strategy that simultaneously uses information from N > 2 reference points to generate a path that passes through convexly placed waypoints. This geometric rule is built on the formulation principle of polyellipses (generalized ellipses with multiple foci), which states that a polyellipse can be realized by maintaining an equal weighted sum of distances from all its foci. The shape of the polyellipse depends on the constants of the weighted sum, and accordingly, a general method is developed to determine these weighted sum constants for the polyellipse to pass through all its foci. A variable gain proportional derivative guidance law is designed for the pursuer to traverse all waypoints by implementing the polyelliptic geometric rule. Implementation requires only the distance between the pursuer and all the waypoints. The efficacy of the guidance strategy is investigated through various simulation scenarios, revealing that the developed guidance law is robust to initial heading and separation errors, as well as to the pursuer dynamics.