Pure Pursuit of a Target on a Circular Trajectory

This investigation seeks to obtain estimates on the intercept time associated with a fast Pursuer implementing Pure Pursuit against a Target whose trajectory is a circular arc. The analytical solution of the kinematic equations of motion is not feasible and thus the baseline approach for computing the intercept time is numerical simulation, i.e., numerical integration of the kinematics. This method can obtain the intercept time in (essentially) real time for a single Pursuer against a single Target. Here, the goal is to estimate the intercept time using orders of magnitude less computational time. Although not explicitly explored in this work, the purpose of such approximations is to make feasible the rapid evaluation of Pursuer-to-Target assignments in a massive many-on-many engagement scenario wherein the intercept time may be a key measure. Several approximation methods are proposed here and their merits (or lack thereof) are demonstrated through simulation. Ultimately, assuming the Target is not actually turning may be suitable when its turn radius is relatively large, while assuming intercept occurs at the closest point on the turn circle may be suitable when its turn radius is relatively small.

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DOI: 10.2514/6.2024-0956