Target-centric angle variables in pursuit tracking

Abstract

A method for constructing a dynamic local reference frame centered at the location of a pursuit target is proposed. It uses original fixed reference frame coordinates for three positions: the location of a moving target, the location of a pursuing entity, and a third reference point that defines the instantaneous target trajectory direction. The method involves rigid body geometric operations and creates a consistent local reference frame configuration having its origin at the target location. The local frame also has the target trajectory pointing in the positive x axis direction, and a defined azimuth plane descriptive of the current pursuer location. This plane is determined by a concluding local frame rotation around the set x axis, which specifies a particular y axis direction. If the pursuer position is not on the local frame’s azimuth plane, its perpendicular projection on to that plane serves as an additional position for use in defining angle variables. Three angle variables relevant to the pursuit dynamics (not all mutually independent) are obtained from the three coordinate values of the pursuer position in the local frame: an elevation angle, an azimuth angle, and a bearing angle that basically describes how far off course the pursuer position is from being directly behind the target’s current trajectory path position. To illustrate the method of obtaining these angles and to demonstrate their potential usefulness in characterizing pursuit behavior, example experimental data from a motor control and coordination pursuit task performance are presented and analyzed.