A Metric for Planar Displacements

Metrics, which facilitate the measurement of parameters such as “distance ” and “length ” are used frequently in rigid body guidance problems. Commonly used metrics have a characteristic of being dependent on the choice of fixed or moving reference frame and the units used. Most motion synthesis algorithms require some notion of the “distance” between two desired locations1. The metrics in Euclidean space depend on the coordinate frame and units used. A metric independent of these choices is desirable. In this paper we present a metric which is independent of the choice of fixed coordinate frame