  In this paper we discuss the applications of knotoids to modelling knots in
open curves and produce new knotoid invariants. We show how invariants of
knotoids generally give rise to well-behaved measures of how much an open curve
is knotted. We define biframed planar knotoids, and construct new invariants of
these objects that can be computed in polynomial time. As an application of
these invariants we improve the classification of planar knotoids with up to
five crossings by distinguishing several pairs of prime knotoids that were
conjectured to be distinct by Goundaroulis et al.
