  Twisted skyrmions, whose helicity angles are different from that of Bloch
skyrmions and N\'eel skyrmions, have already been demonstrated in experiments
recently. In this work, we first contrast the magnetic structure and origin of
the twisted skyrmion with other three types of skyrmion including Bloch
skyrmion, N\'eel skyrmion and antiskyrmion. Following, we investigate the
dynamics of twisted skyrmions driven by the spin transfer toque (STT) and the
spin Hall effect (SHE) by using micromagnetic simulations. It is found that the
spin Hall angle of the twisted skyrmion is related to the dissipative force
tensor and the Gilbert damping both for the motions induced by the STT and the
SHE, especially for the SHE induced motion, the skyrmion Hall angle depends
substantially on the skyrmion helicity. At last, we demonstrate that the
trajectory of the twisted skyrmion can be controlled in a two dimensional plane
with a Gilbert damping gradient. Our results provide the understanding of
current-induced motion of twisted skyrmions, which may contribute to the
applications of skyrmion-based racetrack memories.
