A grapnel gun is a device the size and shape of a pistol that is capable of launching and retracting a grappling iron and line.
One is first seen employed by the Baron in Volume I  on the Search Engine before getting close enough to reprogram it. Later, Veilchen uses one in Volume VI  to escape the oubliette, and Violetta uses one in Volume VIII to escape, with Agatha, a Devil Dog. In Volume X,Zola pulls one out to escape from Lucrezia's "Death Trap" but later abandons it, having used it to break a descent rather than to ascend.
Violetta is known to be a Smoke Knight while Zola is known to have received the training as well (as has Tarvek). Along with a number of other similarities between Violetta and Veilchen, the use of the gun leads to the speculation that Veilchen is also a Smoke Knight, with the gun being standard-issue. However, given that the Baron had one, and Sturvin seemed to think he could get one, they are obviously not unique to the Smoke Knights. On the other hand, the Baron's was of a different make (it went "POF!" rather than "choff") and gave no indication that the gun would have been able to retract the line with the force necessary to lift his weight.
Thus far, the grapnel gun has not been named in the comic; the closest direct reference is when Sturvin says,
Possibly relevant outside information Edit
The energy required to lift 50kg — one small adult human — a height of 20m in a gravitational field of 10m/s² is at least 1000J; to do so in less than 2s requires at least 500W of power (⅔hp). One modern brushless DC motor (designed for radio-controlled airplanes) weighing 450g and having a diameter of 63mm can deliver 1.7kW for up to 15 seconds. Combined with an appropriate battery — a suitably large array of small cells — it's conceivable that the retraction feature could fit into the depicted device.