The chassis C of the bogie carries two opposed Bissel trucks B1, B2 which, while each supporting one of the two wheelsets of this bogie, are articulated on this chassis C about vertical axes Z. Each Bissel truck is extended, on the opposite side to the wheelset and towards the other Bissel truck, by a head (6a, 6b) bearing an articulation A which controls its pivoting movement. According to the invention, this control articulation A surrounds the pivot (5) of the bogie and is connected, via connecting rods (27), to means (28) detecting the relative angular movement of the bogie C with respect to the chassis V of the vehicle. The means (28) act on the connecting rods (27) in order to pivot the Bissel trucks B1, B2 and to give the geometric axes of rotation G1, G2 of the wheelsets (9) an orientation in which these axes substantially progressively converge towards the centre of the curve of the track.