Locomotion device with castors for moving over the ground, this device including: - a footplate extending primarily in a plane termed the "footplate plane" and on which at least one of the feet of the user is intended to be placed when the device is being used by that user, - at least one castor mechanically connected to the footplate to roll over the ground, this castor being mounted to rotate about a rolling axis parallel to the plane of the footplate and also about a rotation axis perpendicular to the plane of the footplate, - a braking device (80; 152) adapted to exert on the castor a braking torque the amplitude of which varies as a function of a turn angle, the turn angle being the angle between: • a longitudinal axis of the footplate, this longitudinal axis being fixed with no degree of freedom relative to the footplate and contained in the plane of the footplate, and • the orthogonal projection on the footplate plane of the instantaneous direction of movement of this footplate, characterized in that: - the braking device (80; 152) is a controllable electromechanical device adapted to exert a braking torque on the castor that varies as a function of a received braking command, and - the locomotion device includes: • an inertial center adapted to measure a physical parameter representing the turn angle, and • a central unit programmed to establish the braking command as a function of the physical parameter measured by the inertial center and to transmit the established braking command to the braking device so as to exert on the castor a braking torque that varies as a function of the turn angle. - a footplate extending primarily in a plane termed the "footplate plane" and on which at least one of the feet of the user is intended to be placed when the device is being used by that user, - at least one castor mechanically connected to the footplate to roll over the ground, this castor being mounted to rotate about a rolling axis parallel to the plane of the footplate and also about a rotation axis perpendicular to the plane of the footplate, - a braking device (80; 152) adapted to exert on the castor a braking torque the amplitude of which varies as a function of a turn angle, the turn angle being the angle between: • a longitudinal axis of the footplate, this longitudinal axis being fixed with no degree of freedom relative to the footplate and contained in the plane of the footplate, and • the orthogonal projection on the footplate plane of the instantaneous direction of movement of this footplate, • a longitudinal axis of the footplate, this longitudinal axis being fixed with no degree of freedom relative to the footplate and contained in the plane of the footplate, and • the orthogonal projection on the footplate plane of the instantaneous direction of movement of this footplate, - the braking device (80; 152) is a controllable electromechanical device adapted to exert a braking torque on the castor that varies as a function of a received braking command, and - the locomotion device includes: • an inertial center adapted to measure a physical parameter representing the turn angle, and • a central unit programmed to establish the braking command as a function of the physical parameter measured by the inertial center and to transmit the established braking command to the braking device so as to exert on the castor a braking torque that varies as a function of the turn angle. • an inertial center adapted to measure a physical parameter representing the turn angle, and • a central unit programmed to establish the braking command as a function of the physical parameter measured by the inertial center and to transmit the established braking command to the braking device so as to exert on the castor a braking torque that varies as a function of the turn angle.