The kinematics of straight-trajectory forward locomotion has been extensively studied, but the motor strategies used for changing direction have been rarely investigated. We recently found in the mouse that the stimulation of V2a reticulospinal neurons in the gigantocellular nucleus (V2aGRN) leads to locomotor turning. Nevertheless, the complete body movements associated with this induced behavior, and their relevance in the context of spontaneous locomotion, remain underexplored. We address this here, by characterizing and comparing, with 3D motion capture at high spatial and temporal resolution, the kinematics of both V2aGRN-induced and spontaneous turns in freely moving mice. We reconstruct the tridimensional body movements during turning, tracking 22 infrared-reflective markers applied on multiple joints, and generate a dataset by computing biomechanical metrics along three categories. First, we collect global metrics such as body speed, reorientation, and features in the frame of the arena. Second, we compute body axis-based metrics with features regarding the head's six degrees of freedom, the trunk and the tail, in the mouse's frame. Third, we assess limb-based metrics describing the step cycle, such as duty factor, stride length asymmetries, and limb lateralization. Finally, by applying unsupervised clustering in the space defined by these metrics, we categorize the multiple strategies adopted for turning during spontaneous locomotion, and classify V2aGRN-induced turns within these strategies. In all, our results map the kinematic space of spontaneous turning strategies, revealing their diversity, and of V2aGRN-induced turns, revealing their ethological relevance. This work also provides a base to extend the models of quadrupedal locomotion.