Abstract: Annotating unlabeled motion captures plays an important role in Computer Animation for motion analysis and motion edition purposes. Locomotion is a difficult case study as all the limbs of the human body are involved whereas a low-dimensional global motion is performed. The oscillatory nature of the locomotion makes difficult the distinction between straight steps and turning ones, especially for subtle orientation changes. In this paper we propose to geometrically model the center of mass trajectory during locomotion as a $C_1$-continuous circular arcs sequence. Our model accurately analyzes the global motion into the velocity-curvature space. An experimental study demonstrates that an invariant law links curvature and velocity during straight walk. We finally illustrate how the resulting law can be used for annotation purposes: any unlabeled motion captured walk can be transformed into an annotated sequence of straight and turning steps. Several examples demonstrate the robustness of our approach and give comparison with classical threshold-based techniques.