  We introduce a model of multi-agent dynamics for self-organised motion;
individuals travel at a constant speed while trying to adopt the averaged body
attitude of their neighbours. The body attitudes are represented through
unitary quaternions. We prove the correspondance with the model presented in a
previous work by the three first authors where the body attitudes are
represented by rotation matrices. Differently from this previous work, the
individual based model (IBM) introduced here is based on nematic (rather than
polar) alignment. From the IBM, the kinetic and macroscopic equations are
derived. The benefit of this approach is twofold: firstly, it allows for a
better understanding of the macroscopic equations obtained and, secondly, these
equations are prone to numerical studies, which is key for applications.
