A key problem for biological motor control is to establish a link between an idea of a movement and the generation of a set of muscle-stimulating signals that lead to the movement’s execution. The number of signals to generate is thereby larger than the body’s mechanical degrees of freedom (DoFs). A mathematical formulation that provides this link is presented in this paper in the form of a layered, hierarchical control architecture. It is meant to synthesise a wide range of complex 3-dimensional muscle-driven movements (doi: 10.1007/s00422-020-00856-4).