Due to technological development, robotics applications are growing in many industrial sectors and even in applications such as medical ones (micro manipulation of internal tissues or laparoscopy) or in entertainment (special effects in cinema). Robotic devices with high performance in precision and speed are required for all these advanced functions. Through a new approach to the study of robotic manipulation this paper presents some constructive matrices
structures which can be used to design force controllers. It is based on the well{known geometric control of system dynamics. In such a framework some typical problems in robotics can be mathematically formalized and analyzed. A generalized linear model is used and a careful analysis is made. The main result consists of proposing an explicit new matrices structure for grasping internal forces.