The capability of grasping and lifting an object in a suitable, stable and controlled way is an outstanding feature for a robot, and thus far, one of the major problems to be solved in robotics. No robotic tools able to perform an advanced control of the grasp as, for instance, the human hand does, have been demonstrated to date. Due to its capital importance in science and in many applications, namely from biomedics to manufacturing, the issue has been matter of deep scientific investigations in both the field of neurophysiology and robotics. While the former is contributing with a profound understanding of the dynamics of real-time control of the slippage and grasp force in the human hand, the latter tries more and more to reproduce, or take inspiration by, the nature's approach, by means of hardware and software technology. On this regard, one of the major constraints robotics has to overcome is the real-time processing of a large amounts of data generated by the tactile sensors while grasping, which poses serious problems to the available computational power. In this paper a bio-inspired approach to tactile data processing has been followed in order to design and test a hardware-software robotic architecture that works on the parallel processing of a large amount of tactile sensing signals. The working principle of the architecture bases on the cellular nonlinear/neural network (CNN) paradigm, while using both hand shape and spatial-temporal features obtained from an array of microfabricated force sensors, in order to control the sensory-motor coordination of the robotic system. Prototypical grasping tasks were selected to measure the system performances applied to a computer-interfaced robotic hand. Successful grasps of several objects, completely unknown to the robot, e.g. soft and deformable objects like plastic bottles, soft balls, and Japanese tofu, have been demonstrated.