Tactile data processing method for the reconstruction of contact force distributions

• The ill-posed problem of force reconstruction from tactile sensor data is defined.
• The Boussinesq approach has been used as a discretized Green solution.
• An optimization procedure accounting for the physical constraints is introduced.
• FEM simulations validate the algorithm for Hertzian and non-Hertzian contacts.
• The proposed method is general as to contact shapes, applied forces, sensor types.

The main task of robotic skin is recognition of tactile stimuli acting on the surface of a soft elastic layer through the outputs of embedded sensor arrays. The focus of this work is the development of an algorithm for estimating the spatial distribution of contact forces as well as their intensities and directions starting from sensor data. This requires the solution of an inverse problem where only incomplete information (e.g. normal stress on the sensors) is usually available. The proposed method discretizes external forces at the nodes of a grid. The more practical solution is fixing the node number equal to the number of sensors. In this case, the inverse problem of retrieving the force distribution from sensor data is trivially solved if normal forces are applied. For multi-component force distributions, on the other hand, the problem is in principle ill-posed. A solution is achieved through an optimization procedure accounting for the physical features of the problem by the use of the Moore–Penrose pseudo-inverse matrix and of a vector depending on two continuous and adjustable scalar parameters. The algorithm has been tested on simulated single-contact problems (both Hertzian and non-Hertzian normal force distributions) with encouraging results for both accuracy and robustness of the solution.