A Mathematical Model of the Pneumatic Force Sensor for Robot-assisted Surgery

Restoring the sense of touch in robotic surgery is an emerging need several researchers tried to address. In this paper, we focused on the slave side proposing a pneumatic sensor to estimate contact forces occurring during the interaction between surgical instruments and anatomical areas. It consists of a tiny pneumatic balloon, which, after being inflated, appears near the tip of the instrument during the measurement phase only. This paper presents a mathematical method relating the intensity of the contact force to the variation of pressure inside the balloon. The latter was modeled as a spherical elastic membrane, whose behavior during contact was characterized taking into account both the deformation of the membrane and the compression of the contained gas. Geometrical considerations combined with an energetic approach allowed us to compute the force of interest. The effectiveness of our sensing device has been confirmed by experimental results, based on comparison with a high-performance commercial force sensor.