Statics Modeling of Discrete Joint Surgical Probes with Tendon-based Stiffening

Minimally-invasive surgical (MIS) robots can reduce post-operative pain and complications but must be able to follow tortuous paths to reach deep into the body. Our prior work on an MIS robot called the highly articulated robot probe (HARP) achieved follow-the-leader motion using two concentrically driven segmented tubes that alternate between locking and advancing each segment. This paper presents a 3D statics model for the HARP that includes link-to-link friction effects and external loading conditions and enables the maximum admissible external load to be determined for any given robot shape. We investigate how the payload capacity is influenced by both the robot's shape and the actuation tendon forces and validate the statics model experimentally on a prototype HARP platform. Our results across a set of four configurations demonstrate that the proposed model can predict the payload capacity with a mean and max error below 6.1% and 15.8% of the configuration's payload, respectively. The model presented in this paper will enable future design, control, and planning methods with HARP robots to optimize their payload capacity for MIS tasks.