Force Sensing along Continuum Robots using Compliance Matrix and Shape Acquisition

Continuum robots are promising for minimally invasive surgery. They consist of thin and flexible structures whose shape can be continuously deformed using re- mote actuators, allowing them to be inserted in small tubular cavities. For safety reasons, it is important to be aware of the forces applied to surrounding tissue during deployment. Because common force sensors are too cumbersome to be embedded into continuum robots, alternative shape-based force estimation methods have been developed. Such methods estimate the contact location and the corresponding force based on the com- parison between a measured robot shape (for instance using Fiber Braggs Gratings sensors or vision sensors) and the one predicted from robot modeling (typically computed using Cosserat rod modeling and actuator po- sitions [1]). The applied force is then estimated through optimization procedures, with [2] or without [3], [4] explicit knowledge of the force application point. These algorithms have shown promising performance but are restricted to passive Cosserat rods models, whereas in practice continuum robots are active structures. Recently, Aloi et al. extended the work from [4] in the case of a 2- DOF tendon-driven robot, for which they experimentally validated their method [5]. All the previous solutions have two limitations. First, they assume contact forces to be perpendicular to the robot’s curvilinear axis: hypothesis (H1). Since con- tinuum robot shapes can be highly curved, one might question how strongly the tangential component of the force can affect the global deformation of the robot. Second, they consist of iterative optimizations during which the whole robot model is computed at each iteration using convex optimization routines. Such an approach can be computationally time-consuming and does not necessarily yield a global optimum. The present paper introduces a new Compliance-based approach to estimate an external force applied to a continuum robot in any direction. Results obtained with a simulated Concentric Tubes Continuum Robot (CTCR) are presented and discussed.