Effect of Path History on Concentric Tube Robot Model Calibration

INTRODUCTION A variety of models have been developed to describe the kinematics of concentric tube robots [1,2]. While some of these are based on mechanics-based modeling [1], others employ parametric [1] and nonparametric [2] models. Almost all modeling attempts neglect historydependent effects, i.e., the dependence of robot shape and tip location on prior motion. Physically, these effects can arise from phenomena such as friction and hysteretic stress-strain. Furthermore, such state dependency has been observed experimentally. While the neglect of these effects may be justifiable in order to simplify and speed kinematic computations for real-time control, it is worthwhile to understand the effect of unmodeled state dependency on the accuracy of state-independent models. Consider the three-tube robot in Fig. 1 that consists of a proximal pair of tubes that rotate, but do not translate with respect to each other and a distal tube that can rotate and translate with respect to the proximal pair. The robot configuration (neglecting rigid body displacements) can be defined by two relative rotation angles and one translation. Considering only the two rotations, a specific configuration can be approached from four angular “directions,” which actually result in four robot tip positions for the same configuration.