Lie Group Formulation and Sensitivity Analysis for Shape Sensing of Variable Curvature Continuum Robots With General String Encoder Routing

This article considers a combination of actuation tendons and measurement strings to achieve accurate shape sensing direct kinematics continuum robots. Assuming general string routing, methodical Lie group formulation for the these robots is presented. The expressed using arc-length-dependent curvature distributions parameterized by modal functions, Magnus expansion integration used express as product exponentials. tendon length kinematic constraints are solved coefficients configuration space body Jacobian derived. noise amplification index reconstruction problem defined optimizing string/tendon routing paths, planar simulation study shows minimal number strings/tendons needed reconstruction. A torsionally stiff segment experimental evaluation, demonstrating mean (maximal) end-effector absolute position error less than 2% (5%) total length. Finally, compliant demonstrates approach deflections routings. We believe that methods this can benefit design process, sensing, control soft