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

**Index Terms—**Continuum robots, human–robot collaboration,
Lie group methods, shape sensing, soft robots.


All credit goes to: Power User: Garrison Johnston, Elan Z. Ahronovich , and Nabil Simaan