Geometric Calibration of Continuum Robots: Joint Space and Equilibrium Shape Deviations

Currently, surgical continuum robots (CRs) are predominantly used as telemanipulators where modeling errors are overcome by the user. Such errors preclude their use for autonomous tasks. In this paper, we investigate the calibration of CRs with specific focus on capturing joint space errors due to homing offsets, assembly errors causing twist about the robot's backbone, and uncertainty in the equilibrium bending shapes of segments of these robots. A kinematic framework focusing on multibackbone CR is presented with emphasis on deriving calibration identification Jacobians. This framework captures the coupling between twist and the equilibrium shapes of a continuum segment as a function of its bending angle. To capture equilibrium shape variations as a function of bending, a homotopy of curves is defined and represented by respective modal coefficients. The estimation of the calibration parameters is cast as a nonlinear least-squares problem. The framework is validated by simulations and experimentally using a single-port access surgery robot. We believe this calibration framework will facilitate semiautomation of surgical tasks carried out by CRs.