Reduced Cartesian Kinetostatics for Tendon-Driven Continuum Robots: Residual-Stabilized Full-Shape Propagation

What happened

arXiv:2609.31771v1 Announce Type: new Abstract: Many planning and control tasks for tendon-driven continuum robots (TDCRs) require the complete Cartesian backbone geometry. Residual correction suppresses propagation drift across the tested step sizes while adding only about 0.98% to the mean update time of uncorrected Euler.

The proposed method requires 0.508 ms per update on average, approximately 11 times faster than pointwise GVS solves. The backbone is represented by two global position fields.

Following exact variation, a Taylor-Galerkin reduction condenses prescribed spatial properties and distributed loads into offline moment vectors, yielding analytic reduced residuals and Jacobians without online spatial quadrature or numerical differentiation. Analytical differentiation and residual correction yield first-order rate systems requiring one fixed-dimensional linear solve per rate evaluation after initial equilibrium alignment on a regular branch.

Key facts

• Residual correction suppresses propagation drift across the — tested: step sizes while adding only about 0.98% to the mean update time of uncorrected Euler
• The proposed method — requires: 0.508 ms per update on average, approximately 11 times faster than pointwise GVS solves