Closed-form model speeds up shape prediction for tendon-driven robots
Closed-Form Cartesian Forward Kinetostatics for Spatial Multi-Segment Tendon-Driven Continuum Robots
Robotics
Summary
Predicting the shape of flexible robots pulled by cables usually takes a lot of computer time because it involves solving complex equations repeatedly. The authors developed a new mathematical model that calculates how these robots bend and stretch much faster by providing an explicit formula. Their method works segment by segment without needing slow, repeated computations, while still accounting for how the robot's materials stretch and bend. Tests show their model is very accurate and thousands of times faster than existing methods.
What this means in practice
- •For robotics engineers: Predict the shape of multi-segment tendon-driven continuum robots rapidly to improve real-time control and design iterations.
- •For computer graphics developers: Generate accurate and fast deformations of cable-driven flexible structures for simulation and visualization environments.
Authors
Ke Wu, Fangju Yang, Xiaohui Zhang, Junda He, Guanjun Bao, Jingang Yi, Jian S. Dai
Abstract
Forward kinetostatics of spatial tendon-driven continuum robots typically requires a nonlinear equilibrium solve for each actuation input. This paper develops a force-to-Cartesian-configuration model with a closed-form solution in quadratures for spatial multi-segment robots under tendon actuation. The Cartesian backbone centerline and accumulated material twist serve as generalized coordinates, from which the strain measures and tendon geometry are derived. Variational equilibrium yields explicit axial and bending relations and establishes zero equilibrium material twist within the proposed model for admissible longitudinal non-helical routing. The solution is propagated segment by segment without an iterative equilibrium solve, while retaining axial deformation, spatially varying axial and bending stiffnesses and tendon-routing diameter, and segment-dependent tendon participation. Numerical comparisons with a full-strain geometric variable-strain model (GVS) yield maximum length-normalized tip-position discrepancies of 8.91 x 10^-6 and 1.01 x 10^-5 for the single- and three-segment robots, respectively. Mean evaluation times of 1.52 μs and 2.94 μs, with corresponding speedups of approximately 1864x and 3348x over the baseline, demonstrate the computational advantage of the explicit force-to-configuration mapping in the reported benchmark.