A new hybrid optimization intelligence for cable-driven continuum robot motion: two-obstacle simulation and real-data...

Cable-driven continuum robots enable dexterous motion in confined spaces, but inverse kinematics remains difficult because different internal shapes and cable states can produce the same end-effector position.

This study presents a design-aware hybrid optimization framework, DA-IHHO-DELS, for inverse kinematics of a three-section continuum robot. A piecewise-constant-curvature forward model generates physically consistent section positions, cable-length estimates, and feasibility terms. The optimizer combines geometry-consistent seeding, opposition learning, improved Harris hawks search, differential-evolution exploitation, grey-wolf leader guidance, Cauchy/Levy perturbations, and bounded local refinement. Its multi-objective score includes the arc-length consistency residual, orientation error, cable-length dispersion, inter-section smoothness, actuation effort, and constraint violation, and it is compared with GA, ABC, ACO, DE, HHO, TLBO, BOA, GWO, WOA, and POA.

In the regenerated obstacle-constrained simulation, DA-IHHO-DELS achieved a median $F_1$ residual of 0.00491 mm, a median reconstructed Cartesian error of 0.00255 mm, 100% success under the strict $F_1<0.01$ criterion, the lowest median aggregate score, and a mean runtime of 0.56883 s. A secondary benchmark using measured CBHA/Robotino XT actuator lengths further assessed transfer of the geometry-guided optimization consistency to real measured continuum-robot data.

The results show that design-aware hybrid optimization can combine analytical continuum-robot kinematics with robust search to obtain accurate, feasible, and smooth inverse-kinematic solutions. The real-data benchmark supports consistency transfer while remaining distinct from a direct hardware test of the same three-section cable-driven robot.