Marker-free algorithm reconstructs continuum robots with sub-millimeter accuracy in 0.5s

Continuum robots—slender, flexible manipulators used in aerospace, inspection, automation, and minimally invasive surgery—are notoriously difficult to model from physics alone. Measuring their deformed shape accurately is critical for validating models and building reference datasets, but traditional approaches rely on manual photogrammetry or attaching physical markers, which is tedious and can interfere with the robot. A team led by Matthias K. Hoffmann has now published a marker-free solution that fits a parametric 3D curve directly to image pixels using an optimization-based shape-registration algorithm within a photogrammetric pipeline.

The method requires no prior knowledge of where the robot appears in each image and automatically matches reconstruction points to robot pixels. In simulation, it swept across 10,645 configurations and stayed within 1mm (0.67% of robot length) of ground truth for most cases—a strong showing given the robots' slender, highly curved shapes. On real concentric-tube continuum robots, the algorithm agreed with ten discrete manual photogrammetric measurements across 18 configurations, while replacing the manual process with an automated pipeline running in roughly 0.5 seconds per configuration. The updated paper also includes a comparison with differentiable rendering. By cutting measurement time from minutes to half a second and eliminating markers, the approach promises to accelerate model validation and enable continuous shape feedback for control in confined, occlusion-prone environments.