Reconstruction method with twisting measurement and compensation for shape sensing of flexible robots

Flexible robots can reach a target treatment part with a complex shape and zigzagging path in a limited space owing to the advantages of a highly flexible structure and high accuracy. Thus, research of the shape detection of flexible robots is important. A reconstruction method including torsion compensation is proposed, then the method with a numerical method that does not include torsion compensation is compared. The microsegment arc between two adjacent measurement points is regarded as an arc in a close plane and a circular helix in three-dimensional (3D) space during the shape reconstruction process. The simulation results show that the two algorithms perform equally well regarding 2D curves. For the 3D curves, the Frenet-based reconstruction method with torsion compensation produced a higher fitting accuracy compared with the numerical method. For the microsegment arc lengths of 40 mm and 20 mm, the maximum relative errors were reduced by 11.3% and 20.1%, respectively, for the 3D curves when the reconstruction method based on Frenet with twisting compensation was used. The lengths of the packaging grid points were 40 mm and 20 mm, and the sensing length was 260 mm for the no-substrate sensor. In addition, a shape reconstruction experiment was performed, and the shape reconstruction accuracies of the sensors were 2.817% and 1.982%.