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%.

柔性机器人具有结构高度柔性、精度高等优点，能够在有限的空间内到达形状复杂、路径曲折的目标治疗部位。因此，柔性机器人形状检测的研究具有重要意义。提出了一种包含扭转补偿的重构方法，并与不包含扭转补偿的数值方法进行了比较。在形状重建过程中，两个相邻测量点之间的微段弧被视为封闭平面中的圆弧和三维（3D）空间中的圆形螺旋。仿真结果表明，两种算法对于二维曲线的表现同样好。对于3D曲线，基于Frenet的扭转补偿重建方法比数值方法具有更高的拟合精度。对于微段弧长为40 mm和20 mm的情况，采用基于Frenet扭转补偿的重构方法，3D曲线的最大相对误差分别降低了11.3%和20.1%。封装网格点的长度为40毫米和20毫米，无基板传感器的感应长度为260毫米。此外，还进行了形状重建实验，传感器的形状重建精度分别为2.817%和1.982%。