Finite Arc Method: Fast-Solution Extended Piecewise Constant Curvature Model of Soft Robots with Large Variable Curvature Deformations

Accurate deformation modeling of soft flexural robots is of high practical importance, especially for high-risk tasks such as surgery. In this study, a new mechanistic model, that is, finite arc method (FAM), for soft robots, for example, tendon-drive, was proposed and validated. First, the catheter was modeled as a finite number of arcs, each with a constant bending curvature, hence the name FAM. Afterward, using a validated Bezier shape approximation, the deformation was parameterized, and the governing equations of the robot were derived. Also, a fast and recursive algorithm was proposed and implemented for the mechanical solution of the robot's deformation. To validate the proposed method, two validation studies were performed. In Study I, the FAM's predicted deformations for eight load cases in each two-dimensional and three-dimensional space on a 40 mm long flexure were compared with the nonlinear finite element method (FEM). In Study II, a representative set of lateral forces on a cardiac catheter (obtained in our previous study) was used to find its FAM-based deformation and was compared with the experimental reference. The error between FAM and FEM deformations was 0.23 ± 0.89 mm with computation times of 3 mseconds (FAM) versus 1244 mseconds (FEM). Also, the error of FAM compared with ground-truth in Study II was 1.41 ± 1.47 mm with a computation time of 7 mseconds. The proposed method showed acceptable performance for the accurate prediction of highly complex large deformations in real time.