Analytical and numerical methods for the stiffness modeling of cable-Driven serpentine manipulators

Cable-driven serpentine manipulators have advantages in compact structure, light weight and superior dexterity. They are suitable for applications in unstructured environments. However, the flexibility of the driving cables reduces the manipulator's stiffness and brings concerns on system performances. Therefore, stiffness is a key problem. This paper aims to establish a general framework for studying the stiffness of cable-driven serpentine manipulators. We firstly established the kinematic and static models, and then proposed the analytical and numerical methods to calculate the stiffness matrix. Simulation validations show that the relative difference of the stiffness matrices by the two methods is negligible. But traditional stiffness models that neglect Jocobian matrix's variations and/or use pseudo-inverse calculations could cause large error. Further comparisons show that the analytical method has advantages in accuracy, calculating speed and real-time performance, but requires complex formula derivation. Based on these results, suggestions are given on how to choose the proper method. Lastly, discussions are made on the numerical model's accuracy and the cable control model selection. The proposed methods are useful for the stiffness analyses of cable-driven serpentine manipulators, and could further provide a theoretical tool for structural optimization, deformation compensation, variable stiffness control, compliance control, etc.