Kinetostatic Modeling of Soft Robots: Energy-Minimization Approach and 99-Line MATLAB Implementation

Soft robots have received a great deal of attention from both academia and industry due to their unprecedented adaptability in unstructured environment and extreme dexterity for complicated operations. Due to the strong coupling between the material nonlinearity due to hyperelasticity and the geometric nonlinearity due to large deflections, modeling of soft robots is highly dependent on commercial finite element software packages. An approach that is accurate and fast, and whose implementation is open to designers, is in great need. Considering that the constitutive relation of the hyperelastic materials is commonly expressed by its energy density function, we present an energy-based kinetostatic modeling approach in which the deflection of a soft robot is formulated as a minimization problem of its total potential energy. A fixed Hessian matrix of strain energy is proposed and adopted in the limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, which significantly improves its efficiency for solving the minimization problem of soft robots without sacrificing prediction accuracy. The simplicity of the approach leads to an implementation of MATLAB with only 99-line codes, which provides an easy-to-use tool for designers who are designing and optimizing the structures of soft robots. The efficiency of the proposed approach for predicting kinetostatic behaviors of soft robots is demonstrated by seven pneumatic-driven and cable-driven soft robots. The capability of the approach for capturing buckling behaviors in soft robots is also demonstrated. The energy-minimization approach, as well as the MATLAB implementation, could be easily tailored to fulfill various tasks, including design, optimization, and control of soft robots.