Solving the Non-Linear Dynamic Equations of Motion of a Variable Curvature Continuum Robot Using Runge-Kutta Method and MATLAB Software - Djeffal, Selman; Mahfoudi, Chawki; Ghoul, Abdelhamid (Journal of Applied Nonlinear Dynamics, 2026)
Continuum robots have remarkably exceeded rigid robots’ abilities for specific tasks, such as the adaptation to twisted paths and their capacity to perform medical surgeries thanks to their flexible structure yet their dynamic modeling are complicated, in particular the highly non-linearity of their equation of motions. To this end, a simplified dynamic model for a variable curvature continuum robot is established and thoroughly developed based on Euler-Lagrange method, namely an approximate formula relating the robot’s each unit is integrated in the dynamic model in order to reduce the number of the generated coordinates in the equation of motions. The equation of motions are figured out using Runge-Kutta method through MATLAB environment. To verify the effectiveness of the developed dynamic model, simulation examples through MATLAB are carried out. The first simulation is dedicated to a spatial single section variable curvature continuum robot, in which the robot is initially tilted from its equilibrium position then released and its behavior (oscillation) is graphically represented based on the equation of motions that are solved by Runge-Kutta method. While the second simulation example addresses the behavior of a variable curvature continuum robot when subjected to a force. It is found that the developed dynamic model properly simulates the behavior of variable curvature continuum robots and the Runge Kutta method can be considered as an effective numerical method to deal with the non-linearity of continuum robot’s equation of motions.