Dynamical model for Parallel Continuum Robots using the Cosserat rod theory

Parallel continuum robots are new structures that have enormous advantages in terms of safe human-machine interaction, the possibility of miniaturization, or lower weight, but there are still areas that need to be explored further. One of these is dynamics. There are plenty of static models of parallel continuum robots, but few are studying their dynamics. The purpose of this work, therefore, is to create a dynamic model for parallel continuum robots that will be fast and accurate, so that it can be used for real-time applications. To create a model of the robot, the flexible elements need to be modelled. To do this, it was decided to apply Cosserat's theory of elasticity. From this model, partial derivative equations are obtained. To solve numerically the equations is used an algorithm composed of three loops one inside the other. The most internal is used for integration in space. The central one contains the optimization algorithm. The algorithm starts from a guessed result, iterating it changes the value of the guessed until the boundary conditions are met. Finally, the outermost loop is used to advance in time. Three different simulations have been performed, with a cantilever rod, with a Stewart-Gough continuum robot, and with the Triskele-bot, a continuum parallel robot developed inside the Femto-st laboratory. They are performed in order to understand how the simulation parameters affect the results, how big is the noise due to the simulation, and if the model is valid for both forward and inverse dynamics. Finally, trying to validate the model two experiments are performed with the Triskele-bot. In the first one, an external force was applied to the robot and after it was released. In the second one, a step input is given with the actuators. They are made to observe the free oscillation of the robot.