Identification of General Stress-Strain Relations for Continuum Joints with a Robotic Manipulator

Abstract

Since continuum robotic elements are compact and highly robust, they are suited for a broad range of potential applications, and are correspondingly the subject of active and increasing research interest. An important part of the research is the development of models describing the behavior of elastic soft continuum mechanisms (ECM). These models are needed for the design and the simulation of an ECM, as well as for controlling it in later applications. One approach to obtain a precise model is to develop it based on a continuum mechanical beam model, which includes stiffness parameters describing the stress-strain behavior of the ECM. In this thesis, a tendon-driven ECM made of silicone modelled as a Timoshenko beam is considered. A method is developed where the stress-strain parameters are excited independently for experimental identification. An independent excitation of one stress-strain parameter is achieved when a force in only one axial direction or a torque around only one axis along the entire beam is applied. Since in the experiment a position-controlled robotic manipulator is used to deform the ECM, it is challenging to find deformations of the ECM that induce the desired load. For the axial, torsional and bending stiffness a suitable deformation can be found. The shear stiffness cannot be identified with the experimental setup used. A six-axis force-torque sensor is used to measure the applied load while the deformation of the ECM is measured by an optical measurement system. The identification process is implemented in an automated way to control the robotic manipulator and to take the required measurements. For the control of the robotic manipulator a joint level controller and a Cartesian impedance controller are used. The final identification of the stiffness parameters, based on the assumption that they are constant along the length of the ECM, is conducted using linear regression. The identification is performed for three ECMs of different hardness and afterwards it is evaluated how well a linear approximation fits for each stiffness parameter. The stiffness parameters of the hardest ECM are the worst to approximate linearly with an accuracy of more than 10%. The other two ECMs provide an accuracy in the range of 1.21% and 9.82% for all stiffness parameters. Furthermore, the identified parameters are provided with an estimation of uncertainty with respect to measurement inaccuracy.