Modeling of Elastic Robot Joints with Nonlinear Damping and Hysteresis

Elastic robot joints gain in importance since the nowadays robotics tends to the lightweight structures. The lightweight metals and composite materials deployed not only in the links but also in the joint assemblies affect the overall stiffness of robotic system. The elastic joints provide the loaded robot motion with additional compliance and can lead to significant control errors and vibrations in the joint as well as operational space. A better understanding of the compliant joint behavior can help not only to analyze and simulate robotic systems but also to improve their control performance. Elastic robot joints are often denoted as flexible joints or compliant joints as well. The former modeling approaches aimed to describe the dynamic behavior of elastic robot joints lead back to Spong (1987). Spong extended the general motion equation of a rigid roboticmanipulator to the case of joint elasticity captured by a linear connecting spring. Remember that the general motion equation derived either from Lagrange or Newton-Euler formalism for a class of rigid robotic manipulators (Sciavicco & Siciliano (2000)) can be expressed as