A versatile, non-linear and elasto-static stiffness model of articulated industrial robots

Current challenges in robotics are human-robot interaction, light-weight design, and energy-efficient use of robots. Safety for human-robot interaction can be fundamentally established throughout mechanical design using variable stiffness actuators and/or light-weight robotic link design. Also, light-weight design enables energy-efficient use of robots which becomes increasingly important for manufacturing industries. However, decreasing mass of robotic links increases flexibility and, thus, has a negative effect on a robot´s accuracy. In view of absolute position accuracy, an elasto-static robot stiffness model is presented considering mechanical flexibilities of both joints and links. Its intended purpose is the implementation of an analytical stiffness model in the design stage of an articulated robot with six revolute joints. Robot stiffness is modelled based on the concepts of structural analysis and is evaluated and verified with finite element analysis (FEA). Joints exhibit a non-linear and pose-variant stiffness behaviour while links are modelled as soft and flexible structures. The presented method performs accurately, compared to FEA, with an error less than 0.03% while showing the potential of real-time computation suitable for enhanced robot control. Furthermore, a stiffness performance index, the energy of deformation, is adopted. It provides physical correctness contrary to mathematical operators applied to the commonly used Cartesian stiffness matrix and is thus promoted as a suitable metric for robot stiffness assessment. Furthermore, applications are discussed where stiffness modelling might be of great benefit such as robot calibration and various on-site tasks.