An Input Observer-based Stiffness Estimation Approach for Flexible Robot Joints

This letter addresses the stiffness estimation problem for flexible robot joints, driven by variable stiffness actuators in antagonistic setups. Due to the difficulties of achieving consistent production of these actuators and the time-varying nature of their internal flexible elements, which are subject to plastic deformation over time, it is currently a challenge to precisely determine the total flexibility torque applied to a robot's joint and the corresponding joint stiffness. Herein, by considering the flexibility torque acting on each motor as an unknown signal and building upon Unknown Input Observer theory, a solution for electrically-driven actuators is proposed, which consists of a linear estimator requiring only knowledge about the positions of the joints and the motors as well as the drive's dynamic parameters. Beyond its linearity advantage, another appealing feature of the solution is the lack of need for torque and velocity sensors. The presented approach is first verified via simulations and then successfully tested on an experimental setup, comprising bidirectional antagonistic variable stiffness actuators.