# A Novel Virtual Sensor for Estimating Robot Joint Total Friction Based on Total Momentum
## 5 Discussion and Conclusions  
In this paper, the total generalized momentum concept was introduced for the first time to design a virtual sensor for observing robot joint total friction torque, including both motor-side and link-side friction, without joint torque sensors. The advantage of the proposed algorithm is that a complicated friction model is not needed, and only a robot joint dynamics model is needed. By compensating for the observed friction with the controller, the controller performance, especially the velocity performance, was improved in low-velocity conditions. To validate the proposed method, simulations with a 2-DOF manipulator and experiments based on a single-joint system were conducted. The simulation results show that the virtual sensor can accurately estimate the desired friction disturbance by selecting the appropriate gain coefficient \(K_{\mu}\). A large \(K_{\mu}\) made the observed results more precise; however, a large \(K_{\mu}\) value is not appropriate under all conditions. Too large a \(K_{\mu}\) value can increase the amount of noise in an estimation and reduce the estimation accuracy. The experimental results show that the velocity step response of the controller can be improved by 6-10 ms for low-velocity motion and 1-3 ms for high-velocity motion after observed friction compensation. In addition, an appropriate gain coefficient \(K_{\mu}\) can be obtained by comparing the velocity step response times in the experiments. The velocity tracking performances without payload were improved by up to 33.1% for low-velocity motion and \(-1.2\%\) for high-velocity motion, respectively. When the link payload was considered, the velocity tracking performances were improved by up to 9.8% for low-velocity motion; however, they displayed a value of \(-3.0\%\) for high-velocity motion because of inaccurate friction estimation and compensation. Besides, the improvement in the position tracking performance of the controller was less than that for the velocity tracking performance in the experiments and the explanation for this has been given above. In addition, the velocity step response and velocity tracking performance of the controller improved more at low velocities than at highvelocities in the experiments because more uncertainties, such as model error and noise, affect the performance of the virtual sensor and controller at high velocities. Furthermore, the results of the comparison experiments show that the proposed method can obtain more accurate friction torque estimation than the classical Coulomb and viscous friction model. Finally, it should be noted that although the method is only simulated for a 2-DOF robot and tested based on a single-joint system, the proposed method can be extended to multi-joint robots. The observed total friction torque in the algorithm is only compensated for by classical inverse dynamics control in this paper. However, impedance controllers have been increasingly used in cooperative robots and compliant motion control. Therefore, the trajectory performance might be improved and compliance guaranteed with an impedance controller by compensating for the total joint friction observed by the algorithm. In addition, the proposed method was only tested for a single-joint system. Therefore, we will apply the algorithm to multi-joint robots with impedance controllers developed by our laboratory in the future. The simulation and experimental data are available online at [[https://share.weiyun.com/5](https://share.weiyun.com/5) kVakNh]([https://share.weiyun.com/5](https://share.weiyun.com/5) kVakNh). Conceptualization, T.X. and J.F. ; methodology, T.X. ; formal analysis, T.X. and Q.F. ; validation, T.X., J.F., and S.W. ; data curation, T.X., Q.F., and S.W. ; writing--original draft preparation, T.X. ; writing--review and editing, T.X., Y.Z., and J.F. ; supervision, J.Z. ; project administration, J.F. and J.Z.