# A Novel Virtual Sensor for Estimating Robot Joint Total Friction Based on Total Momentum
## 1 Introduction  
In recent years, robotic intelligent control technology has been rapidly developed. The effects of robot joint friction can strongly influence the system control performance, and friction identification and compensation techniques play important roles in robot control applications [1; 2; 3]. Friction can result in 50% errors for some heavy industrial manipulators [4]. Therefore, to achieve a good control performance and high position and velocity tracking accuracy, the friction torque must be adequately determined, and a compensation technique must be employed. Friction identification and compensation are basic issues in motion control, so there is a large body of literature on these topics, only a small part of which is cited here. Some static friction model methods have been proposed, such as the classical Coulomb and viscous model [5; 6; 7]. The main idea of the model is that friction opposes motion and that its magnitude is independent of velocity and contact area. Another classical static model is the Stribeck method [8], in which friction decreases with the increase of velocity in the low-velocity status. When velocity exceeds a threshold, friction will increase with the velocity. Besides, some modified Stribeck methods, such as [PERSON]'s model [9], have also been proposed. However, these static models have all failed to describe the dynamic properties of friction. For this reason, some dynamic friction models were proposed, such as the Dahl model [10; 11], [PERSON] model [12; 13], and LuGre model [14; 15; 16]. Although these models can describe the dynamic properties of friction, the Dahl model cannot describe the static friction and Stribeck effects. Besides, the Bristle model is complex and is inefficient in simulations due to its complexity. Furthermore, it is difficult to identify the friction parameters of the LuGre model. In addition, some friction models that consider temperature have been proposed in [17; 18; 19]. Although these models can describe some features of friction to a certain extent, unknown friction models are extremely complex because friction is related to many factors, such as the relative velocity, displacement, temperature, and material properties of the contact surfaces. Therefore, these model-based methods, both static friction models and dynamic friction models, are relatively inaccurate since they cannot describe the complete friction characteristics. In addition to those friction model-based methods, Proportion-Differentiation control which does not rely on the specific friction models is the earliest way to solve the friction effects [20]. However, high gain coefficients will result in system instability. Besides, some adaptive algorithms [21; 22] and sliding mode control techniques [23; 24] have been used to cope with problems related to friction variations with time, system operating conditions, and other factors. These approaches seem to provide appropriate solutions, but there are two main problems [25] that should be considered. First, some friction parameters in these algorithms are difficult to determine. Second, some system dynamics that depend on the unknown parameters noted above are not measurable. To solve the first problem, an adaptive parameter estimation method [26] was proposed. Recently, reinforcement learning [27; 28], repetitive control [29; 30], fuzzy control [31; 32; 33], and neural network techniques [34; 35; 36] have been applied for friction estimation to identify and compensate for friction by training models based on massive amounts of data, such as joint velocity and acceleration data. However, the real-time performance of such intelligent methods is usually bad and it is difficult to implement them in real applications. In addition, computationally expensive calculations that require extensive and long hours of training can increase the burden on the controller. Furthermore, the fuzzy rules are usually difficult to obtain and fuzzy control effects are not ideal.