# A Novel Virtual Sensor for Estimating Robot Joint Total Friction Based on Total Momentum
## 1 Introduction
Recently, torque sensor-based methods [37; 38; 39] have been used to solve the problem of robot joint friction. In these methods, torque sensors are fixed at the robot joints to measure torque. The torque sensor reading data contain friction torque and friction does then not need to be considered in the robot dynamics equations. Although this method does not need to consider a friction model and has good control effects, the cost of torque sensors is expensive and it is also difficult to fix these sensors in a robot. Besides, it can also increase the difficulty of robot wiring. Disturbance observers [40; 41; 42], which are also not based on a particular friction model, have been typically used in robotics control and have generally displayed a good practical performance in recent years. The principle of the disturbance observer is to establish the nominal model of the robot object, and various disturbance torques, including friction, are then obtained from the output residual between the actual model and the nominal model. Specifically, in [40], a friction observer was designed that was inspired by momentum-based collision detection algorithms [43; 44; 45]. In the friction observers, friction is regarded as an external disturbance. However, this approach only considers the motor momentum and the motor-side friction, and the relation between link-side momentum and link-side friction is not taken into account. In addition, joint torque sensing devices are needed in the aforementioned friction observer. Recently, a sensorless friction observer based on generalized momenta was proposed for an elastic joint robot [46]. However, this approach also failed to consider the link-side momentum and link-side friction. In this paper, a virtual sensor is developed to estimate the total friction torque of robot joints, which is based on the concept of total momentum considering both motor momentum and link momentum without joint torque sensors. The advantages of this method are that a complicated friction model is not required and only a joint dynamics model is needed. In addition, this approach does not require the acceleration signals and does not need to solve the inverse of the inertia matrix. Moreover, there is only one simple diagonal gain coefficient matrix to adjust in this algorithm, thereby avoiding excessive and complex parameter adjustment and yielding a practical method. The main contributionsof this paper are as follows: (1) To the knowledge of the authors, it is the first study to introduce the total momentum concept to estimate the total joint friction, including both the motor-side friction and link-side friction; (2) a simple and fast manual tuning rule is introduced to adjust the gain coefficient of virtual sensors during the experiments; and (3) the joint torque sensors in the proposed algorithm are not needed because the motor torque is estimated by the current in our developed driver. The paper is organized as follows. Section 2 describes the theoretical derivation process of the virtual observer for robot joints and proves the whole system stability. Section 3 sets up a 2-DOF planar manipulator simulation, and the simulation results are analyzed in detail. In Section 4, velocity step experiments, sinusoidal trajectory tracking experiments, and payload experiments are conducted to verify the effectiveness of the proposed algorithm for a single-joint system. Finally, the discussion and conclusions are given in Section 5.