# Application of External Torque Observer and Virtual Force Sensor for a 6-DOF Robot
## 2 Related Research  
This paper aims to establish a position and force hybrid controller for the arm. To achieve this, an accurate dynamic model of the mechanical arm needs to be established. Traditional dynamic models are established using Lagrangian Mechanics or Newton-Euler Equations [1; 2; 3; 4; 5]. The accuracy of identifying unknown parameters is ensured through the design of excitation trajectories. Among the many parameter identification methods, the weighted least squares method and the extended Kalman filtering method are two commonly used methods. Ref. [1] compares these two methods and states that the parameter estimation of the two methods is very similar. However, the extended Kalman filtering algorithm has a longer convergence time and is highly sensitive to initial conditions. Refs. [2; 3] propose parameterization and optimization criteria for excitation trajectories, which ensure the average nature of time-domain data and effectively measure noise. Ref. [4] introduces the artificial bee colony algorithm for estimating unknown parameters and verifies the dynamic model's ability to estimate the torque of the mechanical arm. The results show that the correlation coefficient between the predicted torque of the first axis and the actual torque is 0.9272. Ref. [5] obtains the best approximate solution using the newly established unknown parameter approximation method and compares it with the least squares method. The results show that it is superior to the least squares estimation method. Ref. [6] improves the cuckoo search algorithm for parameter identification by incorporating chaotic operators and emotional operators, which help the algorithm escape from local optimal solutions. Through the literature mentioned above, it has been confirmed that it is possible to establish a traditional dynamic mathematical model by estimating unknown parameters using algorithms. In addition to the traditional method of establishing dynamic models using mathematical equations, mentioned above, there has been a recent trend in establishing inverse dynamic models through machine learning with the advancement of artificial intelligence. It is stated that both traditional mathematical equations and machine learning can be used to establish inverse dynamics and achieve a certain degree of torque prediction. Compared to the traditional mathematical method, establishing a dynamic model requires a significant amount of knowledge, whereas machine learning relies on a sufficient amount of relevant information for modeling [7]. The proposal suggests utilizing physics simulation and deep learning techniques for the dynamic control of a robotic arm. This method does not require deriving the aforementioned traditional dynamic mathematical equations. The numerical data simulated by the physics engine are utilized as training data. It has been experimentally demonstrated that neural networks can accurately predict the torque of each joint, with a dynamic error controlled within 10% [8]. This meets the requirements for basic robotic arm dynamic control. XGBoost is a machine learning algorithm that has been developed in recent years. It is a framework based on decision trees. XGBoost is characterized by its fast speed, ability to handle large amounts of data, high flexibility, and support for regression functions. It is commonly used in data analysis and other situations [9]. This paper will use the aforementioned XGBoost to establish an inverse dynamic model of a six-axis robotic arm. Through machine learning, the goal is to analyze the nonlinear terms that cannot be solved by traditional mathematical methods when calculating inverse dynamics. This analysis aims to improve the accuracy of torque prediction. It will also compare the prediction results of the machine learning methods and the traditional mathematical methods mentioned above. In recent years, there has been a shift in the application of robotic arm control towards emphasizing human-machine interaction and collaboration.