# Vibration Suppression of Collaborative Robot Servo with Dual Encoders
## 1 Introduction  
In recent years, collaborative robots have seen a surge in adoption across various industries, particularly in the assembly of computers, communication, and consumer electronics (3 Cs), as well as in material handling and human-robot collaborative tasks. As the demand for precision and efficiency grows, performance metrics have emerged as a critical focus for research and development efforts. Among these, vibration suppression has garnered significant attention as a pivotal performance indicator, driving advancements in robotic stability and operational accuracy. By adjusting and optimizing the control parameters of the current loop, speed loop, and position loop, a significant portion of vibrations can be suppressed. Achieving optimal control of each loop relies on engineers' experience and increases debugging time. Furthermore, its drawback lies in the challenge of exerting a significant effect on flexible components. Additionally, the implementation of filters, such as notch filters and othersignal processing methods, can effectively suppress vibrations at specific frequencies. However, the notch filter's drawback is that it is only useful for specific frequencies. Methods such as incorporating current loop feedforward elements and speed loop feedforward elements have been shown to be effective in vibration suppression [1]. In reference [2], three distinct techniques were proposed for vibration suppression in multi-degree-of-freedom industrial robots: optimal S-curve trajectory planning, robust zero-vibration input shaping, and dynamic zero-vibration input shaping. These methodologies were systematically developed to address vibration control challenges in industrial robotic systems, demonstrating significant improvements in motion precision and operational stability. In reference [3], a comprehensive rigid-flexible coupled dynamic model of the collaborative robot was established through the integration of finite element analysis and Lagrange methodology, from which the robot's vibration equations were systematically derived. The trajectory optimization process was implemented with the excitation force as the primary optimization objective. Furthermore, the trajectory planning methodology was significantly refined to effectively mitigate vibrations in the collaborative robot, demonstrating enhanced operational stability and precision. In reference [4], a novel learning-based exponential jerk trajectory planning method was proposed to effectively suppress residual vibrations in industrial robots. A trajectory optimization model that minimizes time and jerk has been proposed. Adopting an optimization method based on the Comprehensive Learning Particle Swarm Optimization (CLPSO) algorithm to solve optimization problems. This method is designed to suppress the vibration of industrial robots [5]. In conventional robotic systems, the encoder is typically installed on the motor side, facilitating accurate measurement of the motor's position and subsequent calculation of its rotational speed. However, the primary concern in robotic applications often lies in the vibration of the link or the robot's end effector rather than the motor itself. The reducer, which acts as a critical interface connecting the motor to the link, is inherently characterized by mechanical play and flexible components. These factors contribute to discrepancies between the motor-side and link-side dynamics. Consequently, incorporating an additional encoder on the reducer side to directly measure its rotational speed and integrate these data into the control system presents a promising solution for vibration suppression. Additionally, there is limited research literature on dual encoder control strategies. The relevant literature has proposed a dual encoder scheme, but they focused on solving the position error of the dual encoder. Additionally, it was not included in the control, nor was it mentioned in terms of speed fluctuations [6; 7].