# Robot Joint Vibration Suppression Method Based on Improved ADRC
## 1 Introduction  
Robots are widely used in various industries, freeing people from heavy, dangerous, and harsh working environments. In industry 4.0, robots are dedicated to performing complex and dangerous tasks, such as automated, high-temperature, full-time, and long-duration assembly line work [1]. With the further development of computer technology, artificial intelligence technology, sensing technology, and control technology, the robotics industry has entered the fast lane of development. Reference [2] proposed a robot system based on a serial manipulator for picking up and placing, classification, and other object operation tasks. Due to mechanical mechanisms and control strategies, vibration problems are inevitable in robot systems during actual operation. Robot vibration not only affects the performance and stability of robots, but also has significant impacts on production efficiency, product quality, working environment, and personnel safety. Robot vibration can cause the following problems: (1) Affect the positioning accuracy and control stability of the robot [3]. (2) Increase the torque ripple of robot joints [4]. (3) Reduce production efficiency. (4) Cause fatigue and damage to the components and structures of robot systems, and shorten the lifespan of robots. In order to improve the control performance of robots, researchers have conducted lots of research on robot vibration suppression technology. [PERSON] established residual vibration dynamic equations for four types of mobile robots considering the concentrated mass based on the finite element method (FEM) and [PERSON]'s spatial beam element (SBE) model, which are used to suppress the residual vibration of robots [5]. [PERSON] et al. proposed a new method that can suppress the out-of-plane vibration of planar CDPRs without affecting their in-plane positioning control, using a switching stiffness control algorithm to suppress robot vibration [6]. [PERSON] et al. studied the elastic vibration model of torsional motion of chain-like structure linkages based on multi-rigid body dynamics and established a control method based on optimized control gain design to suppress robot elastic vibration by controlling input redundancy [7]. [PERSON] proposed a dynamic flexible force control strategy to address the vibration and over-grinding phenomena in robotic belt grinding systems. The vibration was suppressed by controlling the dynamic flexible contact force with the robot [8]. [PERSON] proposed a position control scheme for flexible joint robots based on online gravity compensation, designed a nonlinear state feedback controller, and analyzed the overshoot on the motor side and residual vibration on the link side [9]. [PERSON] et al. studied the method of applying iterative learning to the first axis to suppress time-varying nonlinear residual vibrations [10]. [PERSON] et al. proposed a switching stiffness vibration control method by decoupling robot dynamics [6]. [PERSON] et al. found that the resonant/antiresonant phenomenon is effectively reduced by increasing the viscosity of the ER damper [11]. At present, the methods for suppressing robot vibration mainly focus on improving the mechanical structure of robots, optimizing the trajectory of robot bodies, and optimizing the motion control algorithms of robots. However, these methods still have shortcomings as follows:  
1. The parameters of dampers or structural optimization are fixed, making it difficult to cope with dynamic load variations or complex environments (such as changes in temperature and humidity). 2. Although mechanical vibration absorbers can achieve broadband vibration suppression, their adjustment range is limited by the physical properties of the materials and cannot adapt to high-frequency abrupt vibrations. 3. Model-based active control, such as input shaping algorithms, requires an accurate robot dynamics model. However, the nonlinear and time-varying characteristics of robot systems can easily lead to changes in the model. 4.