# Dual PID Adaptive Variable Impedance Constant Force Control for Grinding Robot
## 1 Introduction  
In the manufacturing process of molds, aircraft panels, sculptures, etc., grinding and polishing are used to reduce the surface roughness and improve the machining accuracy [1, 2]. However, most grinding and polishing operations are still performed manually, resulting in low manufacturing efficiency, poor workpiece surface quality, and worker health problems [3, 4]. The automatic grinding and polishing processes represented by computer numerical control machine tools (CNCs) and industrial robots have become the main solutions [5, 6]. CNCs not only have excellent stiffness and high precision positioning, but can also concurrently control trajectory, pose, and force [7]. However, the grinding space of CNCs is small, they have poor flexibility, and the machine tools need to be designed individually for large-scale special-shaped surfaces, which limit the application [8]. Robots have the advantages of a large working range, high flexibility, and have gradually become a research hot-spot in the field of grinding and polishing. Robot grinding is a typical constrained operation. According to [PERSON]'s law, the amount of workpieces removed increases monotonically with the increase in grinding force, tool speed, and residence time, the most important of which is the control of the grinding force [9]. Therefore, controlling the robot end contact force is of great significance to improve the surface quality [10, 11]. However, applying position-based industrial robots directly to grinding and polishing processes involving contact motion is not straightforward [2, 12]. An accurate and smooth contact force control method is the key to realize high-quality automatic grinding and polishing of robots. Robot end contact force control methods are mainly divided into passive force control [13; 14] and active force control [15; 16]. Passive force control is achieved through energy absorption or the storage of the auxiliary flexibility mechanism, and the robot is still in position control mode [17; 18]. Typical force control devices mainly include voice coil motor actuators [19; 20], parallel mechanism actuators [21; 22], pneumatic actuators [23; 24; 25], mechanically flexible structures [26; 27; 28; 29], force control joints [30], etc. [PERSON] et al. [31] adopted a dual force sensor to decouple the dynamics between the macro robot, micro robot, and workpiece to achieve high-precision force control. However, passive force control requires the installation of an actuator at the robot end, which puts forward higher requirements for the design of the end actuator in the case of a limited end load of the robots. Therefore, active force control is more feasible. Active force control is the use of designed control strategies to actively control force through the feedback of contact force information [32]. In the aspect of force control algorithms, the design of the force controller is the most important, and the common force control algorithms are impedance control [33; 34] and hybrid position/force control [35; 36]. For uncertain environments, that is, when the stiffness and position of the environment are unknown, it is difficult to obtain an accurate model, which makes it difficult to achieve high-precision force tracking. There are three main solutions: (1) Indirect adjustment of the reference trajectory: the basic method is to identify environmental information, including stiffness and position [37; 38]. (2) Direct adjustment of the reference trajectory: the basic method is to update the reference trajectory with prior information [39; 40]. However, this method ignores the dynamic physical characteristics of the robot and the environment and usually results in a large force tracking error. (3) Adaptive variable impedance control: this method adaptively adjusts the controller parameters according to force feedback information [41; 42; 43]. To improve the accuracy of force tracking, the researchers combined the adaptive algorithm with other force control methods to obtain better force control results [44].