# Research on Robotic Peg-in-Hole Assembly Method Based on Variable Admittance
## 1 Introduction  
The Assembly operations are a typical step in production and manufacturing and are also the most labor-intensive processes [1]. With advancements in robotics technology, many assembly tasks are now performed by robots, with peg-in-hole assembly being a significant application in the manufacturing industry [2, 3, 4]. In the peg-in-hole assembly process, the posture of the workpiece end is critical; even minor motion deviations can result in significant changes in contact force, potentially causing severe damage to the robot [5, 6]. Assembly tasks in factories are typically planned using a teach-by-demonstration approach to establish trajectories [7]. However, due to inherent motion errors in robotic arms, the accumulation of these errors over extended operation can potentially lead to failures in peg-in-hole assembly tasks [8]. Investigating robotic shaft-hole compliant assembly techniques holds significant application value for improving the level of intelligent automation, production efficiency, and economic benefits in industrial manufacturing [9]. In recent years, scholars worldwide have focused their research on robotic peg-in-hole assembly technology, primarily in two directions: active compliance control methods and methods based on deep reinforcement learning [10, 11, 12]. Active compliance control mainly includes force and position hybrid control, impedance control, and admittance control [13]. This method measures the force at the endof the robotic arm using a six-axis force/torque sensor or joint current. The arm completes the assembly by adjusting its compliance in response to force variations [14]. [PERSON], [PERSON] and colleagues designed an impedance controller based on a six-axis force/torque sensor, eliminating the need to establish a complex contact status model, and successfully completing the shaft-hole assembly task [15]. [PERSON], [PERSON] and colleagues introduced an oblique spiral search method based on impedance control and applied it to shaft-hole assembly, thereby accelerating the assembly speed [16]. Although the aforementioned admittance control demonstrated satisfactory performance in peg-in-hole assembly tasks, the algorithms in these studies set the admittance parameters based on empirical values, which deviated from the optimal parameters. Thus, there is still room for further improvements in admittance control. As artificial intelligence technology advances, deep reinforcement learning has been applied in the field of peg-in-hole assembly [17]. Applications of deep reinforcement learning in shaft-hole assembly are primarily divided into two approaches: directly training the control of motion amplitude to manage contact force during insertion, and indirectly training system parameters to ensure safe contact forces [18]. [PERSON], [PERSON] et al. used the Deep Deterministic Policy Gradient (DDPG) algorithm to directly output translational and rotational amplitudes for successful hole-insertion tasks [19]. [PERSON], [PERSON] et al. successfully transferred the reinforcement learning (RL) policy from the simulation environment to the real robot without dynamics randomization using the Operational Space Control framework (OSC) and system identification techniques [20]. However, the training of assembly tasks that do not rely on the underlying controller usually takes a long time to converge. Other studies employed deep reinforcement learning for position-based control to ensure compliance during assembly [21]. [PERSON], [PERSON] et al. combined the Model-Driven Deep Deterministic Policy Gradient (MDDPG) algorithm with a fuzzy reward system to accelerate robotic shaft-hole assembly training [22]. [PERSON], [PERSON] et al. compared Proximal Policy Optimization (PPO), DDPG, and State Action Reward State Action (SARSA) algorithms in impedance-controlled shaft-hole assembly but did not detail the reward system composition [23]. Although RL has shown promise in assembly tasks, further improvements are still needed.