# Research on Robotic Peg-in-Hole Assembly Method Based on Variable Admittance
## 3 Results and Discussion
### Experimental Verification and Analysis
#### 3.1.2 Experimental Analysis  
This experimental design conducted a control experiment. During assembly, the robot moved from a fixed point above the axis of the deviated hole. The only difference between the experimental conditions of variable admittance control and fixed admittance control was whether the admittance parameters were variable, while the other experimental conditions were the same. First, we completed 20 assembly experiments using fixed admittance control and recorded the data. Subsequently, we conducted another 20 assembly experiments using variable admittance control and recorded the data as well. From these experiments, we selected a pair of assembly results, and the changes in contact force during the assembly process are shown in Figures 10-13. According to the assembly force curve in Figures 10 and 11, as the control group, the total time for the fixed admittance parameter assembly shaft-hole experiment was 25.4 s.  
t0-t1 represents the hole seeking stage, where the end of the robot moved along the Z+ direction of the end tool above the hole. This process is illustrated in Figure 1a of the Section 2. When the axis touched the hole wall, the forces in the XYZ directions increased. Figure 10: Constant admittance assembly force diagram. Figure 9: Training reward curve chart. t1-t2 represents the adjustment stage, during which the robot encountered a jam. The process is illustrated in Figure 1b of the Section 2. The robot needed to maintain a certain  
Figure 11: Constant admittance assembly torque diagram. Figure 12: Variable admittance assembly force diagram. Figure 13: Variable admittance assembly torque diagram. axial contact force to straighten its posture. It can be seen that during this stage, the force in the \(X\)-direction was about 0.5 N, the force in the \(Y\)-direction was about 5 N, and the force in the \(Z\)-direction was about 1.5 N. The torque around the tool's \(X\) axis ranged from 0.4 to 0.5 N\(\cdot\)m.  
t2-t3 represents the insertion stage, at which point the robot had completed the alignment of the end tool axis and hole. The moment acting on the axis in the \(X\)-direction was below 0.05 N. The robot continued to insert downwards into the hole along the \(Z\)+ direction of the tool to reach the bottom of the hole until the force in the \(Z\)-direction suddenly changed to 6 N, completing the assembly. As an experimental group, the force results of the variable admittance assembly experiment are shown in Figures 12 and 13, and the assembly time was 23.1 s.  
Before the variable admittance assembly experiment, the reinforcement-learning model was imported, and then the peg-in-hole assembly was carried out. The force analysis process was the same as the fixed admittance parameters assembly, which was divided into the hole seeking stage, adjustment stage, and insertion stage. During the adjustment stage, the force in the \(X\)-direction was around 0.3 N, the force in the \(Y\)-direction was around 4 N, the force in the \(Z\)-direction was around 1 N, and the torque around the tool's \(X\) axis was between 0.3-0.4 N\(\cdot\)m. The force in the \(X\)-axis direction during the insertion stage was smaller than the force in the \(Z\)-axis direction. The data from the 20 comparative assembly experiments are presented in Table 3. The maximum forces during assembly reflect the compliance of the process: smaller forces mean less deformation and reduced risk of robot damage. The table lists the average values of the instantaneous maximum contact force and contact torque during the adjustment stage. Data show that variable admittance control reduces these forces, achieving better compliance than fixed admittance control. The table also shows the average assembly time, standard deviation, and coefficient of variation (CV) of assembly time, highlighting process consistency. Variable admittance control has an average assembly time of 23.0 s, compared to 25.2 s for fixed admittance control, making it 9.6% faster on average.