# Variable Admittance Control in Sliding Mode for Robust Physical Human-Robot Interaction
## 4 Experimental Validation
To investigate if including acceleration feedback can resolve the above issue, the proposed control algorithm in Equation (52) is implemented. Considering the operational safety when feeding a noisy acceleration signal back to the control loop, a small gain is selected at the initial test, i.e., \(Q_{i}=3.0\). Again, the same modeling errors, i.e., \(m_{1}=2.3\) kg and \(m_{3}=0.65\) kg, on link mass are included to examine the controller's robustness. The built-in accelerometer measures acceleration at the endpoint of manipulator. The results appear in Figure 13. As expected, the overshooting is appropriately attenuated. However, an oscillatory signal is observed and is not favorable. The reason could be the resonance between high-frequency unstructured dynamics and the noisy acceleration signal. To obtain smooth acceleration data with less distortion and phase lag, a structure composed of a second-order low-pass filter and a modified parabolic sliding mode filter (M2-PSMF) (refer to [43]) is applied to the measured acceleration as well as equivalent acceleration (i.e., \(\ddot{\mathbf{x}}_{s}\)). With the filter being applied, tracking performance is promoted, as shown in Figure 14. Also, no high-magnitude overshooting signal is observed. The decent results that match the simulation results in Figure 8a demonstrate the proposed controller's effectiveness and robustness. The performance of the filter is shown in Figure 15.  
Figure 11: Tracking performance of applying indirect tracking approach for human-leading VAC with a constant sliding mode gain, \(K_{smc}^{i}=20\). The mass of links 1 and 3 are modified to be \(m_{1}=2.3\) kg and \(m_{3}=0.65\) kg in the controller. Figure 5.0 Tracking performance of applying indirect tracking approach without AFC for human-leading VAC. The proposed variable sliding mode gain and variable boundary layer thickness methods are employed. The mass of links 1 and 3 are modified to be \(m_{1}=2.3\) kg and \(m_{3}=0.65\) kg in the controller. Figure 5.1 Tracking performance of indirect tracking approach with AFC for human-leading VAC. The proposed variable sliding mode gain and variable boundary layer thickness methods are employed. Acceleration error gain is selected as \(Q_{i}=3.0\). The mass of links 1 and 3 are modified to be \(m_{1}=2.3\) kg and \(m_{3}=0.65\) kg in the controller. Furthermore, to verify the robustness of the proposed overall control law when the modified mass is greater than the actual value, the mass of link 3 is changed to 2.75 kg in the model. Accurate tracking performance appears in Figure 5.2  
Figure 5.3 Tracking performance of indirect tracking approach with AFC for human-leading VAC. The proposed variable sliding mode gain and variable boundary layer thickness methods are employed. The structure composed of a second-order low-pass filter and M2-PSMF filter is applied to acceleration signals. Acceleration error gain is selected as \(Q_{i}=3.0\). The mass of links 1 and 3 are modified to be \(m_{1}=2.3\) kg and \(m_{3}=0.65\) kg. Figure 5.4 Filtered measured acceleration and equivalent acceleration signals using the M2-PSMF filter. To further verify the repeatability of the above comparison, five tests are conducted for each method being used in obtaining results in Figures 9, 12 and 14 to provide a simple statistical overview of the performance. The absolute values of tracking errors (i.e., \(\dot{\mathbf{x}}-\dot{\mathbf{x}}_{\mathbf{c}}\)) are shown in Figure 5.5 It is straightforward that the new sliding surface and variable sliding mode methods gain improved tracking accuracy. Moreover, the method that includes filtered acceleration feedback to equivalent control further enhances tracking accuracy and suppresses overshooting. It is important to note that outliers in the results of applying indirect tracking methods without AFC (i.e., methods in obtaining Figure 12) represent the overshooting signals.