# Variable Admittance Control in Sliding Mode for Robust Physical Human-Robot Interaction
## 4 Experimental Validation  
Experiments are conducted on a 7-DoF manipulator, Kinova Gen3, with the above-proposed control models implemented. The same 3-DoF configuration described earlier in Figure 4a is adopted. The user grabs the handle to move the robot in the x-y plane, and the motion is random on the premise of avoiding kinematic singularity. For the kinematic and dynamic parameters (1) the length and mass of each link of the manipulator are referred to values in the user manual of Kinova Gen3; (2) the length and mass of F/T sensor and handle are measured and included; (3) the center of mass and moment of inertia are roughly approximated. The conventional SMC for VAC in human-leading is implemented first. In this case, the sliding mode gain and boundary layer thickness are constants, and no acceleration feedback is included. For admittance control, the proposed variable damping model and PER are applied. In the initial test, \(K_{smc}^{i}\) and \(\phi_{i}\) is selected as 20 and 0.1, respectively. The actual mass of each link is applied in the dynamic model, where \(m_{1}=3.70\) kg, \(m_{2}=1.61\) kg, and \(m_{3}=1.75\) kg. Link 1 is proximal to the manipulator base, and link 3 is the distal link. It is observed in Figure 9 that tracking is relatively accurate during acceleration and deceleration phases but less accurate in tracking the desired response under the constraint of maximum allowed velocity, 0.1 m/s. It is essential to clarify the difference between the actual link mass of the physical manipulator used here and those values in simulation (c.f. Figure 5). The link mass of manipulator in the Simscape model is extracted from the 3D model provided by Kinova, while the mass of the physical link is from the user manual. Figure 8: Implementation of SMC in VAC for Kinova Gen3, where acceleration feedback is included. **(a)** displays the interaction force. **(b)** illustrates the control in human leading case. A smooth and perfect tracking is observed compared to Figure 5b. In **(c)**, stiffness is updated proportional to the human interaction force, then is regulated by PER. As a result, system passivity is preserved, i.e., \(\frac{1}{2}\dot{K}_{d}^{i}\) (\(\dot{x}_{i}^{2}\leq\mu D_{d}^{i}\dot{x}_{i}^{2}\). Moreover, tracking of \(\mathbf{x}_{r}\) by \(\mathbf{x}_{e}\) and \(\mathbf{x}_{e}\) by \(\mathbf{x}\) are both realized. The modeling errors are designed the same as in Figure 5.  
Then, the same algorithm is applied with a higher sliding mode gain, \(K^{i}_{smc}=70\), which yields results as shown in Figure 10. Though the tracking accuracy is improved from the perspective of the dominant trend of actual velocity, the oscillatory signal indicates that the selected gain value is too high. It is experimentally verified that optimizing the trade-off between tracking accuracy and vibration-free motion for the conventional method in dealing with VAC is practically difficult. Figure 10: Tracking performance of applying indirect tracking approach for human-leading VAC with a constant sliding mode gain, \(K^{i}_{smc}=70\). Figure 9: Tracking performance of applying indirect tracking approach for human-leading VAC with a constant sliding mode gain, \(K^{i}_{smc}=20\). The robustness test is then conducted by reducing the mass of link 1 and link 3 to be \(m_{1}=2.3\) kg and \(m_{3}=0.65\) kg in the dynamic equation, where \(K_{smc}^{i}=20\). As expected, tracking performance is further degraded, as appears in Figure 11, due to the constant sliding mode gain insufficiently tackling the included modeling uncertainties. Then, the variable boundary layer thickness (or variable sliding mode gain) approach is applied to address the above issue. The robustness test is also included where the mass of links 1 and 3 are modified to be \(m_{1}=2.3\) kg and \(m_{3}=0.65\) kg in the dynamic model, which yields results in Figure 12. The tracking accuracy is improved, and the vibration is attenuated. Nonetheless, the overshooting phenomena are observed when actual velocity hits the constraint.