# A MLP-Hedge-Algebras Admittance Controller for Physical Human-Robot Interaction
## 5 Experiments
### Discussion  
The mean of velocity step for each admittance controller is presented in Table 8; for the proposed MLP-HA-based admittance controller, the linear velocity step is 0.3757 mm/s, and the angular velocity step is 0.0042 rad/s, whereas the linear velocity steps are 0.4647, 0.6498 mm/s and angular velocity steps are 0.0054, 0.0062 rad/s for the Bi-HA-based and fuzzy-based admittance controllers, respectively. In addition, for the proposed MLP-HA-admittance controller, the percentage errors of linear velocity and angular velocity are 3.19% and 6.6%, respectively. These percentage errors increase to 3.52% and 8.1% for the Bi-HA-based admittance controller, 4.56% and 9.24% for the fuzzy-based admittance controller. In Figure 13, maximum steps of linear and angular velocities are about 4 mm/s and 0.05 rad/s for the proposed MLP-HA-based admittance controller, whereas those values are around 6 mm/s and 0.1 rad/s for Bi-HA-based admittance controller, and approximate 10 mm/s and \(-\)0.1 rad/s for fuzzy-based admittance controller, respectively. This analysis has shown that the proposed MLP-HA-based, Bi-HA-based and fuzzy-based admittance controllers give favorable conditions to avoid instability during the cooperation even when the external wrench is suddenly changed. Moreover, the MLP-HA-based admittance controller provides better cooperation compared to other admittance controllers. In addition, even if the external wrench is larger than the allowed value, the velocity of the end-effector always belongs in a safe domain as the applied values of the external wrench in every DOF in the interactive space are always constrained based on the ISO10218 standard to guarantee safe and natural pHRI. Figure 12: Experimental results using fuzzy-based admittance controller, (**a**) presents the inputs \(\ket{\text{I}}\)\(\ket{\text{N}}\), \(\ket{\text{M}}\)\(\ket{\text{Nm}}\) and \(P\) (W); (**b**) and (**c**) present outputs \(\ket{\text{V}}\)\(\ket{\text{(mm/s)}}\) and \(\ket{\text{W}}\)\(\ket{\text{(rad/s)}}\), respectively. Figure 13: The variation of end-effector during teaching task, (**a**) the variation of linear velocity (mm/s), (**b**) the variation of angular velocity (rad/s). Here, MLP-HA is the proposed MLP-HA-based admittance controller, Bi-HA is Bi-HA-based admittance controller, and FA is a fuzzy-based admittance controller. MLP-HA-based admittance controlleris found to provide better cooperation compared to other controllers. In an accurate manner, the proposed MLP-HA-based approach is found to provide better cooperation in comparison with previous methods. However, an aspect should be discussed, which is the computational complexities in different approaches, including conventional methods, fuzzy-based methods, and hedge-algebras-based methods (using average/product operators, four-point bilinear, and MLP interpolation). First of all, the order of the number of necessary rules of fuzzy or HA system is \(O(N)\)[60], here \(N=T^{n}\), \(T\) is the number of fuzzy or HA terms, \(n\) is the number of variables. Based on the rule base of the controller in this paper, \(T=7\), \(n=2\). The difference in the computational complexity of fuzzy and HA mainly depend on operators and interpolation methods, which are used for their inference mechanism. In this paper, max-min composition and centroid defuzzification is used for fuzzy logic. The complexity of max-min composition is \(O(N^{2})\)[61], the complexity of centroid defuzzification is \(O(TS_{1})\)[62], here \(S_{1}=100\), is the total number of samples of physical sub-domains of the output in this paper. In the HA, the computational complexity of the product/average operator is equivalent to the computational complexity of the spline interpolation O(m\({}^{2}N\))[63], where m is the order of the spline function. By contrast, the computational complexity of the bilinear interpolation is nominally \(O(N)\). In fact, the bilinear interpolation considers only \(2\times 2\) neighboring points and requires the least running time [64].