## 7 Conclusions  
The results show that the controller based on fuzzy logic can meet the requirements of accuracy and reliability. Furthermore, by neglecting the calculations of the cutting forces, it is more convenient to deal with only linear algebraic calculations in fuzzy control rules, which in turn help to greatly reduce the time and computation load and increase the efficiency of the robot control system.  
From the simulation results, the fuzzy controller may be even more accurate than the explicit controller, although this is only relative because the presented controllers have not been optimized. The parameters of the above controllers have been selected \"quite randomly\" in simulation cases.  
Theoretically, the explicit controller is accurate when the dynamic model is accurate and contains no perturbations. However, in practice, it is difficult to determine precisely all the system parameters. This leads to errors in the calculation of the control signals.  
Meanwhile, the fuzzy controller computes the control law based on the input and output signal errors and the fuzzy rule. Thus, the calculation results can be flexibly adjusted based on the input and output signal errors. This explains the possibility that the fuzzy controller may be more accurate than the explicit controller. In addition, the last simulation result with initial deviation of the trajectory shows that the fuzzy controller is able to control the system to the required state when there are perturbations.  
The method of developing fuzzy rules and determining the physical value domain implemented in the article gives good simulation results of the fuzzy controller, which can be applied for designing the fuzzy controller for milling robots.  
Difficulties in cutting force calculation and accurately determining the dynamic quantities for complex structural robot systems are always a challenge. Besides, one cannot compensate for all the perturbations such as noise and vibrations occurring due to interactions when the robot is machining or from the environment. Therefore, it is not possible to design an ideal explicit controller. Finding methods to eliminate the aforementioned factors when applying robots in machining is indispensable and compulsory. The controller based on fuzzy logic has been validated to be feasible and reliable via simulation results. It can be developed in practise to overcome the aforementioned uncertainty.  
Methodology, conceptualization and formal analysis, K.B.P.; investigation, K.B.P., H.T.H. and S.V.H.; survey the backgrounds, K.B.P., H.T.H. and S.V.H.; design and collect the preprocessing data, K.B.P., H.T.H.; visualization, writing-original draft, K.B.P., H.T.H.; writing-review & editing, K.B.P.; software, K.B.P.;  
Figure 20: Tool path position errors between desired value and simulation result in cutting force mode increases by 50% due to noise.  
check the draft, H.T.H. and S.V.H.; discussion and estimation the efficiency of this methodology, K.B.P., H.T.H. and S.V.H.; layout editing, H.T.H. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.