# Fuzzy Logic-Based Controller for Bipedal Robot
## 7 Conclusions  
With the proposed fuzzy rule system and the applied fuzzy inference rule, the fuzzy controller applied in the paper provided accurate results. Computational expressions based on fuzzy rules and fuzzy inference rules were very simple and easy to implement.  
Figure 17: Simulation results of controllers for bipedal robots at the final step: (**a**) IDPD controller; (**b**) IDPID controller; (**c**) fuzzy controller.  
The robot model used in the simulation had parameters close to those of a real human and kinematic parameters such as velocity, acceleration, etc. that were also close to human activities. Therefore, it is feasible to apply the research results in practice.  
The dynamic model of human-like bipedal robots is quite diverse, and the dynamic quantities often change with the operations. The problem of controlling the bipedal robot needs to be such that it can simultaneously move according to the set trajectory and satisfy the balance condition because the robot's two-legged structure is less stable. The crisp controllers based on dynamical models require large computations. On the other hand, the dynamical model of a bipedal robot often changes, so with a closed computational model it will be difficult to adapt and flexibly adjust the control quantity to flexibly respond to multi-tasking in a human-like bipedal robot.  
The construction of the fuzzy rule system took into account the influence and relation to the uncontrolled coordinate, which is the angle between the support foot and the ground. Therefore, the fuzzy law system allowed the calculation and adjustment of the driving forces at the controlled joints, so as to both meet the robot's motion trajectory and ensure the relative balance.  
A human, based on natural reasoning and through training, can operate and balance easily in many complicated postures and states.  
The high cost in time and effort in building a fuzzy controller is building the fuzzy rule system (24) and defining the physical value domain in Table 4. However, once the fuzzy rule system has been created and the physical value domain of language variables has been determined, the implementation of fuzzy operations is simple and easy, allowing real-time control requirements to be met. Equations from (21) to (29) are easy to apply and implement.  
During the numerical experiment to find the physical value domain in Table 4, a number of tests based on Modern Evolutionary Synthesis were applied, which provided good results. Applying this algorithm to find the physical value domain and to reduce the calibration time is one of the next studies needed to perfect the fuzzy controller.  
Regarding the fuzzy rule system, it is a rule system built based on natural reasoning, much like the reasoning of humans. To be able to control a human-like bipedal robot that operates flexibly and stably like a human, it is necessary to have a controller capable of operating based on human natural reasoning and at the same time capable of being trained in a way similar to a human. This indicates that the development direction of fuzzy logic-based control is integrated with artificial intelligence, combining fuzzy controllers capable of deep learning, reinforcement learning, ant colony algorithms, Modern Evolutionary Synthesis, and other intelligent algorithms.  
Conceptualization, P.B.K.; methodology, software, formal analysis, investigation, writing--original draft preparation, writing--review and editing, P.B.K. and H.N.X.; validation, P.B.K.; layout editing, H.N.X.; supervision, P.B.K. All authors have read and agreed to the published version of the manuscript.  
The authors received no financial support for the research, authorship, and publication of this article.  
Not applicable.  
The data presented in this study are available on request from the corresponding authors.  
The authors declare no conflict of interest.