Implementation and Control of a Wheeled Bipedal Robot Using a Fuzzy Logic Approach

Round 1

Reviewer 1 Report

This study implemented a wheeled bipedal robot (WBR) and desinged an intelligent motion and balance controller (IMBC) to maintain the WBR standing and moving. Finally, several testing scenarios, including station keeping, moving and rotating, height changing, and posture keeping, are applied to show the effectiveness of the IMBC system for the WBR. This paper is well organized. Mathematics formulas are all right.

Following comments are raised to improve the quality of paper:

(1)The references should be updated. Some recent relevant reference papers should be added and cited in the introduction.

(2)A more detailed discussion regarding the major contribution with regard to the existing works should be given to highlight the motivation of this work.

(3)The author requires to provide how to select the controller parameters.

(4)The authors should provide the experimental video links or a screenshot of the process.

(5)Please check use of English.

I think the contribution of this paper is quite good and therefore good enough to be published in Actuators.

Author Response

1. The references should be updated. Some recent relevant reference papers should be added and cited in the introduction.

Response: Thanks for your comment. In the revised manuscript, more related research references have been mentioned and cited in Introduction on Pages 2 and 3.

2. A more detailed discussion regarding the major contribution with regard to the existing works should be given to highlight the motivation of this work.

Response: Thanks for your comment. The contribution of this study can be summarized as follows. (1) The mechanical structure of the WBR, which has two legs and two wheels with the wheels installed on each foot, is designed and implemented. (2) An experimental setup is presented for the WBR using a low-cost 32-bit STM32F446RE microcontroller. (3) The IMBC system can maintain the balance of the WBR while standing and moving on the ground. (4) The IMBC system can independently control two leg motors to change the robot's height and attitude, enabling the WBR to move over challenging terrain.

3. The author requires to provide how to select the controller parameters.

Response: Thanks for your comment. The controller parameters of the IMBC system require some trial-and-error tuning procedures to determine with considering the stability requirements and possible operating conditions.

4. The authors should provide the experimental video links or a screenshot of the process.

Response: Thanks for your comment. The IMBC system for WBR can be found at https://www.youtube.com/watch?v=AR6yP99sSjs.

5. Please check use of English.

Response: Thanks for your careful reading. The revised manuscript has been checked the linguistic quality carefully.

Reviewer 2 Report

The author has proposed a wheeled bipedal robot (WBR). The study is very interesting, and the novelity is the use of an extra knee joint to maintain body balance when encountering uneven terrain (as claimed by the author). However, the manuscript needs to undergo the following revisions:

(1) References are not enough, and the author must cite at least 40 references. There is a lot of literature on wheeled bipedal robots (WBR). The author must compare their results with published literature in terms of mobility and dexterity for a wheeled bipedal robot.

(2) Concerning English, some minor changes must be made, such as spell check and the grammatical structure of sentences.

(3) Provide the list of symbols or nomenclature (as an appendix) for each symbol to ensure the clarity and completeness of the paper.

(4) The author did not explain what types of factors are responsible for nonlinearity, instability, and under-actuated nature, and how the proposed "intelligent motion and balance controller" overcomes them?

(5) How is this robot beneficial to society? Is it cost-effective? Will it have any application?

Author Response

1. References are not enough, and the author must cite at least 40 references. There is a lot of literature on wheeled bipedal robots (WBR). The author must compare their results with published literature in terms of mobility and dexterity for a wheeled bipedal robot.

Response: Thanks for your comment. In the revised manuscript, more related research references on WBRs have been mentioned and cited on Pages 2 and 3.

2. Concerning English, some minor changes must be made, such as spell check and the grammatical structure of sentences.

Response: Thanks for your careful reading. The revised manuscript has been checked the linguistic quality carefully and corrected all possible errors.

3. Provide the list of symbols or nomenclature (as an appendix) for each symbol to ensure the clarity and completeness of the paper.

Response: Thanks for your comment. In the revised manuscript, a list of symbols has been given in Appendix 1 on Page 23.

4. The author did not explain what types of factors are responsible for nonlinearity, instability, and under-actuated nature, and how the proposed "intelligent motion and balance controller" overcomes them?

Response: Thanks for your comment. From (9), (14) and (15), it shows the nonlinear and under-actuated nature of the WBR system. Further, the proposed IMBC system is designed based on a dual-loop control structure to cope with the under-actuated nature problem of the WBR, which enables the WBR to move according to the control commands by humans while maintaining balance.

5. How is this robot beneficial to society? Is it cost-effective? Will it have any application?

Response: Thanks for your comment. By achieving a higher movement speed and larger movement range, the WBR is designed to be flexible even in the variable terrain of indoor or outdoor environments. The robot is a cost-effective investment due to its safety, productivity, efficiency and reduction of waste. For example, it will be used to automate outdoor security patrols.

Reviewer 3 Report

This paper proposed a control method and implemented a wheeled bipedal robot (WBR). As a control method, fuzzy logic was employed. The balancing and moving performances were proved through experimental results. The idea introduced by the authors is quite interesting. However, there are still some issues that need to be improved.

1. The intelligent motion and balance controller (IMBC) was applied to WBR. In Section 3, 3 controllers (FRBC, FMBC, FYSC) were also designed separately. For the sliding-index in Eq. (13), there is no stability proof. For each controller, the stability needs to be guaranteed through mathematical analysis.
2. The mathematical model was set up Eq. (5) through Eq. (12). However, the model uncertainty and external disturbance were not included in model. Although fuzzy control can handle those nonlinear unexpected terms, those terms need to be estimated and the authors should prove the robustness of the proposed control method. That is, the modeling and controller design equations do not include the disturbance and uncertainties.
3. In Section 4, the controller parameters of IMBC were provided. However, physical specification on WBR was not provided. For the reader’s better understating, more detailed explanation should be added in the manuscript.
4. The author must consider comparing with some other research methods. It would be required to compare the improvement of IMBC with other methods introduced in the part of Introduction.
5. In Section 2.1 mechanical design, the formula for Fig. 1 is explained. However, in Figure 1, there is no information about h_L. If you mention that it is calculated in the same way as h_R, it seems necessary to explain h_L.
6. It is said that the controller proposed in this paper is built based on PID. Then, if the controller is not a sliding mode control, why is the sliding index used? What is the connection between PID and sliding index?
7. The formulas of the controller proposed in this paper and the controller proposed in ref. [34] are almost the same. Then, compared with [34], what is the novelty of the controller proposed in this paper?
8. A description of future work is not provided in the conclusion section. You need to update this part.
9. The author should introduce the detail of external forces in Section 4.1.
10. In Figure 8, It is not clear if the robot shows stable performance. Explain and analyze in more detail for the results in Fig. 8.

Author Response

1. The intelligent motion and balance controller (IMBC) was applied to WBR. In Section 3, 3 controllers (FRBC, FMBC, FYSC) were also designed separately. For the sliding-index in Eq. (13), there is no stability proof. For each controller, the stability needs to be guaranteed through mathematical analysis.

Response: Thanks for your comment. The main advantage of the IMBC system is that it not only achieves stability and robustness of the WBR but also effectively reduces the number of fuzzy rules. The fuzzy rules of FRBC, FMBC and FYSC are constructed using the idea that the sliding-index or error can quickly reach zero by a time-consuming trial-and-error tuning procedure. Thus, thee stability in this study cannot be guaranteed through mathematical analysis.

2. The mathematical model was set up Eq. (5) through Eq. (12). However, the model uncertainty and external disturbance were not included in model. Although fuzzy control can handle those nonlinear unexpected terms, those terms need to be estimated and the authors should prove the robustness of the proposed control method. That is, the modeling and controller design equations do not include the disturbance and uncertainties.

Response: Thanks for your comment. In the revised manuscript, Eq. (9) has been considered the uncertainties including model uncertainty and external disturbance.

3. In Section 4, the controller parameters of IMBC were provided. However, physical specification on WBR was not provided. For the reader’s better understating, more detailed explanation should be added in the manuscript.

Response: Thanks for your comment. In the revised manuscript, the physical specification on WBR was provided on Pages 11-13.

4. The author must consider comparing with some other research methods. It would be required to compare the improvement of IMBC with other methods introduced in the part of Introduction.

Response: Thanks for your comment. In the revised manuscript, to show the effectiveness of the IMBC system, a comparison between the cascade PID control [22] and the proposed IMBC system is presented. Experimental results show that the proposed IMBC system can achieve better control performance than the cascade PID control system due to the IMBC system can independently control two leg motors to change the robot's height and attitude.

5. In Section 2.1 mechanical design, the formula for Fig. 1 is explained. However, in Figure 1, there is no information about h_L. If you mention that it is calculated in the same way as h_R, it seems necessary to explain h_L.

Response: Thanks for your careful reading. In the revised manuscript, the description of h_L has been given in (5).

6. It is said that the controller proposed in this paper is built based on PID. Then, if the controller is not a sliding mode control, why is the sliding index used? What is the connection between PID and sliding index?

Response: Thanks for your careful reading. The typo error has been removed. The proposed IMBC system is not built based on PID approach.

7. The formulas of the controller proposed in this paper and the controller proposed in ref. [34] are almost the same. Then, compared with [34], what is the novelty of the controller proposed in this paper?

Response: Thanks for your comment. The novelty of the proposed IMBC system has been given on Page 10.

8. A description of future work is not provided in the conclusion section. You need to update this part.

Response: Thanks for your comment. In the revised manuscript, the future work has been given on Page 17.

9. The author should introduce the detail of external forces in Section 4.1.

Response: Thanks for your careful reading. The external forces are given by human hands.

10. In Figure 8, It is not clear if the robot shows stable performance. Explain and analyze in more detail for the results in Fig. 8.

Response: Thanks for your careful reading. In the revised manuscript, to show the effectiveness of the IMBC system, a comparison between the cascade PID control [22] and the proposed IMBC system is presented. We hope that the new experimental results will clearly demonstrate the effectiveness of the proposed IMBC system for readers.

Round 2

Reviewer 3 Report

Although the previous comments are quite important, the authors did not give any sound proof for the following comments:

1. As commented in the last report, the stability is very important. However, the authors responded as "Thus, thee stability in this study cannot be guaranteed through mathematical analysis.". I don't think this is proper. It cannot guarantee the stability if the sliding-index or error only can approach to zero after trial and error. At least, the authors should confirm the stability for any case.

2. Eq. (9) is for the dynamical model of WBR. In this equation, it does not contain any model uncertainty or disturbances. Related to comment # 1, to guarantee the stability or robustness, the authors need to prove the robustness of the proposed method after including the uncertainties.

3. The authors said that the external forces are given by human hands. These methods are not analytic or systematic. It is required to apply the external force in more systematical way. And the specific explanation is required to be added in the manuscript.

Author Response

1. As commented in the last report, the stability is very important. However, the authors responded as "Thus, thee stability in this study cannot be guaranteed through mathematical analysis.". I don't think this is proper. It cannot guarantee the stability if the sliding-index or error only can approach to zero after trial and error. At least, the authors should confirm the stability for any case.

Response: Thanks for your comment. Most of the operations in an FC use error and change-of-error as the fuzzy input variables, where the rules table is constructed in a two-dimensional input space. It can be found that the rule tables have skew-symmetry property, where the absolute magnitude of the control input is proportional to the distance from its main diagonal line in the normalized input space. To reduce the complexity of the implementation, a SFC was proposed based on the sliding-mode control scheme, where a new fuzzy input variable called the signed distance was derived. Compared to FC system, the total number of fuzzy rules used in SFC system is greatly reduced, so that the control rules can be easy to generate and adjust. However, due to the linguistic expression of the FC and SFC systems, they have not been easy to guarantee the stability and robustness of the closed-loop control systems.

In this study, the IMBC system depends to a large extent on the expert's knowledge or on trial and error liking FC and SFC systems. It has not been easy to guarantee the stability and robustness of the closed-loop control systems. Future works will study on auto-tuning fuzzy controller, whose fuzzy rules can be tuned online without requiring time-consuming adjustments to ensure the system stability.

2. Eq. (9) is for the dynamical model of WBR. In this equation, it does not contain any model uncertainty or disturbances. Related to comment # 1, to guarantee the stability or robustness, the authors need to prove the robustness of the proposed method after including the uncertainties.

Response: Thanks for your comment. Related to Response # 1, the proposed IMBC system does not require the system dynamics and system parameters of a WBR. It is a model-free and a rule-based control algorithm. To show the robustness of the proposed control method, four experimental scenarios, namely moving and rotating, height-changing, posture-keeping, and one leg on slope movement, were tested. In moving and rotating scenario, an external disturbance by human hands is pushed on both sides of robot body. In height-changing scenario, the system uncertainties caused by robot height variations are considered. The experimental results showed that the proposed IMBC system is capable of providing appropriate control outputs to maintain the body balance of the robot, as well as the motion and steering control of the robot, even under variable environmental terrain, model uncertainty and disturbances.

3. The authors said that the external forces are given by human hands. These methods are not analytic or systematic. It is required to apply the external force in more systematical way. And the specific explanation is required to be added in the manuscript.

Response: Thanks for your comment. Due to the limitations of our experimental equipment, we were unable to apply external forces in a more systematic way, such as using a manipulator arm instead of a human hand. Future works will investigate on specific description of performance comparison, such as giving a more systematic way to apply external forces.

Round 3

Reviewer 3 Report

The overall quality and completeness of the manuscript has been improved compared to the previous submission.