Nonuniform Dual-Rate Extended Kalman-Filter-Based Sensor Fusion for Path-Following Control of a Holonomic Mobile Robot with Four Mecanum Wheels
Round 1
Reviewer 1 Report
This manuscript proposes a non-uniform dual-rate extended Kalman filter fusion algorithm for robot state estimation and improves the pure pursuit path-tracking algorithm, and then builds a simulation platform capable of simulating real scenarios for algorithm validation, which is meaningful for the research of perception measurement and motion control of unmanned systems.
However, the manuscript still has certain problems and areas for improvement:
- P13-14, it should be added to verify the simulation closed-loop control and real closed-loop control in the case of contact with the ground or with load, so that the verification is closer to the reality and will be more convincing;
- This manuscript has improved the pure tracking algorithm, which should be compared with the original algorithm to highlight the performance and advantages of the improved algorithm;
- Fig12 should be adjusted, the result of SR 0.3 is obscured
- Based on the experimental results of Fig13, draw the error value of the tracking trajectory, and compare the path tracking accuracy and performance in different situations more intuitively.
Author Response
Reviewer 1. Comments and Suggestions for Authors
This manuscript proposes a non-uniform dual-rate extended Kalman filter fusion algorithm for robot state estimation and improves the pure pursuit path-tracking algorithm, and then builds a simulation platform capable of simulating real scenarios for algorithm validation, which is meaningful for the research of perception measurement and motion control of unmanned systems.
Reply: Thank you very much for your careful reading of the paper and your valuable inputs. We faced all your concerns, and hence, we believe, the paper has been considerably improved.
However, the manuscript still has certain problems and areas for improvement:
1. P13-14, it should be added to verify the simulation closed-loop control and real closed-loop control in the case of contact with the ground or with load, so that the verification is closer to the reality and will be more convincing;
Reply: We agree with you. A new figure (Fig. 8b) considering the case proposed is added. Indeed, this figure complements Figure 10, where the different responses were obtained with the vehicle wheels in contact with the ground.
2. This manuscript has improved the pure tracking algorithm, which should be compared with the original algorithm to highlight the performance and advantages of the improved algorithm;
Reply: Thank you very much for this convenient suggestion. A new figure (Fig. 13) and a new table (Table 1) have been included in the manuscript to illustrate and analyze the comparison. Additionally, some paragraphs have been added (in Section 5.1: page 17, lines 389-391; and in Section 5.3: page 18, lines 419-426) to respectively introduce the study and comment the results.
3. Fig12 should be adjusted, the result of SR 0.3 is obscured
Reply: Sure! Now, the figure (Fig. 14 in the new version of the manuscript) includes some prolongation of the vertical axis to better depict the case SR 0.3.
4. Based on the experimental results of Fig13, draw the error value of the tracking trajectory, and compare the path tracking accuracy and performance in different situations more intuitively.
Reply: Thank you very much for this interesting suggestion. A new figure (Fig. 16) and a new paragraph to comment the comparison (in page 21, lines 462-470) have been included in the manuscript.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper presents an extended Kalman filter-based sensor fusion approach, which enables a path-following control of a holonomic mobile robot with four mecanum wheels.
The research is very important and the paper is clearly structured. The results are promising. I like the clarity that is provided e.g. by figure 1. However, a few points should be clarified or explained in more detail.
Line 230: please comment why you assume Gaussian Noises (similar line 359), please state how you determine the covariance and explore if this might lead to differences from a real application.
Line 319: please describe the real vehicle in detail (photograph) and describe the collection of real data in detail (I recommend a dedicated sub-section)
I would appreciate if the authors could make the data available. At least the used matrices with concrete values should be included in an appendix.
Author Response
Reviewer 2. Comments and Suggestions for Authors
The paper presents an extended Kalman filter-based sensor fusion approach, which enables a path-following control of a holonomic mobile robot with four mecanum wheels.
The research is very important and the paper is clearly structured. The results are promising. I like the clarity that is provided e.g. by figure 1. However, a few points should be clarified or explained in more detail.
Reply: Thank you very much for your careful review and your positive evaluation. We have coped with all the suggestions made by you. As a consequence, we think, the quality of the paper has been improved.
Line 230: please comment why you assume Gaussian Noises (similar line 359), please state how you determine the covariance and explore if this might lead to differences from a real application.
Reply: Thank you for this instructive suggestion. As well-known, the Kalman filter formulation assumes Gaussian noises for process and measurements. In our simulation, we take advantage of this consideration to emulate possible model uncertainties and measurement noise that may appear in the real application.
Regarding the noise covariance, its determination may be difficult in some practical frameworks. Some methods can be used to help estimate the covariances from data (e.g., the autocovariance least-squares technique, and Bayesian algorithms). In our case, for the matrix R, we have obtained the covariances related to the position measurements by following the manufacture’s manual of the beacon based indoor positioning system, where the precision of the system is indicated. The value obtained is 0.0025. The same procedure was done for the orientation sensor, obtaining the value 0.005. Regarding the velocity of the wheel (assuming contact with the ground), its covariance has been calculated from a histogram of the steady-state response. The value obtained is 0.014. Finally, the matrix Q is tuned by hand, according to the desired uncertainty for the model. As a future work, the real implementation of the control system may help us finely tune these values to get the best possible results.
In the manuscript, the appendix A has been added in order to declare the covariance matrices used and include a summary of the previous explanations.
Line 319: please describe the real vehicle in detail (photograph) and describe the collection of real data in detail (I recommend a dedicated sub-section)
Reply: Thank you for this valuable input. Now, a new subsection 4.2 has been added to the manuscript to show the real vehicle, detail its main components, and indicate how the real data are collected.
I would appreciate if the authors could make the data available. At least the used matrices with concrete values should be included in an appendix.
Reply: Absolutely! The appendix A has been added with the covariance matrices.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Compared with the first draft, the revised paper has made great progress, with complete structure and clear logic. But there is a small tip, which is to make the chart a little clearer and prettier. Figure 16 looks a little confusing.
Reviewer 2 Report
The changes were sensible, in my opinion the paper can now be published.
