Impedance Control Self-Calibration of a Collaborative Robot Using Kinematic Coupling

Round  1

Reviewer 1 Report

Please see attached file.

Comments for author File: Comments.pdf

Author Response

### Point 1

> Can the method be applied to robots that are less sophisticated? What

steps of the calibration need to be modified in order to obtain similar accuracy improvements?

Yes, this method can be applied to less sophisticated robots with no major differences in procedure.

While redundant motion allows many joint configurations for a single Cartesian pose, the results of this process with a non-redundant robot will produce a dataset without redundant configurations.

Simply put, redundant motion produces more joint configurations with less tool movement.

The Discussion section has been updated with this information.

### Point 2

> Section 2.3 Lines 96-100 and Table 2: Does the 7R KUKA robot have any joint axes that are parallel one to another? If so then the MDH model may not be parametrically continuous, as shown by Mooring et al. in [12]. Slight axes misalignments may cause large jumps in some of the kinematic parameters.

No, the KUKA LBR does not have any consecutive revolute joints with nearly parallel axes.

This may be conveniently seen in the alpha column of Table 2, where each consecutive axis is perpendicular to the last.

### Point 3

> I think that Section 4.1 Lines 168-183, which is one the more central pillars of the reported calibration method, needs to be rewritten much more clearly. Some of the jargon of communication architecture and data processing protocols, may not be fully familiar to robotics researchers. I am having a very hard time trying to understand what is written. It may be a good idea to explain each block functionally.

Thank you for the keen critique of the section.

Section 4.1 has been updated to better explain the communication structure and the underlying protocol with less technical jargon and more context.

Reviewer 2 Report

The paper presents a  a closed-loop calibration approach using impedance control.

The work is definitely significant and has a good degree of originality. It is interesting also because it can find practical applications in the industrial environment.

The work is clearly presented in the manuscript, and the scientific content is sound. 

Thus, I recommend publication of the paper, provided that the following minor remarks are taken into account:

- paragraph 4.1 ("Communication") does not appear integrated and consistent with the rest of the work: therefore, I would suggest to remove it from the final version of the paper;

- the histograms in Fig. 11 and 12 are not very clear: the X-axis should be filled with the effective values of the error intervals, and some comments about the plots should be added to the text.

Author Response

### Point 1

> paragraph 4.1 ("Communication") does not appear integrated and consistent with the rest of the work: therefore, I would suggest to remove it from the final version of the paper;

While we appreciate the Reviewer's insight, we believe that this section should remain as part of the described methodology. 

As MDPI Robotics is an Open Access journal with a strong focus on real-world applications, we want our full methodology to be available to all readers.

Furthermore, Section 4.1 has been updated to better explain the communication structure and the underlying protocol with less technical jargon and more context.

### Point 2

> the histograms in Fig. 11 and 12 are not very clear: the X-axis should be filled with the effective values of the error intervals, and some comments about the plots should be added to the text.

The histograms have been updated for clarity, better X-axis interval alignment, and are now further discussed in the text.

Reviewer 3 Report

The paper is well-written and mostly clear. I found only 1 typo. And I have very minor suggestions that the authors may want to consider.

 - In Section 6 Discussion, the last sentence of the second paragraph says "an additional percentage points" where the word "points" should be singular instead of plural.

 - In the abstract, the authors mention "low-cost" but they do not state the relative reduction in cost. I think they should mention this valuable information up front. The actual amount of the reduction in cost isn't revealed until after reading 17 pages. 

 - In the abstract, a maximum error of 58um is mentioned, but I feel that a relative error should be added alongside this number to give a sense of the significance of the error. 

 - The redundant parameters in Section 3 Parameter Identification could use some clarification. For instance, you mention that there are 7 redundant parameters out of 28, but the 7 redundant parameters do not appear to be explicitly identified in Table 2.

 - In Section 6 Discussion, I'm not sure if the monetary values should have units, such as USD, CAD, EUR since their relative values are most important. And the date of the paper will justify changes in pricing over the years as future readers view the paper.

Author Response

### Point 1

> In Section 6 Discussion, the last sentence of the second paragraph says "an additional percentage points" where the word "points" should be singular instead of plural.

Thank you for the keen review.

### Point 2

> In the abstract, the authors mention "low-cost" but they do not state the relative reduction in cost. I think they should mention this valuable information up front. The actual amount of the reduction in cost isn't revealed until after reading 17 pages.

The cost of tooling has been added to the abstract.

### Point 3

> In the abstract, a maximum error of 58um is mentioned, but I feel that a relative error should be added alongside this number to give a sense of the significance of the error.

The absolute error of the impedance control approach has been added to the abstract.

### Point 4

> The redundant parameters in Section 3 Parameter Identification could use some clarification. For instance, you mention that there are 7 redundant parameters out of 28, but the 7 redundant parameters do not appear to be explicitly identified in Table 2.

The redundant parameters are now explicitly denoted by an asterisk in Table 2.

### Point 5

> In Section 6 Discussion, I'm not sure if the monetary values should have units, such as USD, CAD, EUR since their relative values are most important. And the date of the paper will justify changes in pricing over the years as future readers view the paper.

Monetary units have been added to all cost values.