Sequential Optimal Trajectory Planning Scheme for Robotic Manipulators along Specified Path Based on Direct Collocation Method
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsIt is very interesting work. Contains a description of a method helpful in planning of the robot's movement trajectory. The objective function is presented and the problem is formulated as an optimization problem. Very high accuracy of trajectory mapping was achieved.
A critical note is the fact that no details are included regarding the sources on the basis of which the equations were developed, which makes analysis and checking their correctness difficult. The second critical remark is the fact that no comparison was made with other known planning methods showing the differences and advantages of the presented approach. I evaluate the entire work positively.
Author Response
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Reviewer 2 Report
Comments and Suggestions for AuthorsThe work presents a sequential optimal trajectory planning scheme for robotic manipulators by dividing the process into path planning and trajectory planning stages. It employs direct collocation methods (DCMs) to efficiently address discretization errors, ensuring optimal performance in both the Cartesian space and joint constraints, as demonstrated on a six-axis robotic manipulator ROCR6. The manuscript can be improved by incorporating following concerns before accepted for publication.
1.The clarification should be included for the optimality conditions used in the optimization objectives and demonstrate that they are sufficient for ensuring global optimality?
2.What convergence guarantees does the mesh refinement algorithm offer, and are there any proofs or conditions under which convergence to an optimal solution is assured?
3.How does the Hermite-Simpson collocation method address the nonlinearity inherent in robotic manipulator dynamics, particularly in transitions between mesh nodes?
4. Is the proposed trajectory planning method scalable to manipulators with a high degree of freedom, and if so, what are the computational resource implications?
5.How robust is the path planning and trajectory optimization method in the face of model uncertainties and external disturbances?
6.Could you elaborate on why the Z-axis path tracking is particularly affected by increased arc velocities and discuss potential strategies to mitigate this discrepancy?
7. What was the rationale behind choosing IPOPT as the solver, how were its tuning parameters selected, and were alternative solvers evaluated for potential benefits?
8. Has an analysis been conducted on the long-term effects of wider current boundaries and temperature changes due to faster arc-velocities on the robotic components' longevity and wear?
Comments on the Quality of English LanguageThe English language can be improved and make it more fluent.
Author Response
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Reviewer 3 Report
Comments and Suggestions for AuthorsIn this paper the challenges in the area of applying direct collocation methods for the optimal trajectory planning for robotic manipulators. The topic is generally very current, the article requires some improvements.
1. In the section: introduction: It is worth adding an explanation of intelligent manufacturing in the context of the concept Industry 5.0. In the context of the analysis of the use of direct collocation methods for the optimal trajectory planning for robotic manipulators you should present the findings from different authors (e.g. in the form of the Table: “A literature review”) and please implement the research model as well as a research gap. What research niche is still in demand?
2. In the section 2 the research problem is very good described and also the algorithm described in the section 3 is very promised.
3. In the section 4: The research experiment is also well described.
4. In the section 5: Please add the description of practical significance of the obtained test results.
Author Response
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Reviewer 4 Report
Comments and Suggestions for Authors- The authors proposed a sequential trajectory planning scheme of robotic manipulators to minimize the approximation error introduced during discretization.
- Interesting subject, but the paper needs improvement.
- Line 175, From section 2 onwards, no further references are cited (It is only in section 4 that a reference appears again). Many mathematical equations appear in the paper without any explanation, and in some cases the equations lack a reference (to its origin). It is essential that in some parts of the text where mathematical equations are presented (lines 190, 201, 222, 255, 281,292, 319, 349, etc.) the sources (references) that were used to obtain the equations are presented. Improvements are needed!
- Line 185, the authors should use the word Section instead of Chapter. It is important to make it uniform with the rest of the paper's text.
- Line 197, t_0 and t_f , don't they represent time? Why are they identified as signs in the sentence?
- Lines 215-220, the text presents contradictions. Rewriting is recommended.
- Line 218, in this line x_0 and x_f appear, but these variables are not mentioned in equations (5)-(11).
- Line 235, doesn't h_k represent the sampling time? Therefore, why isn't it referred to as so? Normally h is constant in all iterations, but in the approach proposed by the authors h sometimes changes between iterations. What consequences does this have on the control and response time of the robotic manipulator?
- Line 236-238, the x and u have already been identified in this paper in several different ways (pp. 198-199; 215-216-218). It would be a good idea to make it uniform!
- Line 311, Why is s_total mentioned in the text since it does not appear in equations (32)-(41)?
- Line 344, Section 3.2, Improve this section, since it is not clear how the estimation of the path error of the trajectory planning is carried out.
- Lines 373-374, In figure 2 the specified circular path is not clear, it is recommended to present a figure where only the specified circular path is shown.
- Figure 2, There should be a Figure that identifies each of the joints of the robotic manipulator (using the same nomenclature presented in the formulas).
- Line 385, the meaning of IOPT acronym should appear the first time it is used and not after (line 412).
- Lines 397-398, Won't the large number of nodes introduced affect the response speed of the robotic manipulator as the number of nodes increases?
- The caption of Table 1 does not follow the standard.
- Line 407, Section 5, In the experiments that the authors implemented, no comparison of the approach proposed in this paper with other existing approaches is presented. It is important to highlight the advantages of the authors' proposal.
- Figure 7, This figure was never mentioned in the text, therefore it must be referred to or withdrawn.
- Line 427, The Conclusions (Section 6) must be improved since they do not reflect the advantages of the proposed approach.
Comments on the Quality of English Language- The paper must be proofread by a native English speaker, as there are some spelling errors and poorly constructed sentences that can be easily corrected.
- Some spelling errors can be found in lines: 73, 89, 95, 121, 125, 170, 275, 312, 368, etc.
- Some poorly constructed sentences can be found in lines: 189, 371, 373, 391, etc.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 4 Report
Comments and Suggestions for AuthorsDear Authors,
The revised version of your manuscript presents improvements.
At this point, I recommend that this research paper can be accepted for publication.
