Predictable Trajectory Planning of Industrial Robots with Constraints
Round 1
Reviewer 1 Report
This article is in the scope of the Journal, and deals with prediction of trajectory planning for an industrial robot. The paper includes mathematical modelling and a short experiment on an industrial Efort robot to support the claims.
In its current form, this article is mainly a technical paper aiming to solve an engineering problem rather than a solid scientific paper.
One of the first problems is that too many general claims have been made but the developments were applied to very specific areas. If the paper deals with the prediction of trajectory planning for industrial robot with constrains, the authors should write it specifically rather than general term 'robots'. The conclusion that the trajectory can be predicted is also too general; under what conditions it can be predicted? What affect the prediction? What are the limitations?
The way this manuscript is organized, hardly allows the reader to appreciate the value of their results. I encourage the authors to propose a clear research question in the Introduction section and state the potential contributions of a study and to extend the scientific background which is very limited.
The experimental settings should be explained and justified. The authors should extend the discussion on the selected setup and compare their results. Also, the achieved results should be scientifically discussed regarding the accuracy of the prediction achieved.
The discussion of the result in the Conclusions section is OK, but I miss the discussion of the IMPACT of these results. Was it the first time to achieve trajectory prediction? I think not. So the authors should compare the results to the literature and clearly explain why their approach is better.
The figures and the equations are hardly readable.
I encourage the authors to rewrite the paper based on the comments above, which will make it more scientifically solid and to resubmit.
Author Response
Dear professors:
Many thanks for the insightful comments and suggestions of the referees. We have made corresponding revisions according to their advice. Words in red are the changes we have made in the text.
The main revisions are listed as follows:
1. Q: If the paper deals with the prediction of trajectory planning for industrial robot with constrains, the authors should write it specifically rather than general term 'robots'
A: The prediction is limited in more specific areas---industrial robots.
2. Q: Under what conditions the trajectory can be predicted? What affect the prediction? What are the limitations?
A: The trajectory with end-effector and joint constraints can be predicted. The end-effector constraints are given as Equation (1). In practice, the end-effector constraints may not be described easily. In the paper, we give two specific end-effector constraints-linear and circular end-effector motions. There are two ways to deal with complicated end-effector constraints. One is to explore the equations of end-effector constraints as Equation (1). The other is to fit complex end-effector motions by linear and circular motions.
3. Q: The reviewer encourage the authors to propose a clear research question in the Introduction section and state the potential contributions of a study and to extend the scientific background .
A: Generally,there are three questions . 1) The motions of the end-effector between via points are not predictable in trajectory planning with end-effector constraints. 2)There is no guarantee that the end-effector will track the assigned paths in trajectory planning with joint constraints. 3)End-effector constraints and joint constraints are seldom considered simultaneously in the previous studies. In this paper, we attempt to solve these problems and hope the proposed method will act as a bridge between End-effector and joint trajectory planning.
4. Q:The experimental settings should be explained and justified.
A: The experiment is performed using a 6-DOF industrial robot Efort robot (ER3A-3C (HD)) that is produced by Anhui Efort intelligent equipment Co., Ltd. The link parameters of the Efort robot is shown in Table 1. The joint velocity limits given by the manufacture is presented in Table 2. The joint acceleration limit is 2×104 (rad/s2).
An actual machining process is performed on the Efort robot. The coordinates of the machined path are listed in Table 3. The path is shown in Fig. 1. The desired Cartesian velocity is 800mm/s. To reduce the vibration, the Cartesian velocities at the corner points are set to be 200mm/s. The machined workpiece is shown in Fig. 5.
5. Q: The authors should extend the discussion on the selected setup and compare their results.
A: The joint trajectories are shown in Fig. 3. The maximum velocity and the maximum acceleration of joint 3 are 5.06rad/s and 2.32×104rad/s2, respectively. Both of the values exceed their limits. The method of joint velocity/acceleration limits avoidance introduced in Section 2.2 is employed to adjust the joint velocity and acceleration trajectories. The maximum velocity and the maximum acceleration of joint 3 reduced to 4.36 rad/s and 1.85×104 rad/s2. The maximum joint velocities and accelerations are shown in Table 4. It is apparent from inspection of the table that most of the values are reduced and all values are in allowable range.
6. Q: The achieved results should be scientifically discussed regarding the accuracy of the prediction achieved.
A: The accuracy of the prediction is left to consider later. Related problems include the size , influence factor and improvements of the accuracy of the prediction.
7. Q: The authors should compare the results to the literature and clearly explain why their approach is better.
A: Roughly speaking, there are two kinds of trajectory prediction: trajectory prediction for future time, trajectory prediction for future tasks. Little attention is paid to Cartesian trajectory prediction that predicts the motion performed by the robot end-effector under joint velocity/acceleration constraints. Our method is not related to the literature that much. There is a great difference in perspectives and emphases between our method and the literature, causing our method has no comparability with other methods.
8. Q: The figures and the equations are hardly readable.
A: Because the the proposed method is using geodesic which is a concept from Riemannian geometry, the equations are indeed complicated. To increase readability, explanations of the equations are given as many as possible. More explanations of the figures are also given.
9. Q:The first word in the abstract misspelt.
A: We are very sorry to make this mistake and the whole paper has been checked carefully.
We appreciate for Editors/Reviewers' warm work earnestly, and hope that the correction will meet with approval. Once again, thank you very much for your comments and suggestions.
Best wishes.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The first word in the abstract in mispelt
The equations in the manuscript are ineligible. The manuscript cannot be reviewed if the equations are unreadable
Author Response
Dear professor,
Many thanks for the insightful comments and suggestions of the referees. We have made corresponding revisions according to their advice. Words in red are the changes we have made in the text.
Sorry for the ineligible equations in the manuscript. I provide another word format.
thank you very much
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
This article can be considered for publication
Author Response
Many thanks for the insightful comments and suggestions
Reviewer 2 Report
1. Good Language clean up is needed. 2. The trajectories mention in the tables need to have a time stamp for each of the via points, otherwise it is a path and not a trajectory. 3. Authors also need to explain if this is a method provides a necessary and/or sufficient proof of joint velocities and accelerations being bounded. 4. Velocity and acceleration profiles should also be plotted.Author Response
Q:Good Language clean up is needed
A: The paper is proofread carefully.
Q: The trajectories mention in the tables need to have a time stamp for each of the via points.
A：Time stamps for the via points are added in Table 3.
Q:Velocity and acceleration profiles should also be plotted.
A: The joint velocity and acceleration trajectories are shown in Figure 3 and 4. The Cartesian velocity of the Efort robot is shown in Figure 2
