Adaptive Sliding Mode PID Control for Underwater Manipulator Based on Legendre Polynomial Function Approximation and Its Experimental Evaluation
Round 1
Reviewer 1 Report
This paper presents an improved method of underwater AUV manipulator control in the presence of unmodelled uncertainties. The theoretical approach is presented along with experimental validation and comparison against prior work.
Whilst the quality of English is good, it could still do with being proof read to improve the syntax.
Introduction: what is 'mental monitoring'? The introduction lacks some context. Hydraulic manipulators are assumed, but never formally introduced. The 'literature review' of AUVs with manipulators is very limited and subsequently there is a lack of relatable context for the paper.
'etc.' should not be used to end a sentence.
Line 60: remove the 'Ref' and just say 'In [17]'. This should be applied throughout the manuscript.
Three FAT approximations are identified in the lit review: Taylor expansion, Fourier and Legendre. The justification to use the Legendre method is lacking and there is no discussion as to why it is a better approach than the other two.
Line 105 should be "...cannot accurately be described"
In Fig 2, it would be very helpful to also plot the target angles, so that it is easier to compare the results and observe the analysis metrics.
Units are missing from Table 2b.
Lines 299 - 301 are redundant and should be removed as they are a repetition of the material in the tables. The same comment applies to lines 328 - 330 and 350 - 352.
The label for Fig 3b is on the wrong page.
Section headings for 4.2 ad 5 are on the wrong page.
Author Response
Response to Reviewer 1 Comments
Point 1: Introduction: what is 'mental monitoring'? The introduction lacks some context. Hydraulic manipulators are assumed, but never formally introduced. The 'literature review' of AUVs with manipulators is very limited and subsequently there is a lack of relatable context for the paper.
Response 1:
(1) For the first reviews, this is a mistake made by the author's work attitude. Then the author modified the first sentence of the manuscript as follow.
“In the complex sea, autonomous underwater vehicles (AUVs) play an irreplaceable role for various missions, such as exploration of marine resource, environmental monitoring, seabed topographic survey, and target search [1–2].”
(2) For subsequent comments, the author modified the first and second paragraph of the manuscript as follows.
“ In the complex sea, autonomous underwater vehicles (AUVs) play an irreplaceable role for various missions, such as exploration of marine resource, environmental monitoring, seabed topographic survey, and target search [1–2]. In recent years, with the deepening of marine development, simple detection and target search cannot meet the operational requirements. However, the underwater vehicle-manipulator system (UVMS) which consists of underwater vehicle and manipulators, and its operating technology have been rapidly developed and widely used in the fields of scientific research and ocean systems engineering for performing interactive tasks such as opening and closing of valves, cutting in coordination, and so on [3–4]. An AUV when equipped with a manipulator becomes a kinematically redundant system, it has more degrees of freedom (DOF) than is required to perform a task in its operational space. In TRIDENT EU FP7 project, an underwater electric manipulator was developed and equipped on multipurpose intervention-AUV [4]. An underwater electric manipulator (MARIS 7080, 7 DOF manipulator) was equipped on semi-autonomous underwater vehicle for intervention mission (SAUVIM) [5].
In UVMS, the underwater manipulator is a key component, and its joint control accuracy directly determines the operating accuracy of the UVMS. At present, underwater manipulators are mostly control objects with joint redundancy, and the accuracy mainly depends on the control performance of joints [6]. However, due to the nonlinear, time-varying of dynamic properties and other factors (i.e. external disturbances such as ocean current disturbance) [7–8], the system dynamic model has uncertainties, which will affect the joint control of manipulator based on the dynamic model. Besides, for most hydraulic manipulators, the joint control performance is also affected by joint lag [6,9,10], which means that the joint lag will affect the control accuracy of manipulator joint. In conclusion, under the influence of the above factors, it has great research significance and practical value to develop the joint control technology of underwater manipulators for improving the accuracy and efficiency of underwater operation. ”
Point 2: 'etc.' should not be used to end a sentence.
Response 2: According to the reviewer's comments, remove 'etc.' in the revised manuscript.
Point 3: Line 60: remove the 'Ref' and just say 'In [17]'. This should be applied throughout the manuscript.
Response 3: Agreed. According to the reviewer's comments, remove 'Ref' in the revised manuscript.
Point 4: Three FAT approximations are identified in the lit review: Taylor expansion, Fourier and Legendre. The justification to use the Legendre method is lacking and there is no discussion as to why it is a better approach than the other two.
Response 4: According to the comments, the author modified the third paragraph of the original manuscript; the details are as shown in the fourth paragraph of the revised manuscript.
Point 5: Line 105 should be "...cannot accurately be described"
Response 5: Agreed. The author modified the line 105 in the original manuscript.
“ Where, the nonlinear term H(η, t) contains all uncertainty factors, and cannot accurately be describe. For this reason, we will approximate H(η, t) online. ”
Point 6: In Fig 2, it would be very helpful to also plot the target angles, so that it is easier to compare the results and observe the analysis metrics.
Response 6: Agreed. According to the opinions of reviewers, add the target curve in Figure 2 of the original manuscript, shown in Figure 3 of the revised manuscript.
Point 7: Units are missing from Table 2b.
Response 7: This is a mistake made by the author's work attitude. Apologizes. The author made corrections in the revised manuscript and checked the article again.
Point 8: Lines 299 - 301 are redundant and should be removed as they are a repetition of the material in the tables. The same comment applies to lines 328 - 330 and 350 - 352.
Response 8: According to the reviewer's comments, the above content was deleted and optimized in the revised manuscript.
Point 9: The label for Fig 3b is on the wrong page.
Response 9: Thank you to the reviewers for pointing out this shortcoming, the author corrected it in the revised manuscript.
Point 10: Section headings for 4.2 and 5 are on the wrong page.
Response 10: Thanks to the reviewers for the comments. According to the opinions, the author modified the section headings of 4.2 and conclusions. The specific modification is shown in the "red" part of the revised manuscript.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper presents an adaptive sliding mode PID controller for a manipulator of underwater vehicle. Following are my comments. 1- The literature review is not good. Authors have to go thoroughly the literature and clarify the open problems and the main demerits of the existing work in the literature. 2- The main contributions are not clear. 3- It is better to add a schematic diagram for the manipulator and mention the forces and torques acting on it. Also, indicate the angles and the control inputs for each joint. 4- A control system block diagram showing the inputs, outputs, feedback signals, and control level is important to add, as it will make the controller design easy to understand. 5- The main parameters of the control system have to be added (manipulator weight, length and weight of each link, ... etc). 6- Why the control voltage is important to measure and obtain in the results? I think the torque of each joint is more important than the control voltage? please explain.Author Response
Response to Reviewer 2 Comments
Point 1: The literature review is not good. Authors have to go thoroughly the literature and clarify the open problems and the main demerits of the existing work in the literature.
Response 1: Agreed. In the revised manuscript, more details of literature are discussed. For this reason, the literature review of the original manuscript is changed, as shown in the third and fourth paragraphs of revised manuscript.
Point 2: The main contributions are not clear.
Response 2: Thank you very much for the opinion of reviewer. In the revised manuscript, the author optimized the content of author contributions. The author contributions are written according to the journal template.
Point 3: It is better to add a schematic diagram for the manipulator and mention the forces and torques acting on it. Also, indicate the angles and the control inputs for each joint.
Response 3: According to the review comments, the author added the mechanism diagram of the underwater manipulator in Figure 2c of the revised manuscript. And in Section 4, the main parameters of underwater manipulator are added in Table 1 of the revised manuscript, which is used to indicate the rotation angle range of each joint, the length and the weight of each joint.
However, since the controller output of the proposed method is the voltage, and because of the current experimental conditions, no torque sensor or torque feedback for each joint of the manipulator, it is impossible to indicate the precise torque of the joint. On the other hand, the voltage change of the controller output can directly affects the torque of the joint driven motor, and then affects the change of the joint torque. Therefore, the change of joint torque can be expressed by the control voltage. And in Section 4.2, the experimental results show that the changes of the control voltage, which can reflect the joint torque of the underwater manipulator.
Point 4: A control system block diagram showing the inputs, outputs, feedback signals, and control level is important to add, as it will make the controller design easy to understand.
Response 4: Agreed. In the revised manuscript, the control system block diagram of the controller in this article will be added in Section 3.2.2 to directly display the inputs, outputs, feedback signals.
Point 5: The main parameters of the control system have to be added (manipulator weight, length and weight of each link, ... etc).
Response 5: Agreed. In the revised manuscript, the main parameters of the control system of the adaptive controller are added to the third paragraph of Section 4. At the same time, the relevant parameters of the manipulator are made into Table 1 of the revised manuscript.
Point 6: Why the control voltage is important to measure and obtain in the results? I think the torque of each joint is more important than the control voltage? please explain.
Response 6:
(1) The output of the controller of the proposed method is the control voltage, which directly affects the motion performance of manipulator joint (such as speed, motion stability, torque, etc.). Therefore, the comparative analysis of the superiority of the proposed method is performed using control voltage.
(2) Actually, the motion performances of manipulator joint are directly related to the joint torque, so I agree with the opinions of reviewers. For the manipulator in this paper, the controller of the proposed method directly controls the joint driven component (DC brushless motor), and then control the joint movement of the underwater manipulator. The control amount of the motor is the control voltage (controller output), and the change of the control voltage directly affects the torque of the motor and then the joint torque of the manipulator. Therefore, the change of the control voltage and the joint torque are consistent. However, since the control voltage can be obtained directly, a comparative analysis of the effectiveness of the proposed methods is performed through the control voltage in this paper.
Author Response File: Author Response.pdf
