Review about the paper
Please find the review answers in this text format
Tajti – Szayer – Kovács – Burdelis: Mobile robot navigation tests for civil engineering considerations
We have studied your detailed, useful remarks, and we would like to thank you for your comments and questions, which were very useful for our work. We have marked all significant changes in the text using yellow color.
In the next section we will respond to your comments question by question.
1. The mathematical notation must be explained; some notation could be unknown for civil engineers (e.g. the abbreviation of sine or cosine as s or c isn’t used in civil engineering practice – like cϕ in the rotation matrix).
Thank you your comment: sin and cos are now used instead of s and c in the corrected manuscript.
= − ∆
∆0 ∙ cos 0
− 00 0 1 (2.3)
2. If the formula contains a function, which is not common, like Rot(z,ϕ) or Trans(x,Δx), then these functions must be explained.
Yes, such explanation was missing. Thank you. We have added the description of Rot(z,ϕ),Trans(x,Δx),and Trans(y,Δy) functions.
The transformation between the world coordinate system and the robot coordinate system can be described as (2.1). (See Figs.
1 and 2.),
→: ℜ !,#$%∙&'()* +,∆+$,-∙&'()* .,∆.$,-
/00000000000000000000000000001 ℜ (2.1)
where is the rotational transformation around axis z, and are the linear transformations along axes x and y.
3. In (2.4) some variables aren’t described (v, ω).
The description of (v, ω) variables are added.
The inverse kinematical functions of a 2-wheeled robot with differential drive can be described as (2.4) and (2.5), 2 3=3
456 −37∙ 8 ∙ 29 (2.4) 2 7=3
4 : ∙ 2 3+ 8 ∙ 2$ (2.5)
where L is the distance between the wheels and : is the radius of the wheels. In this case the robot has two wheels with drives (2 3, 2 7) and one wheel with free rotation and free steering, 6 and 2 are the velocity and the angular velocity of the robot.
4. Equation (2.6) is failing. Maybe a consecutive numbering must be done at the end of editing the manuscript.
Thank you for your remark. The numbering of the equations now are corrected in the paper.
= <4∙=4>?7 4∙=4-@A + B (2.6) = <4∙=4>C7 4∙=4-∙ cos @A + B (2.7) = <4∙=4>C7 4∙=4-∙ sin @A + B (2.8)
5. In chapter 3 (Path planning) the explanation about potentials is OK, but there is no word about the solution of the problem.
Thank you for this advice. The manuscript has been extended with this description.
The artificial potential method is based on the idea that obstacles generate repulsive force, and the target generates attractive force to the robot. The aim of calculating potential and force fields is to calculate the path to a predefined target position. The sum of attractive and all repulsive forces is moving the robot according to Newton’s laws as (3.5).
GH =∑ JKLL G,MN,MOV$CJPQR G,MN,MSTU$
PWX (3.5)
where Y'Z is the mass of the robot.
The path planner algorithm calculates the trajectory path, starting from an initial position with zero velocity and sequentially calculating the next position by taking the double integral of the acceleration in (3.5).
6. Reference 2 (in Chapter 3) seems also wrong: path planning and satellite trajectory control sound somewhat strange.
Yes. The context of Reference 2 is corrected. Reference 2 is a general path planning method. It is an example for path planning, which is different from the most common methods used in mobile robotics.
Several path planning algorithms are generally used in engineering for motion in 3D space [2], but for 2D motion of mobile robots, commonly used methods are genetic algorithms, sampling-based motion planning, fuzzy systems, neural networks, and artificial potential field (APF) methods.
7. U
att(x, v ) function in Eq. 3.1 has one velocity vector as input (declared in the function header), but two velocities are in the definition part (namely robot and target velocities). The vector notation is also unusual; they should be written in small bold letters, e.g. v. In the whole paper the font type of the functions, variables must be revised (normal, bold, italic etc. must use consequently).
Thank you for this useful comment. The equation and notation style were corrected according to the usual way and the journal template. Both velocities were also marked as inputs of functions.
[( G, MN, MO$ =
\+|G A$|V+ \M‖MN A$ − MO A$‖) (3.1)
where |G A$| is the Euclidean distance between robot and target, MN A$, MO A$ denote the velocity of the robot and the target at time t, respectively; ‖MN A$ − MO A$‖ is the magnitude of the relative velocity between robot and target; \+, \_ are scalar positive parameters; and Y, are none-negative constants.
8. The same notation failures are also in the definition of the repulsive potential.
Yes, thank you. We have corrected that part as well.
We propose a repulsive potential function as (3.3) in order to avoid collisions and handle moving obstacles:
['`a G,MN, MSTU$=
bc d
ce− fghi |G A$| + j*`k+ j'Z$l
−m‖_n7(?MSTU‖>
opq
−m‖MN7(?MSTU‖>
opq
r i G + j*`k+ j'Z$ < 1 tft
u (3.3)
where j*`k is a constant expressing a safe distance between the robot and the obstacle, in order to avoid collisions. j'Z is the radius of the robot assuming a cylinder-shaped robot. i, m are non-negative constants, MN, MSTU denotes the robot and obstacle velocity vectors respectively. The maximum acceleration of the robot is vwxy.
9. In Eq. 3.2 there is an x vector for robot position. Implicitly the authors mean that the coordinate system must be chosen so, as this vector must have always positive values, otherwise the log-function results error.
Yes, we meant and implemented the magnitude of x vector. We have corrected the equations accordingly. Please note that (3.2) was renumbered to (3.3).
We propose a repulsive potential function as (3.3) in order to avoid collisions and handle moving obstacles:
['`a G,MN, MSTU$=
bc d
ce− fghi |G A$| + j*`k+ j'Z$l
−m‖_n7(?MSTU‖>
opq
−m‖MN7(?MSTU‖>
opq
r i G + j*`k+ j'Z$ < 1 tft
u (3.3)
where j*`k is a constant expressing a safe distance between the robot and the obstacle, in order to avoid collisions. j'Z is the radius of the robot assuming a cylinder-shaped robot. i, m are non-negative constants, MN, MSTU denotes the robot and obstacle velocity vectors respectively. The maximum acceleration of the robot is vwxy.
10. How do the authors mean online calculation of the attractive and repulsive potentials? Do they think on real-time computation instead?
Yes, we mean real-time calculation of the potential functions at that point. Generally, we mean online path planning, where the trajectory of the obstacles are not known in advance, therefore real-time calculations are needed based on sensor data. We have corrected this mistake.
11. In Eq. 3.3 there’s no word about the forces (supposed the attractive and repulsive forces).
The mass of the robot isn’t defined (explained).
We have completed the chapter with the calculation of repulsive and attractive forces.
Equation (3.2) and (3.4) were added, and other equations were renumbered accordingly. The missing definition of mass was also added.
The force vector function pointing from the robot to the target is calculated by taking the derivative of the potential function according to equation (3.2).
z( G, MN, MO$ = −∇[( G, MN, MO$ =
|}KLL G,MN,MO$
|G ~NO+| M|}KLL G,MN,MO$
N $?MO $$~NO (3.2)
where ~NO is the unit vector pointing from the robot to the target and ~NO denotes the unit vector pointing from the robot in the direction of the relative velocity of the robot with respect to the target (i.e. the velocity of the robot in the frame of reference of the target).
The repulsive vector force function pointing from the obstacle to the center of the robot is calculated as (3.4).
'`a G, MN, MSTU$ = −∇['`a G, MN, MSTU$ =
|}PQR G,MN,MSTU$
|G ~SN+|hM|}PQR G,MN,MSTU$
N $?MSTU $l~SN (3.4)
where ~SN is the unit vector pointing from the obstacle to the center of the robot and ~SN denotes the unit vector pointing to the relative velocity direction of the robot with respect to the obstacle (i.e. the velocity of the robot in the frame of reference of the obstacle).
12. What are the dimensions (especially in Z) in Fig. 4?
Yes, thank you for your remark. The missing dimensions of the layout were explained. The
dimension of axis Z was scaled and indicated.
13. There is quite a lot about the accuracy and positional errors in Chapter 4. Just after Fig. 7 starts the description about cost function.
Yes, the organization of this chapter had to be revised. We have added a new initial paragraph that introduces the odometry error and energy consumption related performance measurement criteria. Also, the odometry error and its root causes are discussed more to make that part of the paper more easily readable.
The performance criteria have to be defined to evaluate the results of the path planner output. Two main aspects are discussed in this chapter: the estimated energy consumption and the position losses of the odometry based navigation. These performance estimations are properly described with their corresponding cost functions.
The odometry-based navigation error can be intensely accumulated depending on the motion of the robot. As a simple example, wheel slipping cases are more frequent in case of acceleration states compared to a linear, straight movement with constant velocity.
14. In Chapter 4 there are some bullets about position and orientation errors. The style of the bullets aren’t the same. The third bullet contains some data about inaccuracies. Are they own or literature data?
The bullets style was corrected according to the journal template. The data about manufacturing inaccuracies and their effect to the position error are our own measured and calculated data in the case of Ethon’s platform. Now, this is mentioned at the end of that sentence.
But the minimization of odometry error is still an important goal in real-time control systems, in order to obtain a better feedback at a much lower sampling rate compared to the vision based-solutions. For understanding position losses, the following root cause phenomena have to be considered:
• The slip of the wheels [4,6]
• The alternating contact points between the floor and the wheels in case of omni-wheels (see Fig. 5), or in case of a differential drive assembled with wheels having wide contact surfaces
• The production accuracy of the robot mechanics and wheels contains some ‰ of errors (For example in the case of Ethon, 0,1 mm difference between the diameters of the wheels causes at least 6‰ orientation error and 1‰ position error related to the travelled path)
15. W
2B in the same column seems a typographical error.
Yes, we have corrected it, thank you. (W
1refers to Wheel number 1.)
In case of a kiwi platform, the constant parameters in the inverse kinematical functions express the distance between the center of the robot geometry and the contact points of the wheels, which alternates between W1A and W1B and it can cause 5,4% error in the robot position and orientation.
16. The last sentence of the left column of page 4 is unclear for me, please reformulate it again.
The sentence was reformulated in the following way: The odometry error increase was obtained by getting the absolute value of the first derivetive of the odometry error.
17. I do not understand from the paper, why the error increase is important, why do the authors study them?
Thank you for your suggestion. The organization of this chapter has been revised and the odometry error and its root cause are discussed in more detail in order to make that part of the paper more easily readable. Also, the negative effect on real-time control is mentioned in the corrected paper.
But the minimization of odometry error is still an important goal in real-time control systems, in order to obtain a better feedback at a much lower sampling rate compared to the vision based-solutions.
18. In Fig. 6 what does the continuous and the dotted line mean? It should be in the figure caption.
The description of the lines has been added to the legend of the figure.
Fig. 6 Odometry position (b) and orientation (c) errors along the bechmark trajectory (a) In (a) the normal line represents the reference path and the dotted line is the real path. In (c) the grey line is the absolute value of the derivative of the orientation error
and the dotted line is the absolute value of the orientation.
19. In the same figure the abbreviation ABS repeats several times. Does it mean the absolute value? Why do the authors use it instead of the signed values?
We changed the “ABS” abbreviation to “absolute”. We have added an explanation in the paper, with some extra comments, as below:
We use absolute values instead of signed values, because during the tests we are interested in the absolute amount of error. If we define positive and negative directions for motion, the robot will make the same errors in positive and in negative directions also, so signed values are not meaningful in this experiment. Furthermore during changes of orientation, the robot moves along the x and y axes and the positive and negative errors cannot compensate for each other and both have effects on the robot position.
20. It’s also unclear how (a) and (b) are coupled. If the robot turns after 50 cm (Fig. part a), why don’t we see it just after ~230 cm (Fig. part b)?
Thank you very much for your remark. There was a timing problem during the data plot in the matlab source code. We have made the corrections and we have changed the figures
accordingly.
21. Orientation absolute errors are enough for accuracy testings? (Fig. part c)
In this case we are interested only in the absolute amount of error in relation with the change of the orientation. As previously explained, it does not make sense to consider the signed value of the orientation because the robot moves among x and y axes so the positive and negative directions of the errors cannot compensate for each other, but it is important to consider that both errors have significant effect on the robot’s position.
We use absolute values instead of signed values, because during the tests we are interested in the absolute amount of error. If we define positive and negative directions for motion, the robot will make the same errors in positive and also in negative directions, so signed values are not meaningful in this experiment. Furthermore during changes of orientation, the robot moves along the x and y axes and the positive and negative errors cannot compensate for each other and both have effects on the robot position.
22. Typo also for the word benchmark (again several times)!
The typo has been corrected in the paper.
For evaluation, benchmark tests were carried out over the past few years using many different robots along the same trajectories, but under different conditions (e.g. the wheels were changed, or motion control parameters were differently adjusted.)
23. How shall the angular velocity understand? (what is its dimension in Fig. part c)
In Fig. 6 part c there is angular position along the path. We have corrected this part of the text and the figure also.
Figure 6 (a) shows one of the bechmark trajectories, which was measured along an angular path, where the dotted line is the robot path and the normal line is the reference path, (b) shows the position odometry error increase along the trajectory, and finally, (c) shows the orientation error increase, where the dotted plot shows the angular position and the normal grey plot shows the derivative of the angular error.
24. If the paper has the focus on the Ethon robot (with kiwi drive), why is the differential type also involved? The comparison limits only on the two robot types, not on their costs or usage in buildings.
We performed more clarifications about the aim of the paper from this point of view. First in
the introduction, and then in some smaller corrections through Section 4.
The working environment of a robot has a significant effect on the power consumption and on the navigation performance. The aim of this paper is to provide feedback to the field of civil engineering, regarding to these two performance criteria. Our recommendations are based on theoretical investigation and experimental results obtained by using differential and kiwi drive mobile robot platforms.
The performance criteria has to be defined to evaluate the results of the path planner output. Two main aspects are discussed in this chapter: the estimated energy consumption and the position losses of the odometry based navigation. These performance estimations are properly described with their corresponding cost functions.
The odometry-based navigation error can be intensely accumulated depending on the motion of the robot. As simple example wheel slipping cases are more frequent in case of acceleration states compared to a linear, straight movement with constant velocity.
Otherwise the documentation of the comparison of the two robot types is also incomplete:
only some measures can be read, there’s no detail about the methodology.
The measurements were carried out with existing measurement systems, therefore we did not describe it in detail, but we have added the reference for further details.
The odometry errors were measured with different robots, in measurement experiments, which estimated the real position with better accuracy by using sensor fusion with optical flow position measurements based on ADNS9500 sensors, similar to the ones in [6, 7] and with distributed camera vision system of the Mechatronics Department of the Budapest University of Technology and Economics [8].
[8] Viktor, D., Antal, D., József, M., Péter, T., An Ethological Motion Capture System, in 12th IEEE International Symposium on Computational Intelligence and Informatics, CINTI November, 2011, Budapest, Hungary, IEEE Press 2011, pp. 487-491. DOI:
10.1109/CINTI.2011.6108555
25. Table 1 contains angular acceleration. Why is it important?
Wheel slip can occur easier when the wheels accelerate (or decelerate), this can be caused by linear acceleration and also by standstill turning. For example, in case of standstill turning, the angular acceleration will cause most of the slip.
26. The abbreviation n.a. in the same table seems also useless. It isn’t an English abbreviation.
In the corrected paper, “n.a.” has been corrected to “n/a” as the abbreviation of “not applicable”
27. In Fig. 7 the word ratio should be replaced by proportion. Ratio can be defined only between two components. The “error increase” is furthermore unclear.
Yes, thank you for this remark. “ratio” has been replaced by “proportion”. And the calculation method of the odometry error increase has been reformulated to be made more readable.
28. The involvement of height in the cost function chapter is useless, because the goal doesn’t require it, only the formulas are more complicated.
In case of more complicated buildings, where ramps (like wheelchair ramps) are usually used, the height can affect the final results so it seems to be important to mention this part of the equation.
The total amount of energy consumption by following the path can be calculated from the sum of the energy consumption of all time intervals. During the path planning experiments we did not use ground plans with different heights, like wheelchair ramps (∆h(t)=0) and we have investigated the energy as a function of the path instead of a function of time.
29. The references of the equations are wrong (Eq. 4.2, 4.3 etc).
Yes, thank you for this remark. The numbering of the equation is corrected in the paper.
30. The ratio of τ values is fine-tuning for me, there is no need in such a civil engineering approach.
The ratio of the τ numbers are important at the Experimental results section to get the final numbers at Table 2, what is an additional result at section 6.
During the tests the robot could move 13% more with angular rotation so the ratio of * and # can be described as (4.4), what is important at the experimental results section to get the final numbers in Table 2.
= 1,13 (4.4)
31. The comparison of two floor plans has only then meaning if the functionality of the office is clear. Otherwise the differences between these two variations are only possibilities without any connection to the reality. When the designed two variations fulfill the functional requirements, their analysis has really great importance. The shown trajectory is somewhat random, there is no explanation why the starting and end points are selected so in the illustrated case. Is there a comprehensive analysis and evaluation of such scenarios for path planning and robot motion?
We didn’t want to restrict the paper to a specific robotic task or functionality. The start and end points of the path can be chosen arbitrary. We have extended the experimental results with more explanations, consisting of specific criteria indicators which are independent from the Euclidean distance of the end points of the path, and Table 2. The main contribution of the paper is a method to measure the robotic compatibility of different options of ground plans.
The goal of this paper is not restricted to a limited robotic task or functionality. The start and end points of the path can be chosen arbitrarily. The main contribution is to propose a method to measure the robotic compatibility of different options of ground plans. To run the tests we have designed a Graphical User Interface (GUI), where the ground plans can be imported from bitmap (.bmp) image files and the parameters of the path planning methods can be changed. (See Fig. 8.) From the calculated path, the results of the energy and odometry loss cost functions can be calculated for differential and also for holonomic drives.
Fig. 1 The GUI of the proposed path planning method
The absolute odometry losses and the energy consumption related to the whole path have to be divided by the Euclidean distance between the start and end points of the path, in order to get specific performance criteria indicators that are independent from the exact functionality. The results can be seen in Table 2. …
Table 2 Odometry error and energy cost results Energy and odometry
cost results
Differential Holonomic Odom. [%] Energy
[%]
Odom.
[%]
Energy [%]
Fig. 9. (a) 116 E1 124 1,08E1
Fig. 9. (b) 109 0,72E1 117 0,81E1
Fig. 10. (a) 121 E2 129 1,09E2
Fig. 10. (b) 138 1,13E2 147 1,22E2
32. In the conclusion chapter one can read the expression “initial conclusion” which is unclear for me.
Thank you for your remark. We have changed “initial conlcusion” to “first conclusion”.
33. The caption of Fig. 9 has an expression “grayed out shapes”, which is not a correct notation.
We have replaced it to “gray filled shapes”.
34. In the Reference list item 3 has different format as the others, it should also be formatted as required.
Thank you. The format of reference [3] is corrected.
[3] S.S. Ge, Y.J. Cui, Dynamic Motion Planning for Mobile Robots Using Potential Field Method, in Autonomous Robots 13, 2002, pp. 207–222. DOI: 10.1023/A:1020564024509
