Driverless Bus Path Tracking Based on Fuzzy Pure Pursuit Control with a Front Axle Reference
Round 1
Reviewer 1 Report
A path tracking controller for driverless bus is proposed. On the basis, path tracking is divided into lateral and longitudinal control. First, for lateral control, a path tracking controller based on FPPC-FAR is indicated. Meanwhile, the reference point of PP is moved from rear axle to front axle.
In general, authors present a path tracking controller for driverless buss. Authors should consider the following comments to clarify the main contributions of their paper.
1.- In the page 1, in the introduction, authors say "and slid model control (SMC) algorithm are applied", it should be " and sliding model control (SMC) algorithm are applied".
2.- In the page 1, in the introduction authors say "The lateral controller controls the driverless bus to flow a desire path. Some model free methods, such as proportional-integral-derivative (PID) method [7], fuzzy logic control (FLC) algorithm [8] and slid model control (SMC) algorithm are applied.", in this part, authors should include references [a], [b] for the proportional-integral-derivative method, and references [c], [d] for the sliding model control.
[a] Robust feedback linearization for nonlinear processes control, ISA Transactions, Vol. 74, pp. 155-164, 2018.
[b] Structure Regulator for the Perturbations Attenuation in a Quadrotor, IEEE Access, Vol. 7, No. 1, pp. 138244-138252, 2019.
[c] Design of robust fractional order fuzzy sliding mode PID controller for two link robotic manipulator system, Journal of Intelligent & Fuzzy Systems, Vol. 35, No. 5, pp. 5301-5315, 2018.
[d] Hybrid controller with observer for the estimation and rejection of disturbances, ISA Transactions, Vol. 65, pp. 445-455, 2016.
3.- In the page 6, authors say " the centroid method is adopted as denazification method. ", it should be " the centroid method is adopted as defuzzyfication method. "
4.- In the page 6, authors consider a fuzzy algorithm, they should describe it with more equations.
5.- In the page 6, authors consider a fuzzy algorithm, they should clarify if it has a control purpose.
7.- In the page 7 in the equation (13), authors use a pid control, they should clarify if the pid control and fuzzy are combined in one form.
Author Response
Response to Reviewer 1 Comments
A path tracking controller for driverless bus is proposed. On the basis, path tracking is divided into lateral and longitudinal control. First, for lateral control, a path tracking controller based on FPPC-FAR is indicated. Meanwhile, the reference point of PP is moved from rear axle to front axle.
In general, authors present a path tracking controller for driverless buss. Authors should consider the following comments to clarify the main contributions of their paper.
Point 1: In the page 1, in the introduction, authors say "and slid model control (SMC) algorithm are applied", it should be " and sliding model control (SMC) algorithm are applied".
Response 1: Thank you for your reminding. Due to our negligence, there is an error about the full name of SMC. The “slid” is corrected as “sliding”. Equally, the “denazification” in " … as denazification method." is replaced by “defuzzification”. Meanwhile, we also replaced “fuzzy algorithm” by “fuzzy logic algorithm” and so on.
Point 2: In the page 1, in the introduction authors say "The lateral controller controls the driverless bus to flow a desire path. Some model free methods, such as proportional-integral-derivative (PID) method [7], fuzzy logic control (FLC) algorithm [8] and slid model control (SMC) algorithm are applied.", in this part, authors should include references [a], [b] for the proportional-integral-derivative method, and references [c], [d] for the sliding model control.
[a] Robust feedback linearization for nonlinear processes control, ISA Transactions, Vol. 74, pp. 155-164, 2018.
[b] Structure Regulator for the Perturbations Attenuation in a Quadrotor, IEEE Access, Vol. 7, No. 1, pp. 138244-138252, 2019.
[c] Design of robust fractional order fuzzy sliding mode PID controller for two link robotic manipulator system, Journal of Intelligent & Fuzzy Systems, Vol. 35, No. 5, pp. 5301-5315, 2018.
[d] Hybrid controller with observer for the estimation and rejection of disturbances, ISA Transactions, Vol. 65, pp. 445-455, 2016.
Response 2: I am so grateful about your kindly comments. After reading those references, we think those references improve the readability and persuasiveness of the articles. As suggested by the reviewer, those references are sited in the introduction. And “Design of robust fractional order fuzzy sliding mode PID controller for two link robotic manipulator system” is cited in fuzzy logic algorithm, too.
Point 3: In the page 6, authors say " the centroid method is adopted as denazification method. ", it should be " the centroid method is adopted as defuzzification method. "
Response 3: Thanks for your comments. The denazification is revised by defuzzification. Furthermore, the terminologies in fuzzy logic algorithm are also standardized. The fuzzy law is corrected by reasoning rules.
Point 4: In the page 6, authors consider a fuzzy algorithm, they should describe it with more equations.
Response 4: Thanks for your comments. We are so sorry that the improper descriptions about fuzzy logic algorithm makes you feel confuse. We discuss this section for more than three times and reference several papers. The description of fuzzy logic algorithm is reconstructed.
Firstly, we add a Figure at the beginning of 2.2 Lateral Controller. The Figure is shown as Figure 5. It describes the framework of lateral controller clearly. And the fuzzy logic algorithm is introduced to calculate the appropriate k and . The descriptions under 2.2 Lateral Controller is “As shown in Figure 5, the lateral controller is divided into PPC-FAR and fuzzy logic algorithm. The PPC-FAR calculates the desire steering wheel angle. Meanwhile, the look ahead distance and ratio in PPC-FAR are modified by the fuzzy logic algorithm.”
Figure 5. The framework of lateral controller.
Secondly, we also rewrite the 2.2.3 Parameters Self-tuning Based on Fuzzy Logic Algorithm. The fuzzy logic algorithm is divided into input set, output sets and reasoning rules. The curvature ( , 1/m) of desire path and velocity ( ) of driverless bus are defined as the inputs of fuzzy logic algorithm. Meanwhile, k and are defined as the outputs. The gaussmf type is used as membership function[6]. Figure 9 illustrates the fuzzification of inputs and defuzzification of outputs. The velocity and curvature are quantized into 7 qualitative variables ({NB, NM, NS, ZO, PS, PM, PB}). Equally, the outputs are also quantized into 7 sets. The fuzzy reasonings are shown in Table 2, which maps the input sets to outputs sets. Meanwhile, the center of gravity method is adopted as the defuzzification method. In addition, the fuzzy logic rules are defined according to the appropriate k and which are obtained through real bus experiments in lane keeping and turn.
(a) (b)
Figure 9. Membership function with gaussmf type. (a) Membership function of inputs. (b) Membership function of outputs.
Table 2 Rule table
|
s v k, l’d |
NB |
NM |
NS |
ZO |
PS |
PM |
PB |
|
NB |
NB |
NB |
NM |
NS |
ZO |
PS |
PS |
|
NM |
NB |
NM |
NS |
ZO |
ZO |
PS |
PS |
|
NS |
NM |
NS |
ZO |
ZO |
PS |
PS |
PM |
|
ZO |
NM |
NS |
NS |
ZO |
PS |
PM |
PM |
|
PS |
NS |
NS |
ZO |
ZO |
PS |
PM |
PM |
|
PM |
NS |
ZO |
ZO |
PS |
PM |
PM |
PB |
|
PB |
ZO |
PS |
PS |
PS |
PM |
PB |
PB |
Point 5: In the page 6, authors consider a fuzzy algorithm, they should clarify if it has a control purpose.
Response 5: Thanks for your suggestion. The same as response to comments 4, the fuzzy logic algorithm is provided to choose optimal k and in different conditions rather than a control purpose. The k and are two important parameters in PPC-FAR. The short look ahead distance cause high tracking accuracy but bring the unstable to lateral controller. Meanwhile, the optimal k in PPC-FAR merges the gap between real bus and vehicle model, but the improper k larges the gap. Furthermore, those two parameters are influenced by the velocity and path curvature a lot. In that case, the curvature of current path and velocity of driverless bus are defined as the inputs of fuzzy logic algorithm, meanwhile, k and are defined as the outputs.
Maybe the unclear description in lateral controller framework makes the function few obvious. To clear the function of fuzzy logic algorithm, Figure 5 is added in 2.2. As shown in Figure 5, the fuzzy logic algorithm is proposed to calculate the k and in PPC-FAR.
Figure 5. The framework of lateral controller.
Point 6. In the page 7 in the equation (13), authors use a pid control, they should clarify if the pid control and fuzzy are combined in one form.
Response 6: Thanks for your sincerely suggestion. The PI control in page 7 and fuzzy logic algorithm are independent. To clarify the function of fuzzy logic algorithm, we add the description under 2.2 Lateral Controller.
Figure 5 shows the framework of lateral controller, while the longitudinal controller is shown in Figure 10. The fuzzy logic algorithm is introduced in lateral control, meanwhile, the PID control is proposed in longitudinal control. Furthermore, the fuzzy algorithm is used to turning the parameters in PPC-FAR, while the parameters of PID is unchangeable.
Figure 10. Driverless bus longitudinal controller framework.
In longitudinal controller, the TD is introduced to smooth the desire velocity according to . Meanwhile the feedforward term is provided to relief the influence of road slope. The TD and feedforward ensure the efficient of longitudinal controller.
Above all, we modify the manuscript as follows: Firstly, we revise the improper vocabularies, such as the “slid” is corrected as “sliding”, and the “denazification” is revised by “defuzzification”. Secondly, the references provided by the reviewer are cited in the new manuscripts. Finally, to clarify the fuzzy logic algorithm, Figure 5 and some descriptions are added under 2.2 Lateral Controller. Meanwhile more details about fuzzy logic algorithm are expressed in 2.2.3 Parameters Self-tuning Based on Fuzzy Logic Algorithm. Furthermore, in order to make the article easier to read, we also insert more details about TD terms.
We have done our best to revise our manuscript according to the comments. And we sincerely hope that the new manuscripts are acceptable to Applied Sciences.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This is a very interesting article which proposes a new control algorithm for the self-driving bus. The author gives a good survey of vehicle control. The author adequately describes the details of the proposed algorithm and gives interesting results in both simulation and real experiments, although, the real experiment seems a little bit simple.
Some English editing is needed for improving quality. like
line 72 "To improve quality of controller" should be "To improve the quality of controller"
line 76 "introduces model of driverless" should be "introduces the model of driverless"
line 265 "track the desire path"
line 285 "Trajectories of driverless bus"
line 345 " decelerate and decelerate"
The "TD" at line 61 and "PI" at line 72 need explanation.
Author Response
Response to Reviewer 2 Comments
Point 1: This is a very interesting article which proposes a new control algorithm for the self-driving bus. The author gives a good survey of vehicle control. The author adequately describes the details of the proposed algorithm and gives interesting results in both simulation and real experiments, although, the real experiment seems a little bit simple.
Response 1: Thanks for your recognition of our work. In the several past years, we have surveyed lots of papers in path planning and control. My work is mainly concerning about path tracking and control in driverless bus. The CMU and other universities study the tacking problem in self-driving cars, while the driverless bus is the most useful in our real life. In that case, our team not only search the way to solve the problems in driverless bus, but also bring it to our real life. The real experiments are carried out in lane keeping and turning for the reason that those sceneries are most significant. Those conditions also illustrate the benefits of FPPC-FAR. In conclusion, not only the work in this paper is significant and not simple, but also the experiments confirm the algorithm is reliable in driverless bus.
Point 2: Some English editing is needed for improving quality. like
line 72 "To improve quality of controller" should be "To improve the quality of controller"
line 76 "introduces model of driverless" should be "introduces the model of driverless"
line 265 "track the desire path"
line 285 "Trajectories of driverless bus"
line 345 " decelerate and decelerate"
Response 2: My English is not excellent, and some vocabularies and phrases are not appropriate. Thanks for your kindly suggestions to correct the mistakes in this paper. The "To improve quality of controller" is revised by "To improve the quality of controller", meanwhile the “decelerate and decelerate” in line 345 is changed to “decelerate and accelerate”. The “desired path” or “desired velocity” is standardized as “desire path” and “desire velocity”. The denazification is revised by defuzzification. Furthermore, the terminologies in fuzzy logic algorithm are also standardized. The fuzzy law is corrected by fuzzy logic rules or reasoning rules.
Point 3: The "TD" at line 61 and "PI" at line 72 need explanation.
Response 3: Thanks for your suggestions. We add the full name of “TD” in line 61, and the new sentence is change to “It uses the gravity acceleration to release the influence of road slope and bus’s mass, and the tracking differentiator (TD) is used to smooth the change of desire velocity.”
Equally, the full name of PI is also added to line 72, thus, the sentence is changed to “proportional-integral (PI) [7-9] controller is used to follow the desire velocity.”
Furthermore, more details about “TD” and “PI” are described in 2.3 Longitudinal Controller.
In conclusion, we revise the manuscript according to the comments of reviewers. Not only the improper sentences are corrected, but also some details about TD and PI are added. Meanwhile, more details about the fuzzy logic algorithm are also explained in the new manuscripts. We have done our best to revise our manuscript according to the comments. And we sincerely hope that the new manuscripts are acceptable to Applied Sciences.
Author Response File: Author Response.pdf
Reviewer 3 Report
Please refer to attached file.
Comments for author File: Comments.pdf
Author Response
Response to Reviewer 3 Comments
Point 1: I appreciate very much this technical and application oriented paper. Interesting introduction reporting development of vehicles path and velocity tracking algorithms. The content of the paper fits very well the scope of Applied Sciences Journal.
This paper belongs to class of papers that are very characteristic nowadays. It is searching for a new quality based on fusion or combination of known and fundamental achievements. This technique of publications is similar to chemical laboratory and similarly offers extremely huge set of possible combinations. Some of them are very interesting.
In this sense the paper extends the range of possible solutions by combining pure pursuit control applied for steering vehicle's axles.
I am not convinced that the Authors are similar with the fuzzy control. A lot of serious mistakes in this matter can be found in the text. A fuzzy section in the paper is very concise. It does not contribute significantly to the paper's contribution. As the title of the paper refers to the fuzzy control, the reader expects much more than one concise subsection. The fuzzy base rule is completely omitted. The announced fuzzy auto-tuning is not described at all.
The Authors proposed rather heuristic (in part fuzzy) path tracking controller based on experience, conventional control approaches, simulation and experimental investigations.
Response 1: Thanks for your comments. The fuzzy logic algorithm is used to obtain the appropriate parameters in PPC-FAR. To describe the fuzzy logic algorithm clearly, we rewrite the expression in 2.2 Lateral Controller, meanwhile, more details about fuzzy logic rules are added.
The description of fuzzy logic algorithm is divided into two parts. Firstly, we provided an over view of lateral controller at the beginning of 2.2 lateral controller. As shown in Figure 5, the lateral controller is structed by the fuzzy logic algorithm and PPC-FAR. The PPC-FAR obtains the desire steering angle according to the position error. The fuzzy logic algorithm is provided to calculate suboptimal k and which are two most important parameters in PPC-FAR.
Figure 5. The framework of lateral controller.
Secondly, the details of fuzzy algorithm are re-written in 2.2.3 Parameters Self-tuning Based on Fuzzy Logic Algorithm. The inputs of fuzzy logic algorithm are defined as curvature of current path and velocity of driverless bus. Meanwhile, k and are defined as the outputs. Figure 9 illustrates the member function and sets of inputs and outputs. In order to guarantee the fuzzy logic obtains the suboptimal parameters, we get the suboptimal parameters during in lane keeping and turning conditions real experiments, then the reasoning rules are defined according to the parameters in experiment. Furthermore, the reasoning rules are shown in Table 2.
(a) (b)
Figure 9. Membership function with gaussmf type. (a) Membership function of inputs. (b) Membership function of outputs.
Table 2 Rule table
|
s v k, l’d |
NB |
NM |
NS |
ZO |
PS |
PM |
PB |
|
NB |
NB |
NB |
NM |
NS |
ZO |
PS |
PS |
|
NM |
NB |
NM |
NS |
ZO |
ZO |
PS |
PS |
|
NS |
NM |
NS |
ZO |
ZO |
PS |
PS |
PM |
|
ZO |
NM |
NS |
NS |
ZO |
PS |
PM |
PM |
|
PS |
NS |
NS |
ZO |
ZO |
PS |
PM |
PM |
|
PM |
NS |
ZO |
ZO |
PS |
PM |
PM |
PB |
|
PB |
ZO |
PS |
PS |
PS |
PM |
PB |
PB |
Finally, we standard the expressions in fuzzy logic rules. The “Denazification” is replaced by “defuzzyfication”. The " fuzzy language subsets" is corrected by “fuzzy sets”, and so on.
Point 2: Line 11. I am not a native speaker, but I feel this sentence should be corrected to deliver clear message.
Response 2: Thanks for your comments. The expression is not very appropriate. The first sentence of abstract mainly to show that this paper is concerns about the path tracking problems in driverless bus. Meanwhile, due to the model of driverless bus is not clear, it is difficult to achieve a trade-off between accuracy and stability especially. To make the sentence more clear, we merge the first and second sentence together, and delete some worlds. The sentence is change to “Currently, due to the model of a driverless bus is not clear, it is difficult for most traditional path tracking methods to achieve a trade-off between accuracy and stability especially in the electrical bus.”
Point 3: Lines 69, 86. Please consider to use term fuzzy rule instead of fuzzy law.
Response 3: Thanks for your suggestion. We have made correction according to the reviewer’s suggestion. The “fuzzy law” is replaced by “fuzzy rule”.
Point 4: Line 72. Cit. "To improve quality of controller, the desired velocity is smoothed by tracking differentiator (TD)" Please take into account: the differentiation typically introduces noise and fluctuations instead of signal smoothness.
Response 4: Thanks for your reminding. Maybe the less description about TD makes you confusing. We add more details about TD. Meanwhile, a simulation in Matlab shows the smooth result. The description about TD is shown as:
The longitudinal system is a discrete-time double-integral system. The Discrete Time Optimal Control (DTOC) law controls system to desire value with minimum steps and no overshoot [1]. In this section, DTOC is introduced to give continuous desire velocity. The system of desire velocity is designed as (13).
(13)
where is desire velocity. h indicates step length. Meanwhile, is law of DTOC. r denotes fast factor. k is control step. is desire velocity at k step. is the difference between and . The velocity error is calculated as
(14)
The Mean idea of DTOC [2] is: there exists a region in which the state gets to zero by an optimal curve. If the state is out of the region, the system uses a r acceleration to get to the region. If the state is in the region, an optimal curve is used to get to 0. The law of DTOC in this paper is shown as (15).
(15)
where is symbol function. If the state is in the region, that means , the outputs of is . On the contrary, the state closes to the region with the acceleration of r.
Figure 11. TD simulation result.
In Figure. 11, when r and h are different, TD has different speeds to track the desired velocity. Notably, the inputs of TD are step, but the outputs of TD are a smooth curve. That meets the needs of longitudinal control. It is obvious that if r decreases and h increase, TD uses less steps to get to desired value.
Point 5: Line 89. Cit:" ... influence of the ignorance in bus's kinematic model. " I suppose you can replace model ignorance by more suitable term.
Response 5: Thanks for your suggestion. We replaced the by “… reduces the influence caused by the ignorance of lateral dynamic in kinematic model.”
Point 6. Line 91. Please explain why you use kinematic bicycle model for representing the four-wheel bus model.
Equ. 1. Symbol v is not explained
Equ 2. Please show R in Fig. 1.
Response 6: 1. This study mainly concerns about the path tracking and control in driverless bus. In lateral control, the geometric path tracking controller needs a well describe of kinematic characters[3]. We simplify the driverless bus moves on a plane and the Ackerman geometric is suitable the driverless bus when the velocity is lower than 30km/h. In that case, the kinematic model describes the relationship between the steering angle and the change of driverless bus’s position. Suppose that the driverless bus is located at (0, 0), and the heading angle is 0, we can predict the state of bus according to the bus’s steering angle and velocity. Thus, the kinematic model is used to reparenting the four-wheel bus model.
The reason is added in line 91, too. The new sentences are changed to “ The driverless bus is simplified to moves on a plane and the Ackerman geometric is suitable the driverless bus when the velocity is lower than 30km/h. In that case, the kinematic bicycle model describes the relationship between the steering angle and the change of driverless bus’s position [20] and the model is shown in Figure. 2 . The arc is the trajectory of bus’s rear axle center. The kinematic bicycle model combines the two front wheels and the two rear wheels together. Moreover, there is no lateral sliding and only the front wheel is steerable. Then, the bicycle model is mapped into a two-dimensional plane. is the steering angle. is the center of front axle. Equally, is the center of rear axle. L is wheelbase. The heading of bus is represented as .”
We are very sorry for our negligence of the description about v in Equ. 1 and the miss in figure 2. The v in Equ 1 is the velocity of bus. We add the R in figure 2 and the new figure 2 is changed as:
Figure 2. Kinematic bicycle model.
Point 7. Line 177. ,, Several optimal parameters are got from experiments…”
Firstly, please consider to use suboptimal instead of optimal.
Secondly, please explain in which sense parameters are optimal. Which optimization criterion has been applied?
Response 7: Thanks for your reminding. The “optimal” is replaced by “appropriate”. The stability and tracking accuracy are used to justify the quality of parameters. We carry out several experiments with real bus in lane keeping and turn a 90° bend conditions with different velocity. And we pick up an appropriate parameter to very experiments. Those parameters are used in fuzzy logic algorithm.
Point 8. Line 183. I suppose that not" fuzzy language subsets" but fuzzy sets. Please show the fuzzy sets in a separate figure
Response 8: As reviewer suggested that we add a separate figure in new manuscript. Figure 9 shows the membership function both in inputs and outputs, and The fuzzy reasonings are shown in Table 2.
(a) (b)
Figure 9. Membership function with gaussmf type. (a) Membership function of inputs. (b) Membership function of outputs.
Table 2 Rule table
|
s v k, l’d |
NB |
NM |
NS |
ZO |
PS |
PM |
PB |
|
NB |
NB |
NB |
NM |
NS |
ZO |
PS |
PS |
|
NM |
NB |
NM |
NS |
ZO |
ZO |
PS |
PS |
|
NS |
NM |
NS |
ZO |
ZO |
PS |
PS |
PM |
|
ZO |
NM |
NS |
NS |
ZO |
PS |
PM |
PM |
|
PS |
NS |
NS |
ZO |
ZO |
PS |
PM |
PM |
|
PM |
NS |
ZO |
ZO |
PS |
PM |
PM |
PB |
|
PB |
ZO |
PS |
PS |
PS |
PM |
PB |
PB |
Point 9. Line 186 "Denazification" term is completely false here. You probably mean defuzzyfication.
Response 9: It is really true as Reviewer suggested that the denazification should be replaced by defuzzification. And we corrected the error in new manuscript.
Point 10. Line 204. "Most of time, the desired velocity changes by step. "Please justify why.
Eq. 13. There is none anti-windup limiter applied. This might be a cause of serious practical problems.
Response 10: 1. The driverless bus system consists of environment perception/ global planning/ local path planning/ path tracking and control. The desire path and velocity are given by local path planning and it only decision the maximum desire velocity. Meanwhile, the maximum velocity on street changes by step. Furthermore, to avoid the dynamic obstacles in street, the desire velocity should fall to zero or rise to maximum. Hence, the desire velocity changes by step. In that case, the input desire velocity in Figure 10 changes by step.
Figure 10. Driverless bus longitudinal controller framework.
The sentences are updated to “In feedback term, PI is used to give deceleration according to the difference between current velocity and desire velocity. The desire velocity is calculated by local path planning and it only decisions the maximum desire velocity. Meanwhile, the maximum velocity on street changes by step. Furthermore, to avoid the dynamic obstacles in street, the desire velocity should fall to zero or rise to maximum. Thus, the desire velocity changes by step, and the velocity error changes sharply. Meanwhile, PI is sensitive to errors, so the deceleration changes by step. Hence TD is applied to smooth the change of desire velocity. The longitudinal system is a discrete-time double-integral system [4]. ”
It is really true as Reviewer suggested that we add an anti-windup limiter in Eq. 13. The errors between k-b and k are used in PI.
(13)
Point 11. Please insert additional space do the text.
Response 11: Thanks for your reminding, we add several space in that sentence.
Point 12. Lines 323, 324 Please correct mistakes.
Response 12: Thanks for your reminding. The mistakes are revised and the sentence is changed as “Figure 16(a) illustrates the different performances of PPC-RAR and PPC-FAR. The steering angle oscillates in PPC-RAR. And that results in the oscillation of control system in the field experiments.”
Point 13. Line 325 Cit" The ignorance of kinematic model brings the oscillation in PPC-RAR". I suppose that the main cause is unknown vehicle's dynamics and improper settings of controller or improper controller structure.
Response 13: We agree with Reviewer’s points that the unknown vehicle's dynamics and improper settings of PPC-RAR bring the oscillation. And we modified the settings in PPC-RAR by moving the reference point to front axles. To illustrate the advantages of PPC-FAR, we carry out thousands of experiments both in simulation and real bus experiments. Table 3 and Figure 15 show part of the simulation with appropriate parameters. Not only the different parameters but also the different reference points of pure pursuit (PP) are tested. We observed that the closer to front axle, the PP performs more stable. Thus, the center of front axle is defined as the reference of PP.
Table 3. Performances of path tracking controller
|
Algorithm |
v (km/h) |
ld (m) |
Lateral error |
Final state |
Algorithm |
v (km/h) |
ld (m) |
Lateral error |
Final state |
|
PPC-RAR |
10 |
15 |
0.02 |
oscillate |
PPC-FAR |
10 |
|
|
|
|
20 |
0.03 |
oscillate |
10 |
0 |
stable |
||||
|
30 |
15 |
0.05 |
oscillate |
30 |
15 |
0.01 |
stable |
||
|
20 |
0.05 |
oscillate |
20 |
0.01 |
stable |
||||
|
60 |
20 |
0.06 |
oscillate |
25 |
25 |
0.04 |
oscillate |
|
(a) |
(b) |
Figure 15. Max lateral error. (a) Look-ahead distance is 4m. (b) Look-ahead distance is 6m.
Thus, the oscillation in PPC-RAR is caused by the unknown vehicle's dynamics and improper controller structure. And we rewrite the sentence as “The ignorance of kinematic model and improper settings of controller or improper controller structure brings the oscillation in PPC-RAR”
Point 14. Fig. 13 and in the paper's text along. Please consider to use word desired instead of desire.
Response 14: Thanks for your reminding. The “desired” is standardized as “desire”.
Above all, we modify the manuscript as follows: Firstly, we added more details about fuzzy logic algorithm in 2.2.3 Parameters Self-tuning Based on Fuzzy Logic Algorithm, meanwhile, the TD is expressed more in 2.3 Longitudinal controller. Furthermore, the reason to use kinematic model and why the desire velocity changes by step are also inserted in the new manuscript. Secondly, we revise the improper vocabularies, such as the “denazification” is revised by “defuzzification”. Finally, the references provided by the reviewer are cited in the new manuscripts.
We have done our best to revise our manuscript according to the comments. And we sincerely hope that the new manuscripts are acceptable to Applied Sciences.
References
Zhang, H.; Xie, Y.; Xiao, G., et al. A Simple Discrete-Time Tracking Differentiator and Its Application to Speed and Position Detection System for a Maglev Train. IEEE Transactions on Control Systems Technology 2019, 27, 1728-1734, 10.1109/TCST.2018.2832139. Zhang, H.; Xie, Y.; Xiao, G., et al. Closed-form solution of discrete-time optimal control and its convergence. IET Control Theory & Applications 2018, 12, 413-418, 10.1049/iet-cta.2017.0749. Park, M.; Lee, S.Han, W. Development of Steering Control System for Autonomous Vehicle Using Geometry-Based Path Tracking Algorithm. Etri Journal 2015, 37, 617-625, Zhang, H.; Xie, Y.; Xiao, G., et al. Closed-Form Solution of Discrete Time Optimal Control and Its Convergence. Iet Control Theory & Applications 2017, 12, 413-418,
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
Dear Authors,
I think, the current revision of the paper is much better compared to previous. But still there is a lot to be done to make it perfect. Please find remarks in attached file.
Comments for author File: Comments.pdf
Author Response
Response to Reviewer 3 Comments:
Comments: General remarks
I appreciate, as ever, very much this technical and application oriented paper. The Authors presented interesting technology demonstration clip. I think, that clip is prepared quite well, may be with exception of the last maneuver. However, at least the reversing maneuver and climbing steep gradients should be shown as well. By U-turn maneuver performed by a driverless vehicle, a human driver inside the bus is visible and his interaction with a steering wheel too. This is not a convincing show. The same is if you look in the Fig. 4 in the paper. The driverless bus is illustrated inconsequently with a driver inside. From these observations follow some serious consequences. The paper's title seems to be unjustified in this context and undermines the contribution.
In general, the revision 2 of the paper is much better compared to previous submission. I appreciate efforts of the Authors towards the improvement of the paper quality.
Still, I would like to raise a reservation over the fuzzy control deepness. The fuzzy part of the paper seems to be one of its major weaknesses.
I think, that the term desire path (followed 57 times in the paper) is not the best choice. In automatic control we use commonly: reference, set-point, or eventually desired path or trajectory.
Generally, almost all sentences marked yellow should be verified by a native speaker.
Author response: Thanks for your recognition of our work. Due to our negligence, there are some blurry parts in the clip and paper. We read the comments world by world. The reason for absence of reversing maneuver is explained in 1. Meanwhile, the experiments of climbing steep gradients are shown in the clip and some screenshot are shown in 2. And the road slope is also shown in the new manuscript. Furthermore, the safe officer must set in the driverless vehicle in China, and the details of driver is shown in 3. Figure 4 in the manuscripts is replaced and the driver is removed. In 5, the “desire” is also corrected as “desired”. Finally, we also revised the fuzzy logic interface machine and TD. The detail is shown as:
The purpose of PPC-FAR is to improve the tracking accuracy and robustness of Pure Pursuit in driverless bus when the speed is below 30 km/h rather than reversing maneuver. As shown in Figure 1, the preview point B is in the front of the bus, and the reference point is also moved to the front axle. Thus, the desired trajectory is used to control the bus to move forward. The Kinematic bicycle model of driverless bus is suitable to reversing maneuver. And we apply that to park the driverless bus in the early work. Due to the algorithm is different from PPC-FAR, we do not show the parking video in the clip.
Figure 1. Pure pursuit control with rear and front axle reference.
The driverless bus is used in urban, and the roads in city is lower than 3°. Thus, the steep gradients are absence in urban. In that case, we only carry out the experiments in urban scenes where the slope is below 3° in China. Due to the road slope changes slowly, the experiments results are not observed easily. To illustrate the well performances of longitudinal controller, we show the slopes of desired path in Figure 4.
Figure 1 shows several experiments with different road slopes. Figure 2 (a)(b) are the screenshot in recognize zebra and brake. The road slope is -2.5°. Meanwhile, the road slope changes from 1° to -1° in car following and brake experiments, which are illustrated in Figure 2(c)(d). Additionally, the road slope increase to 2.3° in recognize obstacle and brake/ recognize obstacle and brake experiments. The driverless bus drives smoothly in experiments. And the driverless bus stops behind the stop line.
Figure 3 (c) illustrates the velocity control results, and Figure 3 (d) shows the detail of decelerations and velocity error. And the slopes of desired road are shown in Figure 4. The slopes change from -1° to 2.3°, and the velocity error does not exceed 4km/h. The final error is 1 km/h. Those experiments illustrate the well performance of longitudinal control.
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Figure 2 Real bus experiments with different slopes. (a)(b) Recognize zebra and brake where the pitch is 2.5. (c)(d) Car following and brake. (e) Recognize obstacle and brake. (f) recognize traffic light and brake.
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Figure 3. Results of real driverless bus experiments. (a) Desired path and actual path of bus. (b) Steering angle, car speed, and control deceleration. (c) Lateral error and longitudinal error. (d) Deceleration and longitudinal error.
Figure 4. The slope of desired path.
During the U-turn experiments, the driver did not touch the steering wheel, which is shown in Figure 5 (a). After the driverless bus turns around, the driver toke over the bus. Thus, the driver turned the steering wheel at the end of the clip, which is shown in Figure 5 (b). Furthermore, there always exits one driver in driverless vehicle according to Chinese law. The driver guarantees the safety of driverless vehicle and he also protects the pedestrians from harm. So, the driver always sits in the driverless bus in the clip, not only in U-turn experiments, but also in other experiments.
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Figure 5. U-Turn experiment. (a)(b) Self-driving model. (c) The driver takes over vehicle.
To illustrate the driverless bus more consequently, we remove the driver in Figure 6,
Figure .6 Driverless bus platform.
Meanwhile, we agree with the viewer that the desired path is more suitable. Thus, we correct “desire path” as “desired path” in paper. Equally, the “desire” in Figures is replaced by “desired”, too. And the title of 2.2, 2.2.3 and 2.3 are also revised.
Additionally, we find some help from the native speaker to modify the sentences marked yellow. The “look-head” is corrected as “look-ahead”. And the “framework” is revised as structure. The “we” is removed in line 116. The output of TD is redefined as “the transmit of desired velocity” both in TD term and line 390, and so on.
Comments: Details
Title of subsection 2.2.3 must be modified. It does not reflect well its content.
Author response: Thanks for your comments. The title of 2.2.3 is revised as “Fuzzy Pure Pursuit with Front Axle Reference”. Meanwhile, the title of 2.2 is modified as “Lateral Control”, and the title of 2.3 is revised as “Longitudinal control”.
Line 91. Please consider to insert word model (simplified model). Moreover, the sentence in lines 91 and 92 must be corrected. They are unclear and hard to read. The same applies for the next statement.
Author response: Thanks for your kindly comments. The description of kinematic model is vague. We reconstruct the sentence. Firstly, we introduce the structure of driverless bus. Then the wheels are assumed with no lateral slip and only the front wheel is steerable. Meanwhile， the driverless bus is restricted to move in a plane. The sentences are revised as:
The kinematic model of driverless bus is shown in Figure 2. It collapses the two front wheels into a single wheel at the center of front axles, meanwhile, the two rear wheels are also collapsed into a single wheel at the center of rear axles. Furthermore, there are no lateral slip in wheels, and only the front wheel is steerable.
Lines 185, 186. The description does not correspond with the Fig.9. Please correct.
Fig. 9. Please magnify Fig. 9 or split it into 2 figures. Labels of membership functions are almost invisible.
Author response: Thanks for your careful review. We revise the fuzzy logic interface machine as the reviewer’s comments. Firstly, the Figure 9 is separated into 4 figures, which is shown in Figure 7. The membership function of inputs and outputs are shown in a single figure. Secondly, we correct the description of fuzzy logic interface machine and Figure 7. We introduce the structure of fuzzy logic interface machine, and then show the basic domain of inputs and outputs. The description about Figure 7 is also modified. The manuscripts are changed as:
In this section, to improve the tracking accuracy and robustness of PPC-FAR, a fuzzy logic inference machine is adopted to calculates the appropriate k and . The input quantity of fuzzy logic inference machine are defined as the curvature of desired path and velocity of driverless bus , meanwhile, k and are used as the output quantity. The basic domain of is [0 20], the basic domain of is [0 0.2], the basic domain of is [3 25], and the basic domain of k is [0.5 1].
As shown in Figure 9, the gaussmf type is used as membership function[1]. Both the inputs and outputs of fuzzy logic inference machine are qualitative into 7 sets denoted as NB, NM, NS, ZO, PS, PM, PB, where NB is negative big, and the PB is positive big.
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Figure 9. Membership function. (a) Membership function of . (b) Membership function of . (c) Membership function of . (d) Membership function of k.
Line 187. Fig. 9 does not show any defuzzification.
Author response: Thanks for your reminding. The center of gravity method is used as the defuzzification. The descriptions about defuzzification is added in the new manuscript as:
The center of gravity method is adopted as the defuzzification method, which is shown as (10)
(10)
where is an accurate output value; denotes fuzzy inference output value;is the membership value of ; a and b are respectively the upper and lower bounds of the fuzzy set theory domain of output variables.
Line 189. Strictly "base rule" not "fuzzy reasoning".
Line 189. Not equally but similarly.
Author response: Thanks for your reminding. The “fuzzy reasoning” is corrected as “base rule”. And the “fuzzy equally” is replaced by “similarly”.
Section 2.2.3. I suggest to extend this subsection by a 3D control surface. This finally will illustrate the result of fuzzy control part.
Author response: Thanks for your kindly comments. We revise the explanation about the rule base in fuzzy logic interface machine, and give more details about the rule base. The rule base of and k are divided into Table 2 and Table 3, meanwhile, the interfaces are also shown by a 3D control surface in the new manuscript according to the suggestion of reviewer. The description of rule base is updated as:
The rule base of fuzzy logic inference machine is established based on the trial and error in the real bus experiments. There are two fundamental principles to be followed.
(1) When is small and v is large, in order to guarantee the tracking accuracy and robustness of PPC-FAR, the k and should be large.
(2) When is large and v is small, in order to merge the gap between real bus and kinematic model, the k and should be small.
The rule bases of fuzzy logic inference machine are shown in Table 2 and Table 3. Each rule in the rule base are implemeted in the IF-THEN form, and Figure 8 shows the inturface of outputs.
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Figure 8. The surface of outputs. (a) The surface of . (b) The surface of k.
Table 2 Rule base of l’d
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s v l’d |
NB |
NM |
NS |
ZO |
PS |
PM |
PB |
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NB |
NB |
NB |
NM |
NS |
ZO |
PS |
PS |
|
NM |
NB |
NM |
NS |
ZO |
ZO |
PS |
PS |
|
NS |
NM |
NS |
ZO |
ZO |
PS |
PS |
PM |
|
ZO |
NM |
NS |
NS |
ZO |
PS |
PM |
PM |
|
PS |
NS |
NS |
ZO |
ZO |
PS |
PM |
PM |
|
PM |
NS |
ZO |
ZO |
PS |
PM |
PM |
PB |
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PB |
ZO |
PS |
PS |
PS |
PM |
PB |
PB |
Table 3 Rule base of k
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s v k |
NB |
NM |
NS |
ZO |
PS |
PM |
PB |
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NB |
PB |
PB |
PB |
PS |
ZO |
NS |
NB |
|
NM |
PB |
PB |
PB |
PS |
ZO |
NS |
NB |
|
NS |
PB |
PB |
PB |
PS |
ZO |
NS |
NB |
|
ZO |
PB |
PB |
PM |
ZO |
NS |
NM |
NB |
|
PS |
PB |
PB |
PM |
ZO |
NM |
NB |
NB |
|
PM |
PB |
PB |
PM |
NS |
NM |
NB |
NB |
|
PB |
PB |
PB |
PM |
NS |
NM |
NB |
NB |
7. Fig. 10. With a dotted read lines you distinguished two blocks: acceleration and deceleration. But if you look inside, you see mainly velocity signals, may be with exception of internal acceleration output of TD block. However, this output does not has any meaning on V1. Moreover, in summing point you subtract velocity form acceleration. How do you explain this? Please also clarify why Vt and Vfb have different notations as they are in fact the same.
Author response: Sincerely, the Acceleration and Deceleration in Figure 9 should be replaced by the Acceleration control and Deceleration control. Maybe the improper description makes you confuse. The local path planning only gives the desire velocity and only the velocity error is adopted in PI. Meanwhile, the tracking differentiator (TD) is widely used in control system to smooth the desired value. Such as the velocity control system, the TD is used to provide the transient profile of desired velocity. In that case, you mainly see the velocity singles rather than deceleration.
Furthermore, the velocity in summing point does not come from the acceleration. It comes from the Feedforward term. Compensation of deceleration and velocity is provided to release the influence of road slope. Furthermore, Vt and Vfb all note the velocity of vehicle.
To describe the deceleration control clearly and highlight the contribution of this paper, we reconstruct the description of acceleration, and show the deceleration as Figure 9. Meanwhile, the Vfb is corrected as Vt. The longitudinal control is changed as:
2.3 Longitudinal Control
The velocity of driverless bus is divided into acceleration control and deceleration control. Due to only the deceleration is controllable and the acceleration is controlled by the VCU of driverless bus, only deceleration control is discussed. The structure of longitudinal control is shown in Figure 11.
Figure 11. The structure of longitudinal control.
In Figure 11, the feedback term mainly focuses on deceleration which is calculated according to the velocity error . The PI is introduced to calculate . Meanwhile, the TD is applied to calculated the fast tracking of desired velocity which is shown as . The feedforward term provides the compensation of deceleration and velocity according to the road slope. The compensations are used to release the influence of road slope.
The feedback-forward control algorithm is introduced to deceleration. The deceleration is calculated as (11).
(11)
where is limited as . The deceleration is negative, thus, .
The desired velocity is calculated by local path planning and it only gives the desired velocity rather than a velocity curve. If the driverless bus needs to stop, the desired velocity jump to 0. To smooth the desire velocity, TD is applied to calculate the fast tracking of desired velocity[2]. In this paper, only the fast tracking of desired velocity in TD is used in PI.
Line 235. If you integrate velocity, you obtain displacement not deceleration or acceleration. If you integrate acceleration you obtain velocity not deceleration or acceleration. In the context of previous remark, the statement in line 235 is completely unclear.
Author response: Thanks for your reminding. In ADRC, the TD is used to construct a transient profile that the output of the plant can reasonably follow[3]. For example, a double-integral system which is shown as
where r is constant. And is the desire value for x1. Han propose a time-optimal control (TOC) as
A desired transient profile is obtained according to the TOC. In discrete-time double-integral system, which is shown as
where is the outputs of DTOC.is desired velocity. h indicates step length. is law of DTOC. r denotes fast factor. k is control step. is desired velocity.Han modified the TOC as discrete time-optimal control (DTOC). The DTOC is shown as:
As to driverless bus, the desired velocity also jumps. With the inspire of Han, we introduce the TD of ADRC to smooth the desired velocity.
In that case, the TD does not integrate velocity or acceleration. It is used to calculate a fast track of desired velocity. And the descriptions of TD are revised as:
The longitudinal system is regarded as a discrete-time double-integral system [4]. The discrete algorithm of TD is given as (12).
(12)
where is the desired velocity. is the transmits profile of desired velocity. r denotes fast factor. h indicates step length. is DTOC law[5]. is the outputs of DTOC. k is control step. The law of DTOC is shown as (13).
(13)
where is symbol function.
Figure 12. The fast tracking of desired velocity.
Figure 12 illustrates the different transient profile of desired velocity with different r and h. It is obvious that the fast tracking of desired velocity is smooth. That certainly improves the inputs quality of PI. Furthermore, if r decreases and h increase, TD tracks the desired velocity faster. Thus, the speed to track the desired velocity is adjusted by the r and h.
Line 243. Not current error but control error.
Author response: And the “current error” is replaced by “control error”.
Line 286. "Obviously, the lateral error is close to O". I am not convinced that "obviously" is the best choice. The lateral control error tends to zero but not immediately. In Fig. 13 this error tends to zero along the distance. Much more convenient would be to recalculate and show this figure versus time not versus distance.
Author response: Thanks for your suggestions. The "obviously" is used to highlight that the PPC-FAR improves the stability of Pure Pursuit in driverless bus. By showing the lateral error according to the distance, we could easily observe the status of driverless bus along the road. In that case, we can compare the performances of PPC-FAR and PPC-RAR according to the position. When the velocity is same, the cost distance and time in different path tracking controller and parameters is obvious. If the simulation results are shown by time, we only observe the status of driverless bus along the time, but the status of driverless bus at each location cannot be observed. Thus, we cannot compare the performances of controller. Meanwhile, the cost of distance is also hard to analysis.
Line 293. Please omit "too". Otherwise this sentence does not make sense.
Author response: The “too” is deleted.
Line 385. Not "fuzzy logic algorithm" but fuzzy logic reasoning or fuzzy logic inference machine .
Author response: The “fuzzy logic algorithm” is revised as “fuzzy logic inference machine”.
Line 387. How the differentiator (TD) is able to smooth any signal with non zero frequency band? It is unclear. Maybe you mean n-order lag system? But it is not differentiator.
Author response: Thanks for your reminding. The TD comes from the PID implementation. The is the input signal of PID. Han [3] propose a second-order transfer function to calculate the differentiation of and resolve the aforementioned problem of noise amplification. The transfer function is shown as:
A particular second approximation of a differentiator is s/(τs + 1)2, which corresponds to the differential equation with r = 1/τ.
where tracks , tracks , and r determines the speed.
According to the fast tracking of , Han [3] propose the “ tracking differentiator”. If the is input single, the TD is defined as:
where tracks , and tracks, is the time optimal control (TOC).
In discrete-time double-integral system, TOC is not suitable, Han modified the TOC as discrete time optimal control (DTOC). The DTOC tracks the input by time step h. The DTOC is shown as:
The discrete-time double-integral system with DTOC is:
where is the outputs of DTOC.is desired velocity. h indicates step length. is law of DTOC. r denotes fast factor. k is control step. is desired velocity.
Inspired by the TD proposed by Han, we use the fast tracking of TD to calculate the fast tracking of desired velocity. And the advantage of TD is shown as Figure 12.
Figure 12. The fast tracking of desired velocity.
Above all, we modify the manuscript as follows: Firstly, according to the comments of reviewer, we modify the descriptions about fuzzy logic interface machine The member function of inputs and outputs of fuzzy logic interface machine are added, and the rule base is also redefined and the 3D interface figures are shown, meanwhile, the defuzzification is also added. Secondly, the longitudinal control algorithm is re constructed. The Figure 11 is replaced, and the descriptions about TD are revised. Thirdly, the figure of driverless bus is replaced. Meanwhile, all the sentences remarked yellow are revised.
We have done our best to revise our manuscript according to the comments. And we sincerely hope that the new manuscripts are acceptable to Applied Sciences.
References
Zhang, C.; Hu, J.; Qiu, J., et al. A Novel Fuzzy Observer-Based Steering Control Approach for Path Tracking in Autonomous Vehicles. IEEE Transactions on Fuzzy Systems 2019, 27, 278-290, 10.1109/TFUZZ.2018.2856187. Zhang, H.; Xie, Y.; Xiao, G., et al. A Simple Discrete-Time Tracking Differentiator and Its Application to Speed and Position Detection System for a Maglev Train. IEEE Transactions on Control Systems Technology 2019, 27, 1728-1734, 10.1109/TCST.2018.2832139. Han, J. From PID to Active Disturbance Rejection Control. IEEE Transactions on Industrial Electronics 2009, 56, 900-906, 10.1109/TIE.2008.2011621. Zhang, H.; Xie, Y.; Xiao, G., et al. Closed-Form Solution of Discrete Time Optimal Control and Its Convergence. Iet Control Theory & Applications 2017, 12, 413-418, Zhang, H.; Xie, Y.; Xiao, G., et al. Closed-form solution of discrete-time optimal control and its convergence. IET Control Theory & Applications 2018, 12, 413-418, 10.1049/iet-cta.2017.0749.
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