An LWPR-Based Method for Intelligent Lower-Limb Prosthesis Control by Learning the Dynamic Model in Real Time
Round 1
Reviewer 1 Report
This article describes a control procedure based on learning the dynamic model generated by patients with Lower-limb prostheses. The aim with this is to find the best response of the actuated prosthesis for different types of gait.
In figure 3, it is not easy to appreciate the location of the markers, and apparently they do not coincide with those indicated in the motion capture system, which is a photograph of the screen, I would recommend that it be a screenshot to improve the quality. Regarding the location of the markers, why were those locations chosen?
Regarding the control law proposed in 12, is there a convergence analysis of the controller to determine what will eliminate the difference with the reference model? From there, a range of values can be obtained, in which the gains exposed in 21 must satisfy. Is it so?
It is described that the sample use was n=100? Does this have any argument?
In figure 9, the value of force has units?
In line 217 of the manuscript there is talking of "pretty good compliance", are these arguments accompanied by any corroborating data?
In line 234, the computational efficiency is described, but the manuscript does not mention what computational implementation was used, or the hardware devices that were used for said calculation, the objective is to do it in real time, there should be more knowledge of the hardware used.
Author Response
Point 1: In figure 3, it is not easy to appreciate the location of the markers, and apparently they do not coincide with those indicated in the motion capture system, which is a photograph of the screen, I would recommend that it be a screenshot to improve the quality. Regarding the location of the markers, why were those locations chosen?
Response 1: Thanks for the question. I’m sorry that the Figure is of low quality and lack of any introduction here. The markers are chosen based on the gait dataset collected by [1] which is following the Helen Hayes Hospital marker set. Because this paper only uses the angle of the sagittal plane of one leg, we reduced the number of marker points. After the makers are obtained, the makers will be sent to OpenSim to compute the inverse kinematics [2]. This part is not the importance of this paper, so we try to simplify the introduction and we have simplified this part after revision.
Point 2: Regarding the control law proposed in 12, is there a convergence analysis of the controller to determine what will eliminate the difference with the reference model? From there, a range of values can be obtained, in which the gains exposed in 21 must satisfy. Is it so?
Response 2: It is true that Kp and Kd is closely related to the convergence of the controller. However, it’s difficult to determine the range of this error between the dynamic model and the LWPR model, we intend to prove its convergence by scientific experiment schemes. This paper has been initially transferred this method from simulation to practice. With parameters in 21, the convergence is good. Next, as mentioned at the end of the text, we will try to analysis the error and convergence to master the powerful tool.
Point 3: It is described that the sample use was n=100? Does this have any argument?
Response 3: I see many papers make the n = 5 or n = 10 when compute RMSE. In this paper, n = 100 because the gait period is about 1 second and the sampling time is 0.01s. The RMSE of one continuous gait cycle is more representative.
Point 4: In figure 9, the value of force has units?
Response 4: Force data is the raw data of insole force sensor and has no unit. When GRF is zero, the value of sensor data is 1023. The greater the GRF, the smaller the value. I’m sorry the laboratory has no tools to accurately calibrate the plantar force….
Point 5: In line 217 of the manuscript there is talking of "pretty good compliance", are these arguments accompanied by any corroborating data?
Response 5: In simulation, the compliance can be compared by giving torque perturbations under different modes [3]. But in experiment, the subject’s walking need to be balanced by the handrail under the pure PD mode. However, subject can easily walk under the LWPR + PD mode. The subject think there is good compliance under LWPR + PD mode, which is shown in Figure there is enough displacement during the stance phase. We don’t know the effect of handrail, so we do not compare with two modes here.
[1] Camargo J, Ramanathan A, Flanagan W, et al. A comprehensive, open-source dataset of lower limb biomechanics in multiple conditions of stairs, ramps, and level-ground ambulation and transitions[J]. Journal of Biomechanics, 2021(119-):119.
[2] Camargo, J., Ramanathan, A., Csomay-Shanklin, N., & Young, A. (2020). Automated gap-filling for marker-based biomechanical motion capture data. Computer Methods in Biomechanics and Biomedical Engineering, 1–10.
[3] Sophie Heins, S. Tolu, and R. Ronsse. Online Learning of the Dynamical Internal Model of Transfemoral Prosthesis for Enhancing Compliance. IEEE Robotics and Automation Letters, 2021, 6(4), 6156-6163.
Reviewer 2 Report
The paper describes a control method for an active lower-limb prosthesis based on the real-time identification of a so-called LWPR-based approximation of the system's nonlinear dynamics. The paper includes experimental results obtained from a realistic setup in which the prosthesis are adapted to be used by healthy subjects, which is a reasonable approach for a safe validation of the proposed controller.
Overall, the presentation of the method is clear and the contribution is interesting. However, the following issues need to be addressed:
- there are a few inconsistencies in the mathematical notation of angular variables, namely eq. 1 is clearly quantified in radians, while degrees seems to be used elsewhere (eq. 10 and all the plots of angular variables).
- where relevant, figures should be revised to highlight more clearly swing and stance phases, as is done in Fig. 9 (possibly using an even sharper style, using e.g. vertical dashed lines). Some figures could also be enlarged (e.g. 8b, 9)
- the method applied to tune Kp/Kd control should be described, if possible it would also be interesting to see a comparison of different values.
Author Response
Point 1: there are a few inconsistencies in the mathematical notation of angular variables, namely eq. 1 is clearly quantified in radians, while degree seems to be used elsewhere (eq. 10 and all the plots of angular variables).
Response 1: Thanks for your kind reminder, it’s been revised in the new version.
Point 2: where relevant, figures should be revised to highlight more clearly swing and stance phases, as is done in Fig. 9 (possibly using an even sharper style, using e.g. vertical dashed lines). Some figures could also be enlarged (e.g. 8b, 9)
Response 2: Because there is ground reaction force only in the walking experiment, we highlight the swing and stance phase only in Figure 9. The figures have been enlarged for a little at the revised version.
Point 3: the method applied to tune Kp/Kd control should be described, if possible it would also be interesting to see a comparison of different values.
Response 3: The advice is really wonderful and it should be more experiment to compare the performances. Next, we will plan to study how Kp, Kd and LWPR model parameters and other potential factors influence the performances of the walking experiment. Thanks for your attention.
Reviewer 3 Report
As per the authors, lots of people in the world suffer from limb losses, and they think the prosthesis as the hopeful way to help the amputees back to normal life. To address this, this paper proposes a model called the LWPR (Locally weighted projection regression) model to learn the dynamic model of prosthesis in real time and proposes scientific experimental schemes to verify the control method of the proposed prosthesis model. First, the authors discussed the basic control framework of the lower-limb prosthesis. Then, they derived the control law based on model building and LWPR’s joining. Finally, the authors designed experimental schemes to carry out the control method effectively in a safe way, as per their opinions. Experimental results showed that, as the authors claimed, the control law with LWPR model was able to greatly improve the tracking performance during the swing phase and obtain pretty good compliance during the stance phase. The results also indicated that the LWPR model was able to approximate the dynamic model online. This method, as per the authors, is hopeful to be extended to more applications and fields, in the future.
While the above are appreciated, this paper is based on old references (only one reference is from 2021). All other references are older. The research is not aligned with the state-of-the-art research activities in this field. The proposed control is very basic (a basic PID controller), and the novelty is not clear. Experimental methods and procedures were not presented in detail. For each experiment, the authors should mention its objectives, setup, experiment design, subjects, data collection, data analysis, etc. The analysis based on the captured data is poor in the present form of the manuscript. The results do not prove its generality. The authors should conduct experiments with more subjects and experimental conditions and present the generality of their results through statistical significance. The results are insufficient to support achievements that the authors claimed in the abstract and conclusions.
The authors mentioned ‘learning’. As per the LWPR (Locally weighted projection regression), it is a very simple regression model. The novelty is not clear. The authors need to clarify how they trained the learning model. The integration between the PID and the learning model should be further explained. The authors emphasized on the tracking performance. The stability, response in real time, and human subjects’ subjective evaluations should also be used to justify the effectiveness of the proposed control integration.
Conclusions should be separated from discussions.
Author Response
Response to Reviewer 3 Comments
Thank you for your sincere comments on this article, your comments bring us a lot of topics to be studied. Due to limited space, many places cannot be described in detail in the paper, but we are glad to talk with you and learn from you.
Point 1: While the above are appreciated, this paper is based on old references (only one reference is from 2021). All other references are older. The research is not aligned with the state-of-the-art research activities in this field. The proposed control is very basic (a basic PID controller), and the novelty is not clear. Experimental methods and procedures were not presented in detail. For each experiment, the authors should mention its objectives, setup, experiment design, subjects, data collection, data analysis, etc. The analysis based on the captured data is poor in the present form of the manuscript. The results do not prove its generality. The authors should conduct experiments with more subjects and experimental conditions and present the generality of their results through statistical significance. The results are insufficient to support achievements that the authors claimed in the abstract and conclusions.
Response 1: Thanks for your kind comments. Recently, the state-of-the-art control methods of intelligent lower-limb are mainly based on a finite state machine with impedance control [1] or on phase-dependent trajectories to be tracked [2]. No obvious breakthrough has been made yet. In these methods, a lot of parameters need to be adjusted manually which is a way of poor efficiency to find the model compensation and lack of adaptability. [3] applied multi-Contact models and force-based nonlinear control to tracking the desired trajectory. But the compliance hasn’t been considered in [3]. [4] applied the LWPR model to fit the internal dynamic model which is an idea of model compensation to achieve better impedance control and get a high compliance. The simulation is successfully achieved in [4]. Based on the LWPR model, this paper analysis the control method firstly. Then, four experiments were designed according to the complexity of the model from simple to complex which gradually checks the feasibility of the proposed control method and ensure the safety of people. This paper has been initially transferred this method from simulation to practice. Next, as mentioned at the end of the text, we will further our study in different wearers and terrains.
Authors also think the analysis based on the captured data is not enough. The more serious and powerful evidence should be given. This is a really good topic to study.
Point 2: The authors mentioned ‘learning’. As per the LWPR (Locally weighted projection regression), it is a very simple regression model. The novelty is not clear. The authors need to clarify how they trained the learning model. The integration between the PID and the learning model should be further explained. The authors emphasized on the tracking performance. The stability, response in real time, and human subjects’ subjective evaluations should also be used to justify the effectiveness of the proposed control integration.
Response 2: Thanks for your advice. I think your advice is really wonderful but it’s a long process for us to study. For now, we take the first step to implement this method from simulation to the real world, and it is proved to be feasible in this experiment. The LWPR is an old regression model which isn’t novel. However, using LWPR to fit the internal dynamic model in real-time and achieving a good result are excited especially in the lower-limb prosthesis application. As for lower-limb prosthesis which is a man-machine system, the model building is always a difficult problem. We use regression method to fit the dynamic model (locally) in real time which is a good feedforward term to achieving better tracking performance during swing phase and better compliance during stance phase. The stability is hard to defined because the prosthetic wearer also plays a role in stability. In fact, human subjects’ subjective evaluation is the best evaluation, however it is hard to quantify and it’s less persuasive by saying “good”. Moreover, the compliance is confirmed by the subject during our walking experiment.
Point 3: Conclusions should be separated from discussions.
Response 3: It has been revised in the new version. Thank you.
[1] Sup F, Bohara A, Goldfarb M. Design and Control of a Powered Transfemoral Prosthesis[J]. NIH Public Access, 2008(2).
[2] V. Azimi, T. T. Nguyen, M. Sharifi, S. A. Fakoorian, and D. Simon, “Robust ground reaction force estimation and control of lower-limb prostheses: Theory and simulation,” IEEE Trans.Syst., Man, Cybern. Syst., 2020,50(8), 3024–3035.
[3] Rachel Gehlhar and Aaron D. Ames. Emulating Human Kinematic Behavior on Lower-Limb Prostheses via Multi-Contact Models and Force-Based Nonlinear Control.
[4] Sophie Heins, S. Tolu, and R. Ronsse. Online Learning of the Dynamical Internal Model of Transfemoral Prosthesis for Enhancing Compliance. IEEE Robotics and Automation Letters, 2021, 6(4), 6156-6163.
Round 2
Reviewer 1 Report
About point1: When you are writting your manuscript reminder to write the last part of the paragraph in any point of the introduction, with this deatil the readers could understand better the scope of your work.
About point 2: For determing the values for Kp and Kd there so many methods, on of them is the empiric method. However, if the scientific community would replay your experiments, those gains could work?
About point 3: I consider than 1 minute is not enought to validate the procedure. It is necessary more time than spend time in a cycle of gait.
About point 4: The raw data from force sensor is not correct way to show a relationship between two magnitudes. It is mandatory to identify the sensors in force units. The reason is because the resolution of sensor could be greater than lower changes in dynamical response of the system. The identification does not require special machinary, just with a reference value is possible to validate them.
Author Response
Point 1: When you are writting your manuscript reminder to write the last part of the paragraph in any point of the introduction, with this deatil the readers could understand better the scope of your work.
Response 1: Thanks for your comments. It’s real a mess when I read my manuscript…. I’m sorry that I don’t express clearly due to my poor English. I have revise a lot of introduction in the new version.
Point 2: For determing the values for Kp and Kd there so many methods, one of them is the empiric method. However, if the scientific community would replay your experiments, those gains could work?
Response 2: The adjustment of the values for Kp and Kd in this paper are manual by many tests. Because of the difference of mechanical structure, motor and subjects, I’m afraid that the values of Kp and Kd in the paper can’t work during the replaying and need to adjust manually. But in our experiment, we found that when Kp’ is half of Kp and Kd’ is half of Kd, the performance is pretty good.
Point 3: I consider than 1 minute is not enough to validate the procedure. It is necessary more time than spend time in a cycle of gait.
Response 3: The uploaded video size is limited, so we cut the video to one minute to satisfy the requirement.
Point 4: The raw data from force sensor is not correct way to show a relationship between two magnitudes. It is mandatory to identify the sensors in force units. The reason is because the resolution of sensor could be greater than lower changes in dynamical response of the system. The identification does not require special machinary, just with a
reference value is possible to validate them.
Response 4: Thanks for your advice. The force data has been simply corrected.
The changes have been noted in the PDF.
Reviewer 3 Report
The authors submitted their responses to the review comments. Thanks to the authors. However, the authors only responded to the comments. They did not try to modify the manuscript based on the comments. The reviewer thinks that there are a few previously mentioned issues that need to me addressed properly. For example, motivation, novelty of the control, machine learning detail, experimental detail, etc. I think the authors may consider my previous comments carefully.
Author Response
Please see the attachment. The changes have been noted in the PDF.
Author Response File: 
Author Response.pdf
Round 3
Reviewer 3 Report
The revision clarified some aspects of the manuscripts. However, the learning module needs further detail so that it can be reproduced/verified. The training of the learning module needs further explanation. The integration of learning and PID may make the system slow in response (as the graphs show partly). The authors may further clarify this point.
Author Response
Thanks for your sincere advice.
The learning module has been added as 2.5 in the new version.
The reasons for slow response in Figure 9 have been noted in the PDF.
Thanks again.
