Venue: CoRL 2022 Conference

Reviews:

final_score: rating: Weak Accept: I recommend accepting the paper, but will not argue for my recommendation if the majority of other reviewers have a different opinion.
review_content: summary: This paper considers the problem of tracking a curve path for a vehicle model. The authors apply the neural Lyapunov function approach to a straight line tracking problem. Given the learned Lyapunov function, the authors compute the largest curvature that the Lyapunov function can tolerate. The idea of this paper is straightforward, but the authors evaluated it on hardware.
strengths_and_weaknesses: Strengths:
1. Experiments on hardware.

Weakness:
1. Theoretical contribution is minor.
2. Some presentation issues.
robotics_focus: Sufficient demonstration on hardware
quality_of_the_limitations_section: Limitations are addressed clearly
summary_of_recommendation: Although the idea is simple, the experiments on hardware look promising.
issues: 1. The definition of u_{req} in Line 172 is confusing. Maybe move Eq. (5) here?
2. Caption of figure 2 is too close to the text. Maybe remove the blank space on the top and bottom of the figure?
3. L124: verified -> be verified.
4. Explain the function in Algorithm 1.
review_title: null

final_score: rating: Weak Reject: I recommend rejecting the paper, but will not argue for my recommendation if the majority of other reviewers have a different opinion.
review_content: summary: This paper applies existing techniques on learning Control Lyapunov Function (CLF) to the application of path following of ground vehicles. The main contribution of the paper is the ability to safely use a CLF designed for low curvature paths to paths with higher curvatures without losing the correctness guarantees of the CLF. The paper provides sufficient experimental evidence to support the proposed approach.
strengths_and_weaknesses: Strengths:
- The paper applies the proposed framework to a real-world example with interesting experimental results.

Weaknesses:
- The paper's contribution is limited to applying existing algorithms (i.e., neural-based CLF learning and verification) with minor modifications.

- Control Lyapunov functions for ground vehicles have been extensively studied, and several manually designed CLFs have been discussed in the literature. The paper lacks a clear justification of the motivation behind using a neural-based CLF for this setup. 

- The paper lacks a comparison against other techniques to understand the advantages and disadvantages of using the proposed framework.


robotics_focus: Sufficient demonstration on hardware
quality_of_the_limitations_section: Limitations are addressed clearly
summary_of_recommendation: While the paper provides interesting experimental results on a real platform, the novelty of the paper is limited to applying existing algorithms of neural-based CLF with minor modifications.
issues: - The main technical problem the paper aims to solve is unclear. Does the paper aims to answer the question of "how to obtain a CLF for ground vehicles?". But such a problem can be analyzed manually, and a learning-based approach is not justified. Or does the paper aims to answer the question of "Is neural-based CLF practical and can it be used for real-world example?" for which the use of ground vehicles is just an example to show these limitations? However, to answer this question one would expect the use of neural-CLF on a diverse set of problems to understand its limitations. Or does the paper aims to answer "how to use CLFs designed for paths with low curvatures to obtain guarantees on paths with higher curvature?" and the neural-based CLF happens to be just an example of a CLF? 

- It is unclear how the proposed framework handles the mismatch between the dynamical model (equation 4) and the actual robotic platform. The numerical results section does not describe the effect of this mismatch and applies the CLF designed for the nominal model directly to the platform. 

- How does the proposed approach compare against other non-learning approaches like using MPC with CLF constraints?
review_title: null

final_score: rating: Weak Reject: I recommend rejecting the paper, but will not argue for my recommendation if the majority of other reviewers have a different opinion.
review_content: summary: This paper proposes a framework to search for the best control for path tracking problems using neural control Lyapunov functions. The authors show the proposed method can ensure a bounded deviation of a target path and demonstrate the effectiveness of their algorithm on a real robot.
strengths_and_weaknesses: Strengths:

• This paper is well-written and easy to read. 

• The framework provides a general and simple way to extract a stabilizing feedback controller. 
  
Weaknesses:

• In the experiment section, there is lacking comparison between the proposed method and existing path tracking methods. It would be also interesting to see the performance comparison in controllers extracted by polynomial CLFs and neural CLFs.


robotics_focus: Sufficient demonstration on hardware
quality_of_the_limitations_section: Additional details required
summary_of_recommendation: Overall, this paper contributes to the current research field of search for a reliable controller with a theoretical guarantee and shows the process is practical in real robotic systems. However, it’s unclear to see how effective the proposed method is because of an absence of comparison. 
issues: Does the process encounter issues of scalability?
review_title: null

final_score: rating: Weak Reject: I recommend rejecting the paper, but will not argue for my recommendation if the majority of other reviewers have a different opinion.
review_content: summary: This paper proposes a new way to do path following using neural network based control Lyapunov functions (CLF). For a given vehicle dynamic with straight-line reference paths, the authors construct the neural CLF to satisfy the Lyapunov conditions. Next they derive the curvature bounds to ensure the CLF controller stay valid. Hardware experiments are conducted to showcase the proposed approach's real-time performance.
strengths_and_weaknesses: Strengths: theoretical guarantees for the CLF converging behavior and tolerant reference curvature bound ; hardware implementation to showcase the proposed controller can work in real-time.

Weaknesses: this work is incremental since there are already so many papers in using NN to construct CLF, and no baselines used in the experiments to demonstrate what is the benefit of this new NN CLF method. And they only use this CLF controller in a relative low-dimension experiment. The verification process can only converge within a small RoA.
robotics_focus: Sufficient demonstration on hardware
quality_of_the_limitations_section: Additional details required
summary_of_recommendation: My decision is weak reject. In the past few years we have witnessed so many papers in using neural networks to construct the Control Lyapunov Function, and I don't think this paper brings enough contribution to this field. The experiment is so simple and there aren't enough baselines or different setups to demonstrate the benefit of the proposed approach.

issues: The only novelty I can sense from the paper is the way to derive a bound for the reference curvature so that one CLF can fit for different reference paths. This is good, but how much can we benefit from this? So my suggestion is the following:

(1) For the vehicle experiment, first compare this method to the classical controllers (PID, LQR, MPC...) and to show that this experiment is indeed a hard problem that previous methods cannot really solve it elegantly. And then compare this method with reinforcement learning (I suggest pick some candidates from DDPG, SAC, TRPO, PPO) to show that this is not just another gym environment that can be easily tackled by RL.

(2) Next, add different experiment settings. Compare with vanilla version of the CLF. Can your method converge under more initial conditions? What about the converging speed? How about the training time and model size? What happened if you try the curvature out of the bounded region?

(3) Finally, please try more experiments. One vehicle example in such low-dimension is not persuasive at all. You definitely want to consider more challenging cases (more complicated vehicle models, drones...)
review_title: null

Meta-review: metareview: The paper focuses on path following of a ground vehicle with the use of NN-based CLF. It presents appealing demonstrations in hardware, however it lacks empirical comparisons to prior works. The paper is generally well-written and technically clear, but the theoretical novelty is limited as the approach relies on minor modifications to existing methods. Clearer justification of the significance is needed.

Main pros:
- Promising hardware experiments
- The paper is well-written

Main cons:
- Lack of comparison to baselines in the experiments
- Limited theoretical novelty

Post-rebuttal update: The revised version of the paper has offered comparisons to baselines. The authors also provided further explanations regarding the theoretical novelty. It is important that the final version of the paper will show also experiments with curved path following as the authors discussed with reviewer mRSR.
confidence: 4: The area chair is confident but not absolutely certain
Decision: Accept (Poster)