Reviews that I got from ICRA and IROS

Rejected version -GRP_IROS :(

Review 1

This paper presents an approach to generating path samples for robot motion planning using Gaussian random paths. The paper is well organized and presents both simulation and physical experiments. In Section 3, the continuity and infinite differentialbility of paths are described which while beneficial, does not guarantee feasibility of sampled paths. There is discussion of whether sampled paths can be tracked in Section 3-A, but a method is given for only a unicycle model that effectively provides only orientation continuity for a planar robot. 

The experiments compared the performance of the proposed technique against a look-ahead planner. Since each planner did not maintain the same planning horizon, it is difficult to draw substantial conclusions about the relative performance of each. If the GRPP planner planned to the goal, a feasible sampling-based approach (RRT, PRM, etc.) or a boundary-value trajectory planner may have been more suitable choices for comparing the performance since each would plan all the way to/from the goal (note that there is mention of these in Section IV-B, but it remains unclear why a sampling-based approach would not be applicable to target tracking). 

There appears to be an assumption that robots are only able to move forwards along the paths, which may explain some of the performance challenges in the convex wall scenario.  If it is possible to produce paths

that go both forwards and backwards using GRPs, it would be worth discussing (if not demonstrating) that in the paper.  

Overall I think the approach is interesting and reasonably well presented, though it is difficult to draw substantial conclusions about their comparative performance given the difference in planning horizons in the simulation experiments. 

Specific Comments:

- the mention of the Google Driverless Car in the first paragraph should cite an article

- the discussion around static vs dynamic environments somewhat indirectly describes the problem that I believe the paper is trying to address, which involves responding to frequent (local) updates to a cost/obstacle map

- in the second paragraph of Section I it is misleading to say that planners are hampered by real-time and

kinodynamic constraints, the latter in particular is quite integral to the problem

- it is not quite accurate to say that the path sets in [1]-[6] were all computed a-priori, as at least some were simulated from the estimated robot state

- it was not clear as to why a look-ahead planner cannot incorporate a target location into it뭩 planning framework, as the shape of the look-ahead planner search space can (and has been demonstrated to) be influenced by the target position 

- it would be useful to know if the e run-up method for guaranteeing orientation continuity at the initial position can be applied similarly for terminal orientations.

- there are a few spelling/grammar errors, such as 밙ienct? at the top of Page 8.

Comments on the Video Attachment 

The video does a nice job of demonstrating the performance of the approach in simulation and physical experiments, and the introductory piece on how samples are taken is helpful 

Review 2

This article presents how Gaussian processes can be used for path planning. Application to a fast changing dynamic word is presented in the video attachment.

This work suffers several weaknesses.

- State of the art is largely insufficient: the path set method (LAP) is not the only path planner (mobile robotic

research is not limited to DARPA), nor the more efficient in the considered problem (finding a path connecting anchor points); moreover, Gaussian processes have already been used for path planning (at least once: Tay & Laugier, Modelling Smooth Paths Using Gaussian Processes, in Proc. of the Int. Conf. on Field and Service Robotics, 2007), but no comparison is done with this work (which is not cited)...

- This paper is submitted to a robotic conference, but it does not talk of robot! There should be a section about the considered robot, its motion constraints and how they are handled by the planner. The velocity constraint is handled in the beginning of section III.A, what about others (curvature bound, etc)? A paragraph should consider how these constraints could be added (any robot moving with a speed which is not very low has to respect those). 

이새낀 싸가지가 없다. 

In addition to these critical points, a lot of smaller corrections are also needed, including (but not restricted

to) the following: 

- a lot of words and notations are used undefined (i.i.d., N(), quantization free, ...), some denominations change (covariance function becomes kernel function), ...

- Fig. 6 is not appropriate: it does not show any difference between LAP and GRPP.

- Fig. 7(b) and the associated text use the term "Total Moved Distance", which is not clear and should be replaced by "Length of the Motion".

- Fig. 8(b) does not show any of the collisions indicated in Fig. 8(a).

Comments on the Video Attachment

Much better than the rest.

Review 3

This is a nice approach for generating a large set of smooth paths with some initial constraints. The formulation is clean and the description is good.

However, its applicability to local path planning is a bit dubious. There are other existing approaches that are more appropriate for the local path planning problem. For instance, the current approach generates a large set of paths and then evaluates each of these for collision. These paths don't actually need to be generated on the fly; rather, they could be stored in a lookup table parameterized by the agent state (e.g. heading, curvature) and then you can use arbitrarily complex models for the generation of these paths and can optimize the heck out of them to make them very smooth and executable. 

This is in fact what Howard et al. have done in many cases, including one of the papers cited by the authors (the CMU Darpa Urban Challenge paper). As such, fast path candidate generation online is not that critical. Further, these competing approaches are actually able to adapt the stored trajectories based on the specifics of the environment/agent to fit the environment. And more recent approaches based on very fast nonlinear optimization can incorporate obstacle information directly into the path candidate generation, so that you don't even need the paradigm of generating tons of candidates and then throwing out those that are infeasible.

I like the generation of the gaussian paths and as such, this paper represents a useful contribution. But its

application to the stated motivating domain is not particularly strong, and as such does not represent a big

contribution to local path planning.

Accepted version -LGP_ICRA :)

Review 1

This paper represents a technique for using non-stationary Gaussian Process Regression for robot learning. The main contribution of the authors is a novel regression method that also permits including negative examples to the training set. The papers seems to be methodologically sound, presenting the general theoretical framework, the method itself and test results conducted on a mobile robot. 

This paper lacks a general introduction that puts this work in context of robot learning in general. Learning from negative examples feels quite unique (Kruusmaa et al. "Don't do things that you can't undo", 2007

example is one related work) and is a potentially useful contribution but authors should claim it stronger by

examining already done work. Also, the authors should put their work in context with respect to other works in robot incremental learning (see e.g. Schaal et al 2002) and Gaussian regression model learning (see for example Nguyen-Tuong et al. 2009, ) and other works. Also, as for the experimental results, avoiding moving obstacles is one of a very common mobile robotics task. It is not clear if this method has an advantage upon the existing ones. 

In general, the idea is very interesting and potentially very useful for robotics but the case for robot learning

has to be better made.

Review 2

The authors of the paper develop a new kernel function for Gaussian Process Regression which makes it

possible to learn from both positive and negative samples. Besides the function itself, one of the main

results of the paper is a proof of its positive semi-definiteness. The interpretation in section C gives

the reader a deeper understanding of the introduced concepts.

It is very positive that the reader is provided with basic definitions and background knowledge. However,

especially in section I, the text would become much more readable by adding subsections. This is also true

for section II.B, which mainly deals with the kernel function equation (11) and the corresponding proof of

positive semi-definiteness. The meaning of the hyperparameters in equation (6) should be explained as

thoroughly as for equation (11) ?especially since (6) is highly relevant for the actual research results while

(11) is an alternative approach. The authors should try to separate more clearly between the review of

related work and the methodology actually used in the paper. In some cases it might even be helpful not

to explain every detail. For example, Mercer뭩 theorem is mentioned in the first paragraph although it is

not relevant in the context of the paper.

At the beginning, there is a mix-up of the terms positive definiteness and positive semi-definiteness. It is

very important to correct this inconsistency since the proof of semi-definiteness of the proposed kernel

function is one of the main results of the paper. In the evaluation, it might be interesting to see ?in

addition to the results shown in figure 4 ?how the number of negative samples affects the performance given a constant number of positive samples. For example, decreases the performance after reaching a certain

ratio? Finally, it should be stated more precisely if there is any related research or any other approaches which make it possible to learn from negative samples.

Review 3

The paper proposes a new method for Gaussian process regression that incorporates both positive data (to be modelled in the regression) and negative data (to be avoided).  Theoretical characterization of the problem is provided.  Empirical results show how the method can be useful to perform motion control, both in simulation and using a Pioneer robot. 

The first contribution of the paper is to define a new inference criteria for the GP that incorporates negative

examples into the regression objective. It extends previous results on non-stationary GP regression.  The new kernel (for incorporating negative data) uses a leverage parameter (1 per example) to capture how strongly positive/negative the point should be considered in the regression.  It's not 100% whether this leverage parameter is given or estimated. I presume it is given.

The second contribution of the paper is to show that the proposed kernel is positive semi-definite, and thus

suitable for GP regression.  The proof is reasonably simple, and appears sound; I could follow the full

reasoning, but am not sufficiently familiar with such proof to validate the correctness. 

A first set of experiments is conducted in simulation, use a simple autoregressive GP model. The results confirm that learning can be achieved more quickly (fewer examples) with the incorporation of negative examples.  In this case, the negative training data is acquired as "try to collide with the closest obstacles".  This is ok for a simulator, but seems a bad idea for a real robot system.  Is it plausible to incorporate negative training data that is not so negative as being dangerous or very costly?

Additional experiments are performed on a Pioneer robot, in a task where a robot has to travel 5 meters, and avoid a pedestrian (which conveniently always follows the same predefined path).  I couldn't find how negative examples were generated for this experiment; this seems an important question.  The presented results confirm better performance when negative examples are incorporated into the learning. 

I suggest adding confidence intervals to the results in Table 1.  I presume the differences are significant, given N=20, but it would be good to confirm.

The paper is very well written, clearly explaining both the scientific context, the proposed contributions, the

theoretical properties, and empirical results.

Overall, the paper makes valid contributions, that span the full range from algorithmic to theoretical to empirical.  It is clearly written, well motivated, soundly executed, and the preliminary results are promising.  The main limitation in my view is that it may be difficult or infeasible to acquire valid negative examples on a real robot system;  in reality, there is a cost to acquiring such examples, which the current approach does not consider (though this has been tackled extensively in the reinforcement learning literature, under the exploration/exploitation dilemma).  I encourage the authors to discuss this further. The suggestion that appears in the conclusion, of using the proposed framework to incorporate a measure of reliability (for each data point) into the decision, seems potentially more feasible for a real robot system.