Path Planning of Mobile Robots with an Improved Grey Wolf Optimizer and Dynamic Window Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper proposes an improved version of the Grey Wolf Optimizer (GWO) algorithm for the trajectory planning of mobile robots. It incorporates several improvements, including chaotic piecewise mapping, a nonlinear convergence factor, evolutionary population dynamics (EPD), and dynamic weights. In addition, the Improved GWO (PAGWO) is combined with an Improved Dynamic Window Approach (IDWA) to optimize dynamic obstacle avoidance.

-The title does not accurately reflect the content and contributions of this article. I suggest modifying it to better reflect the work carried out.
-The dynamic obstacle avoidance strategy is based on simple rules (stop and wait for a lateral obstacle, accelerate in the event of a frontal conflict). This approach is reactive, not predictive. Avoidance could be improved by predictive models, such as Kalman Filters or Reinforcement Learning, to anticipate moving obstacles rather than simply reacting to them.

-The PAGWO-IDWA algorithm has been evaluated mainly in trajectory planning scenarios with static and dynamic obstacles. However, to strengthen the approach's validation and enable a more rigorous comparison with other optimization methods, it would be interesting to include additional tests based on the CEC 2022 benchmark.
-Some graphs (convergence curves, trajectory comparisons) are small or poorly captioned, making them difficult to read. The quality of the figures should be improved, high-resolution images used and more explicit annotations added.

 - For Figure 1, add arrows or annotations to highlight areas where the effect of parameter nnn is particularly noticeable.

-Clarification of improvements and comparison with standard DWA i) Add a clear list of the main contributions of improved DWA (IDWA). ii) Include a comparison table between standard DWA and improved DWA, highlighting the performance gains (reduced number of heading corrections, improved smoothness of movement, better management of dynamic obstacles).

-section 4.3. PAGWO-IDWA Algorithm: i)Include a small text below the figure explaining how PAGWO generates the global path and how IDWA optimizes obstacle avoidance locally. ii)Use distinct colors to differentiate between PAGWO (global planning) and IDWA (local navigation) steps.
-What is the cost function used in this paper? Highlight its main components and explain its impact on robot path optimization.

-I find that Figure 4 does not sufficiently highlight the optimization concept proposed in this article. I suggest that the authors add some pseudo-code to illustrate more clearly the smooth running of the algorithm and make it easier to understand.

-I didn't quite understand the real-time optimization mechanism that enables the robot to move smoothly and quickly. Is the optimization performed offline until the optimum parameters are determined, and then are these parameters applied online when the robot moves? Clarification on this point would be helpful.

-It is essential to add a flow diagram explaining the method in a comprehensive way. This diagram should highlight all the main elements, including the optimization algorithm, the robot, the optimized parameters and the objective function, in order to improve understanding of the process as a whole.

 

Comments on the Quality of English Language

 The English could be improved to more clearly express the research. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents a path-planning approach that takes inspiration from existing solutions but improves them systematically. The motivation and objectives of the research are clearly established. The methods used (most of them) are clearly described and justified. The experimental results are appropriate, including comparison with well-established solutions that validate the objectives of the research. The paper is well-structured although the formatting and English writing could be improved. Overall, I consider the quality and contributions of the work strong enough to be considered for publication. I am including a list of comments and recommendations for the authors to address in order to improve the clarity of their work:

-There are several parts where a reference is introduced and no spaces have been included between text. For example, in line 42 "Feng et al.[8]proposed an......".
-The product operator "." used in most of the equations could be removed.
-In line 203, it is important to highlight that the notation (0,0.5) means "open interval", i.e. that p cannot take values 0 or 0.5 because they produce an undefined result.
-Section 3.2 title should start with a Capital letter. There are several format errors like this in the paper.
-Other format errors that happen often are related to references to equations. For instance, in line 215 "From formula(3),a is ......" . Please revise the text adding the spaces when corresponding.
-What does data1 mean in Figure 1?
-Section 3.5 would fit better the Results section, I would suggest moving it.
-Is the theta in Eq (19) the same as the threshold theta illustrated in Fig 3 and described in line 384? if not please correct. Moreover, Fig. 3 should illustrate all the variables used for obstacle avoidance including theta_r, theta_obs, delta_theta used in Eq. 26.
-It would be better if the explanation of head-on conflict and non-head-on conflict is illustrated graphically. The current description is not very clear to me.
-It may be the case of pdf compression, but the quality of some of the images (e.g. Fig. 3 and Fig 5-10) should be improved.

The work addresses both global and local path planning or autonomous robots utilizing well-established algorithms with well-known limitations as the starting point, but addressing their limitations systematically with the goal of avoiding local minima in global plans and ensuring collision-free local plans in dynamic environments. The contributions of this paper are the introduction and validation of two variations of existing algorithms. The first algorithm is an improved Gray Wolf Optimization (GWO) algorithm that employs a piecewise chaotic mapping strategy to enhance population diversity and augment the optimization process's early-stage exploration capability, mitigating the issues of insufficient population diversity and low-quality initialization in conventional GWO algorithms. The second algorithm is an improved Dynamic Window Approach (DWA) that combines DWA with the first proposed algorithm. The globally optimal path generated is decomposed into individual local goal points, and the robot is guided by DWA toward the local goal points, traversing these points to reach the endpoint. Thus, unlike conventional DWA, which only takes the endpoint as the goal point in path planning, this modification allows the robot to complete the path planning task successfully, avoiding getting stuck in local optima or deviating from the optimal path when encountering situations such as U-shaped obstacles. Both proposed algorithms were evaluated in simulation scenarios, testing them in three different scenarios with increasing levels of complexity. In every scenario, the proposed global planning strategy demonstrated an improvement in terms of path length, and running time compared against other existing algorithms. Moreover, the local planning was evaluated by introducing dynamic obstacles occluding the way of the robot, in every trial, the proposed planning strategy demonstrated to be able to avoid collision. These results clearly validate the effectiveness of the proposal and are consistent with the evidence and arguments presented in the conclusions.   

Overall, I consider the quality and contributions of the work strong enough to be considered for publication after some minor corrections. I am including a list of comments and recommendations for the authors to address in order to improve the clarity and presentation of their work:  

Methodology comments: -Since the planning strategy was only tested in simulation, results may not be consistent with real-world requirements. For instance, the results shown in Fig 5-10 demonstrate that the resultant paths are shorter than other solutions. However, the proximity of the robot to obstacles in the environment is a factor that should be considered during path planning to minimize changes of collision due to localization errors. Authors should comment on this limitation, and how the distance between obstacles and robot, the dimension of the robot, and the obstacles would be integrated into their optimization process.
-It would be interesting to see the results of more tests with the improved DWA algorithm considering more than 2 dynamic obstacles. Authors could comment on those results and the potential maximum number of obstacles the planner could handle and/or which situations will be too complex to solve.  

Minor corrections: -There are several parts where a reference is introduced and no spaces have been included between text. For example, in line 42 "Feng et al.[8]proposed an......". -The product operator "." used in most of the equations could be removed. -In line 203, it is important to highlight that the notation (0,0.5) means "open interval", i.e. that p cannot take values 0 or 0.5 because they produce an undefined result. -Section 3.2 title should start with a Capital letter. There are several format errors like this in the paper. -Other format errors that happen often are related to references to equations. For instance, in line 215 "From formula(3),a is ......" . Please revise the text adding the spaces when corresponding. -What does data1 mean in Figure 1? -Section 3.5 would fit better the Results section, I would suggest moving it. -Is the theta in Eq (19) the same as the threshold theta illustrated in Fig 3 and described in line 384? if not please correct. Moreover, Fig. 3 should illustrate all the variables used for obstacle avoidance including theta_r, theta_obs, delta_theta used in Eq. 26. -It would be better if the explanation of head-on conflict and non-head-on conflict is illustrated graphically. The current description is not very clear to me. -It may be the case of pdf compression, but the quality of some of the images (e.g. Fig. 3 and Fig 5-10) should be improved.

Comments on the Quality of English Language

The English writing could be improved 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

After a thorough review of the current version of the article, I recommend its publication.