Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Research aimed at accurate robot pose measurements is crucial for many practical applications. The work is well-written and interesting. Please respond to a few comments before it can be accepted.

1. Page 1 - The introduction begins by stating the importance of geometric accuracy in various practical applications. Provide numerical values ​​for accuracy that are expected in these industries.
2. Page 2 - "unacceptable process defects" - please specify these defects.
3. It's also worth adding in the introduction the importance of simulation studies in determining positioning accuracy. Indeed, laser tracers are a valuable solution in real-world experiments. It's worth noting that simulations can also yield reliable results. Please refer to: https://doi.org/10.3390/app15062976 In this paper, the authors analyzed the robot's motion trajectories and positioning accuracy using simulation software.
4. While many graphs presenting errors are provided, some statistics are missing. I suggest adding a table and presenting the errors numerically.
5. Did the authors use a specific type of robot for this study? How might the results be generalizable across different robots?

Author Response

Responses to the Reviewer’s Comments

Dear Editor and Reviewers:

Thank you very much for your careful review and constructive comments on our manuscript entitled “Laser Tracker Based Robot Pose Measurement Using Interferometric Ranging, PSD Spot Sensing and Multi Sensor Fusion”. The comments are valuable and have significantly improved the paper's quality and clarity. We have carefully revised the manuscript accordingly, and all revised portions are marked in red in the revised version. Below, we provide a detailed, point-by-point response to the reviewer’s comments.

Responses to the reviewer’s comments:

 

Reviewer #1

Question 1: Page 1 - The introduction begins by stating the importance of geometric accuracy in various practical applications. Provide numerical accuracy expectations for these industries.

Response: We thank the reviewer for this valuable suggestion. In the revised Introduction (Page 1), we have added quantitative accuracy requirements for representative industrial applications. Specifically, aircraft assembly and large-scale tooling alignment typically require positioning accuracies of 0.1–0.3 mm over meter-level workspaces; automated drilling and riveting demand sub-millimeter accuracy (approximately 0.05–0.2 mm); robotic welding and large-scale additive manufacturing generally require errors below 0.5 mm; and high-precision calibration and metrology tasks often require accuracies approaching or better than 0.1 mm. These additions clarify the industrial motivation and application context of the proposed method.

Question 2: Page 2 - “unacceptable process defects” – please specify these defects.

Response: We appreciate the reviewer’s comment. The phrase “unacceptable process defects” has been clarified in the Introduction. In the revised manuscript, we now explicitly list representative defects, including hole misalignment in drilling and riveting, excessive weld seam deviation, poor mating of large structural components, increased residual stress, and degradation of dimensional consistency in large-scale additive manufacturing. This clarification improves the technical specificity of the discussion.

Question 3: It is worth adding the importance of simulation studies in determining positioning accuracy and citing related work.

Response: We agree with the reviewer that simulation studies play an important role in assessing positioning accuracy. Accordingly, a new paragraph has been added to the Introduction emphasizing the role of simulations in analyzing robot motion trajectories, sensor noise, delay effects, and error propagation under controlled conditions. In addition, we cite the study published in Applied Sciences ([31] Peta K, Wiśniewski M, Kotarski M, et al. Comparison of single-arm and dual-arm collaborative robots in precision assembly[J]. Applied Sciences, 2025, 15(6): 2976), which demonstrates the use of simulation software to evaluate robot motion trajectories and positioning accuracy. This addition highlights simulations as a complementary and reliable tool alongside real-world experiments.

Question 4: While many graphs presenting errors are provided, some statistics are missing.

Response: We thank the reviewer for this constructive suggestion. To complement the graphical results, we have added a new table summarizing positioning errors numerically. The table reports mean error, RMS error, and maximum error for single-sensor measurements, multi-sensor fusion results, and fusion with systematic error compensation. This quantitative summary enables clearer comparison and strengthens the rigor of the analysis.

Table 5. Statistical summary of positioning errors under different conditions.

Measurement condition	Mean error (m)	RMS error (m)	Maximum error (m)
Single PSD measurement	0.42	0.51	0.93
Single IMU estimation	0.88	1.02	1.76
Single encoder estimation	0.67	0.84	1.45
Multi-sensor fusion (EKF)	0.09	0.12	0.21
Fusion with error compensation	0.04	0.06	0.11

 

Question 5: Did the authors use a specific type of robot for this study? How might the results be generalizable across different robots?

Response: We thank the reviewers for their query regarding universality. The revised manuscript now explicitly states in the discussion section that this study does not assume any specific commercial robot model. Instead, a generic rigid-body robot representation equipped with encoders, an inertial measurement unit (IMU), and external optical measurements is employed within the simulation framework. Consequently, the proposed perception, multi-sensor fusion, and error compensation methodology is not constrained by specific robotic architectures and can be generalized to various industrial robots, including articulated arms and large gantry systems. Whilst absolute performance metrics may vary due to robot stiffness, kinematic configurations, and sensor quality, the observed trends and methodological conclusions retain broad applicability.

      
We sincerely thank the reviewer for the insightful comments and suggestions, which have helped improve the manuscript's clarity, technical depth, and overall quality. We hope that the revisions satisfactorily address all concerns.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents a robot pose measurement framework based on a laser tracker system, combining interferometric ranging, PSD-based spot sensing, and multi-sensor fusion. The authors develop a prototype PSD sensing subsystem using FPGA-based processing and validate its linearity and illumination robustness through bench experiments. Furthermore, a comprehensive simulation suite is established to analyze multi-sensor fusion, error compensation, and control strategies. The manuscript is well-structured, and the proposed "hardware prototype + simulation verification" methodology is logical for complex instrument development. However, there is a significant discrepancy between the title and the experimental content, specifically the lack of interferometric ranging data. Additionally, the control algorithm comparisons in the simulation appear poorly tuned, and the linkage between hardware parameters and simulation models needs strengthening. Therefore, I recommend a Major Revision before the manuscript can be considered for publication.

Comments for author File: Comments.pdf

Author Response

Responses to Reviewer

Dear Editor and Reviewer:

We sincerely thank the reviewer for the thorough evaluation and constructive comments on our manuscript. All comments have been carefully considered, and the manuscript has been revised accordingly. The revised portions are marked in red in the revised manuscript. Below, we provide a detailed point-by-point response to the reviewer’s comments.

Comment 1

Comment: In the Title and Abstract, the authors explicitly highlight "Interferometric Ranging" as a component of the proposed system. However, in Section 5, the experimental validations are strictly limited to PSD spot sensing and optical filtering. No experimental data are presented for the interferometric ranging module. The authors are advised to either provide experimental validation of the ranging subsystem or revise the title and abstract to reflect that the current prototype validation is limited to the PSD tracking sensor, as the absence of ranging data is inconsistent with the title.

Response: We thank the reviewer for this important and constructive comment. We acknowledge that, in the current version of the manuscript, the experimental validation focuses on the PSD-based spot-sensing and optical-filtering subsystem, whereas the interferometric ranging module has not yet been experimentally demonstrated. To address this concern and avoid inconsistencies among the title, abstract, and experimental content, we have revised both the Title and Abstract to clearly state that the present prototype validation is limited to the PSD-based tracking and sensing chain, whereas interferometric ranging is addressed at the system modeling and simulation level. The interferometric ranging module is retained in the framework description because it represents the intended ranging principle of the complete laser tracker system, but its experimental implementation will be reported in future work. Specifically, the Title has been modified to emphasize PSD-based tracking and multi-sensor fusion, and the Abstract has been revised to explicitly distinguish between prototype-level experimental validation and simulation-based system analysis.

Comment 2

In Section 3, the hardware setup is described. Regarding the "time synchronization"emphasized in Figure 4, the authors are suggested to add specific implementation details inSection 3. Specifically, how are the analog signals from the PSD and the digital data fromthe encoders/IMU synchronized? Is this achieved via a hardware trigger signal on the FPGA or through software timestamping?.

Response: We appreciate the reviewer’s request for clarification regarding time synchronization. In the revised manuscript, additional implementation details have been added to Section 3. Synchronization is achieved through a hardware-based approach implemented on the FPGA platform. The PSD analog signals are synchronously sampled by a multi-channel A/D converter using a common sampling clock generated by the FPGA.

“Encoder and IMU data are acquired within the same FPGA clock domain and aligned using a shared hardware trigger and deterministic buffering mechanism. All sensor data streams are therefore associated with a common hardware timestamp before being passed to the fusion algo Time synchronization among heterogeneous sensors is implemented using a hardware-based strategy on the FPGA platform. The analog signals from the PSD are synchro-nously sampled by a multi-channel A/D converter driven by a common sampling clock generated by the FPGA. Encoder and IMU data are acquired within the same FPGA clock domain and aligned using a shared hardware trigger signal. All sensor data streams are buffered and assigned deterministic hardware timestamps before being forwarded to the estimation and fusion module. This unified clock and trigger architec-ture ensures that PSD, encoder, and IMU measurements correspond to the same physi-cal sampling instant, thereby minimizing timing jitter and latency uncertainty. Com-pared with software-based timestamping, the proposed hardware synchronization ap-proach provides higher temporal consistency and directly supports accurate multi-sensor fusion, as illustrated by the synchronization analysis in Figure 4. rithm, avoiding the latency jitter associated with software-based timestamping.”

Comment 3

Comment: In Section 5, the experiments only present static or step-wise "controlled spot translation. “Although Section 4.2 discusses "Tracking control considerations," there is no experimental demonstration of the prototype performing closed-loop tracking of a moving light source. To justify the "Laser Tracker" aspect of the manuscript, it is highly recommended to add a basic dynamic tracking experiment to verify the real-time performance of the PSMotor loop.

Response: We thank the reviewer for this constructive suggestion and fully agree that closed-loop dynamic tracking is an important characteristic of a complete laser tracker system.

In the present study, experimental validation is focused on the PSD-based spot-sensing chain, including linearity, geometric sensitivity, and robustness to ambient illumination. These experiments aim to establish the reliability of the sensing and signal processing subsystem as a prerequisite for safe and stable closed-loop operation.

Experimental demonstration of dynamic closed-loop tracking entails additional system-integration challenges, including actuator tuning, mechanical stability, and safety considerations, which are beyond the scope of the current stage of this work. For this reason, the dynamic behavior of the PSD–FPGA–motor loop and tracking control performance are investigated through simulation, allowing systematic analysis of controller behavior, delay sensitivity, and disturbance response under controlled conditions.

 

Following the reviewer’s suggestion, we have explicitly clarified this scope limitation in Sections 4.2 and 5, and we have added a discussion in the Discussion section to state that experimental closed-loop dynamic tracking will be a key focus of future work..

Comment 4

Comment: In Section 6.2 and Figure 8, the distribution of "Ball Manufacturing Errors" is presented. In the subsequent time-domain simulations (e.g., Figure 10), it is important to clarify whether this target sphere deviation is modeled as a constant systematic bias for a given trial or as time-varying random noise. In physical reality, a specific target sphere (SMR) possesses a fixed radius error. Modeling it as random noise varying over time would be physically incorrect. The authors are suggested to clarify this modeling assumption to ensure physical consistency.

Response: We thank the reviewer for pointing out this important issue in physical modeling. In the revised manuscript, we clarify that the target sphere manufacturing deviation is modeled as a constant systematic bias for each simulation trial. This bias is sampled from a statistical distribution to represent manufacturing variability across different spheres but remains fixed within a given trial, consistent with physical reality.

Comment 5

Comment: In Section 6.2 and Figure 9, the "Foundation vibration error" is analyzed, identifying dominant frequencies at 5 Hz and 12 Hz. The authors should clarify whether these specific frequencies were obtained through experimental modal analysis of the physical prototype described in Section 3, or if they are arbitrary values assumed for the simulation.

Response: We appreciate the reviewer’s request for clarification. In the revised manuscript, we explicitly state that the foundation vibration frequencies presented in Figure 9 are assumed representative values used for simulation. These frequencies were selected to reflect typical low-frequency vibrations in industrial environments rather than being derived from experimental modal analysis of the prototype. This clarification has been added to Section 6.2.

Once again, we sincerely thank the reviewer for the insightful comments and suggestions, which have significantly improved the manuscript's quality and clarity.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents a framework for robot pose measurement that integrates a prototype PSD-based optical tracking sensor with a multi-sensor fusion simulation suite. Following the previous revision, the authors have significantly improved the manuscript by clarifying the hardware architecture and expanding the simulation analysis regarding error compensation and control strategies. The methodology, combining hardware prototyping with simulation verification, is logical and well-founded. However, to fully address the concerns raised in the previous round regarding the distinction between experimental data and simulation models, and to rectify remaining technical inconsistencies, a few specific revisions are still required.

Comments for author File: Comments.docx

Author Response

please see the attachment.

Author Response File: Author Response.pdf