Multi-Depth Uniform Coverage Path Planning for Unmanned Surface Vehicle Surveying

arXiv:2605.13123 · cs.RO · Submitted 2026-05-13 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "Multi-Depth Uniform Coverage Path Planning for Unmanned Surface Vehicle Surveying".

Dev: The gist: The proposed Multi-Depth Non-revisiting Uniform Coverage (MDNUC) algorithm introduces a novel,

Rosa: First, who's behind it and why it matters.

Title and authors: Rosa: So we’re looking at the paper titled Multi-Depth Uniform Coverage Path Planning for Unmanned Surface Vehicle Surveying. It comes from Maider Larrazabal and a few other members of the IEEE. It sounds like they're tackling that big problem of making sure an unmanned surface vehicle covers an area evenly, even when the water gets deeper in places, which is something traditional methods just don't handle well > #pg1.

Dev: Yeah, it’s about taking that standard boustrophedon idea and fixing it because the depth changes constantly, so a fixed pattern doesn't work anymore > #pg2. The authors are trying to solve the issue where a path designed for one depth isn't good when you move to another.

Taro: I’m interested in how they handle that dynamic part, because when you’re out on the water, things aren't constant, so a fixed plan is always going to fail > #pg2. It seems like the paper wants something more flexible than just following a set of points across the surface.

Rosa: Exactly. They introduce this new approach that incorporates some initial depth information to help pre-process the area and then adapt how they generate the path and adjust their sensing range on the fly > #pg1. It’s trying to move away from those fixed, simple patterns like just going back and forth along a line > #pg2.

Dev: So, what does this mean for us on the engineering side? We need to see if this adaptive guidance actually works in real conditions where currents and waves mess with the planned trajectory > #pg2.

Taro: I think it's about making sure that even if the environment is changing, you still get that uniform coverage you need for good data collection > #pg2.

Rosa: That’s right. So, in this next part, we’re going to look at what exactly this paper proposes to do and how they break down the problem.

The paper's summary: Dev: Okay, so the core idea of Multi-Depth Uniform Coverage Path Planning for Unmanned Surface Vehicle Surveying is that they’re using something inspired by a method called NUC, but they’ve customized it for seafloor mapping > #pg1. They aren't relying on those complicated cellular decompositions that take a lot of computational power to set up > #pg3.

Rosa: That’s right, the paper wants to eliminate that complexity because it makes the system much more robust and easier to implement, especially in areas with weird shapes or complex topography > #pg3. They build their plan in a single continuous path instead of breaking it into many small cells > #pg3.

Taro: So, when they talk about the method, they are focusing on how they divide the area into regions based on depth first, and then using that depth information to figure out how the path should move between those regions > #pg6. It’s a two-step process built around height ranges > #pg6.

Dev: And that second step involves something called boundary detection, where they make sure the path never hits an edge it can't cross, meaning entry and exit points are only where the depth regions meet > #pg6. That sounds like it handles feasibility well.

Rosa: It’s trying to ensure that as you move from one depth zone to another, you only use those specific gateway edges for your path planning, which keeps things clean > #pg6. This is a big step because traditional methods struggle with making sure the path is actually physically possible while meeting the coverage goal > #pg2.

Taro: It seems like they’re focusing on creating a way to handle the physical constraints of moving around obstacles while maintaining that uniform data quality across varying depths > #pg6.

Dev: So, we’ve covered what it is: a template-free method that uses depth information to structure the path planning without needing those heavy decomposition techniques > #pg3.

The paper's improvements: Rosa: Now let’s talk about the specific improvements they detail. They focus on three main things that make this work better than what’s out there currently > #pg6. First, they have footprint-width based remeshing, where they divide each section into three quadrilaterals using the center point of that triangle as the division spot > #pg5.

Dev: So, that’s basically a way to reshape the mesh based on how big the sensor footprint is and how deep you want your map to be, aiming for those mostly isosceles right triangles during remeshing > #pg5. It’s tailoring the geometry to the hardware rather than using a generic shape.

Taro: That sounds like they are tuning the path planning directly to how that specific multibeam echo sounder actually works on the water > #pg5. It’s not just a generic mathematical shape; it's tied to physics.

Rosa: Then they have height-based region partitioning and gating, which is where they divide the mesh into depth ranges, and then use that depth data to automatically calculate shared edges between them > #pg6. They select one edge as the gateway between adjacent areas > #pg6.

Dev: That’s how they manage those transitions, ensuring there's only one way in and one way out of a new depth zone, which feeds right into that boundary detection to stop the path from hitting blocked edges > #pg6. It’s a tightly controlled routing mechanism.

Taro: So the improvement here is that they are not just guessing paths; they are using the measured depth data to guide where the path has to go next, which makes it much more intelligent about navigating those complex areas > #pg6.

Rosa: Right. The paper states that this dynamic adjustment of the sensing beam aperture based on local conditions is a key part of their advancement in bathymetry > #pg1.

Conclusion: Dev: So wrapping up, the main thing we’re seeing with this Multi-Depth Uniform Coverage Path Planning for Unmanned Surface Vehicle Surveying is that they've managed to combine template-free route planning with an opening angle that changes based on the depth > #pg1. They claim they get ninety-nine point two eight percent coverage in synthetic tests and about ninety-two point eight one percent in a real Pasaia harbour area > #pg8.

Rosa: That’s a significant jump from the traditional methods, especially when you look at that real-world result of ninety-two point eight one percent, which beats the B andF method's sixty-four point eight one percent and MDB andF method's sixty-five point six eight percent > #pg8. It shows the practical benefit of their approach for actual mapping jobs > #pg8.

Taro: I think what this means for autonomous systems is that you don’t always need a super complex setup to get high-quality coverage; sometimes you just need a smarter way to adapt your sensors to the local environment > #pg1.

Dev: Yeah, but we have to remember their limitations. They mentioned that they are still dealing with the challenge of avoiding dynamic obstacles like other vessels and environmental disturbances like currents and waves, which can cause deviation from the planned trajectory > #pg2.

Rosa: That’s a fair point. So, in summary, this Multi-Depth Uniform Coverage Path Planning for Unmanned Surface Vehicle Surveying paper offers a method that adapts the sensing beam aperture to depth to achieve better seafloor coverage > #pg1. It’s a solid step forward in how we plan these missions > #pg8.

Taro: I think the future work should focus on testing this stuff in more unpredictable, real-world maritime conditions where those dynamic obstacles are truly challenging > #pg2.

AZTI Foundation · Tsinghua University · University of the Basque Country (UPV/EHU) · Robotics Institute, University of Technology Sydney

cs.RO

Submitted: 2026-05-13

Updated: 2026-05-13

Comments: Accepted by ICRA 2026

DOI: 10.1109/ICRA57385.2026.11696941

Code: https://github.com/MaiLa24/mdnuc

License: http://creativecommons.org/licenses/by-nc-sa/4.0/

Importance score: 79/100

The gist: The gist: The proposed Multi-Depth Non-revisiting Uniform Coverage (MDNUC) algorithm introduces a novel, template-free coverage path planning method that adapts to varying seafloor depths by

Key concepts

Coverage Path Planning (CPP): This is the process of determining the most efficient route for a vehicle to survey an entire area without missing any spots. Traditional methods often use fixed patterns, but this paper proposes a dynamic approach that changes its path based on real-time environmental data like water depth.
Footprint-width Based Remeshing: This technique modifies the coverage map by dividing existing triangular areas into three quadrilaterals using the sensor's physical footprint and desired resolution. This remeshing ensures the resulting mesh is physically consistent with how the sensor actually captures data at different depths.
Height-based Region Partitioning: The algorithm divides the survey area into distinct depth ranges. By analyzing data within these height ranges, it automatically determines which edges between regions should be used as gateways for continuous, non-revisiting coverage paths.

Terminology

Unmanned Surface Vehicle — 18× in this paper
Aperture — 5× in this paper · explained in 1 episode
Robustness — 5× in this paper · explained in 5 episodes
Adaptability — 3× in this paper · explained in 1 episode
Multi-Depth Non-revisiting Uniform Coverage — 3× in this paper
Accuracy — 2× in this paper · explained in 1 episode
Adaptation — 1× in this paper · explained in 1 episode
Benchmark — 1× in this paper · explained in 2 episodes
Core — 1× in this paper · explained in 2 episodes
Physical Constraints — 1× in this paper · explained in 7 episodes
Reinforcement Learning — 1× in this paper · explained in 4 episodes
Trace — 1× in this paper · explained in 2 episodes

Summary

The gist: The proposed Multi-Depth Non-revisiting Uniform Coverage (MDNUC) algorithm introduces a novel, template-free coverage path planning method that adapts to varying seafloor depths by dynamically adjusting the sensing beam aperture to achieve optimized, uniform seafloor coverage for unmanned surface vehicle surveying.

Motivation and Problem

Bathymetric surveys often rely on traditional coverage path planning methods like the boustrophedon scheme, which are inefficient because they assume a constant sensor footprint while water depths fluctuate substantially <ref:2605.13123#pg3>. This fixed pattern approach results in gaps when depth variations are not accounted for <ref:2605.13123#pg5>. The problem of coverage path planning (CPP) is complicated by the need for a physically feasible path that simultaneously addresses data quality requirements, especially in a maritime setting with dynamic obstacles and environmental disturbances <ref:2605.13123#pg3>. Traditional methods often rely on cellular decomposition techniques, which suffer from high computational cost and scalability issues due to arbitrary sub-cell definitions <ref:2605.13123#pg5>.

Proposed Methodology

The MDNUC method is inspired by the NUC algorithm [9], designed to generate single, continuous coverage paths without resorting to arbitrary cellular decompositions <ref:2605.13123#pg5>. It extends the NUC framework in three critical ways for bathymetric surveys <ref:2605.13123#pg6>:

Footprint-width Based Remeshing: The mesh is remeshed by dividing each triangle into three quadrilaterals using the centroid of the triangle as the separation point <ref:2605.13123#pg5>. This process is driven by physical characteristics of the MBES sensor footprint and desired bathymetry resolution, aiming to produce mostly isosceles right triangles during remeshing <ref:2605.13123#pg5>.
Height-based Region Partitioning and Gating: The mesh is divided into height ranges, which define regions within the mesh <ref:2605.13123#pg6>. Depth information gathered from these subregions is used to automatically calculate shared edges between them, selecting a single edge as a gateway between adjacent areas <ref:2605.13123#pg6>.
Boundary Detection and Path Constraint: The algorithm ensures the path never intersects with blocked edges, meaning entry and exit points between depth regions are only the gate edges <ref:2605.13123#pg6>.

Experimental Validation

Performance was validated using both synthetic and real seafloor data collected from a bathymetric survey <ref:2605.13123#pg8>. In synthetic scenarios, the MDNUC method consistently achieved the highest coverage in all tested scenarios, reaching 99.28% coverage at 10 cm resolution on a concave shaft dataset. On the saddle surface dataset, MDNUC achieved 99.34% coverage at 10 cm resolution, slightly surpassing the NUC method's 98.03% and the MDB&F method's 75.52%. In a real-world scenario using Pasaia data at 10 cm resolution, MDNUC achieved 92.81% coverage, significantly outperforming the B&F method's 64.81% and the MDB&F method's 65.68% <ref:2605.13123#pg8>.

Conclusion

The MDNUC algorithm demonstrates clear superiority over traditional methods by combining template-free route planning with a variable opening angle for each zone based on depth. This approach allows the dynamic adjustment of the echo sounder’s opening angle, which is a key advancement in the field. The algorithm achieves 99.28% coverage in synthetic scenarios and 92.81% coverage in the realistic Pasaia harbour area <ref:2605.13123#pg8>. An open source C++ and python implementation of the MDNUC software has also been released to support reproducibility and adoption by the community. The paper concludes that combining template-free route planning and adapting the opening angle to depth is the most effective approach for bathymetry.

REFERENCES

[1] B. Kum, D. Shin, S. Jang, S. Y. Lee, J. H. Lee, T. Moh, D. G., Lim, J., Do., and J., Cho., “Application of unmanned surface vehicles in coastal environments: Bathymetric survey using a multibeam echo sounder,” J. Coast. R., vol 95, no SI, pp 1152–1156, 2020.

[2] L. Castano-Londono, S. P., Marrugo Llorente, E., Paipa-Sanabria, D. I., Orozco-Lopez, M. B. F., M., and D. Gonzalez Montoya, “Evolution of algorithms and applications for unmanned surface vehicles in the context of small craft: A systematic review,” Appl. Sci., vol 14, no 21, 2024.

[3] E. Galceran and M. Carreras, “A survey on coverage path planning for robotics,” Robot. Auton. Sys., vol 61, no 12, pp 1258–1276, 2013.

[4] h. Choset, “Coverage of known spaces: The boustrophedon cellular decomposition,” Auton. Robot., vol 9, no 3, pp 247–253, 2000.

[5] T. M., Cabreira, C., Di Franco, P. R., Ferreira, G. C., Buttazzo, “Energy-aware spiral coverage path planning for uav photogrammetric applications,” Robot. Autom. Let., vol 3, no 4, pp 3662–3668, 2018.

[6] Ausable Freshwater Center, “Bathymetric Survey Path on the Ausable River,” www.ausableriver.org/blog/how-are-bathymetric-maps-made, September 2025.

[7] E. Acar, H., Choset, P., Rizzi, A., and Atkar, and D. Hull, “Morse decompositions for coverage tasks,” Intl. J. of Robotics Res., vol 21, no 4, pp 331–344, 2002.

[8] L. Zhao and Y. Bai, “Joint-optimized coverage path planning framework for usv-assisted offshore bathymetric mapping: From theory to practice,” Knowl.-Based Syst., vol 304, p 112449, 2024.

[9] T. Yang, J. Valls Miro, M. Nguyen, Y. Wang, and R. Xiong, “Templatefree nonrevisiting uniform coverage path planning on curved surfaces,” T. Mechatr., vol 28, no 4, pp 1853–1861, 2023.

[10] M. Badamasi, I., Kabir, G., Ahmed, and S. El-Ferik, “Autonomous mobile robot path planning techniques, a review: Classical and heuristic techniques,” Access, 2025.

[11] L. Yi, A. Y., Wan, A. V., Le, A. A., Hayat Q. R., Tang Q., and Mohan R E., “Complete coverage path planning for reconfigurable omnidirectional mobile robots with varying width using gbnn (n),” Expert Syst. Appl., vol 228, p 120349, 2023.

[12] T. Cabreira, L. Brisolara, and F. Paulo R, “Survey on coverage path planning with unmanned aerial vehicles,” Drones, vol 3, no 1, p 4, 2019.

[13] K. R., Jensen-Nau, T., Hermans T., and K. K. Leang K., “Near-optimal area-coverage path planning of energy-constrained aerial robots with application in autonomous environmental monitoring,” T. Autom. Sci. Eng., vol 18, no 3, pp 1453–1468, 2020.

[14] L. Bine, A., Boukerche L., Ruiz L., and Loureiro A., “A novel ant colonyinspired coverage path planning for internet of drones,” Comput. Netw., vol 235, p 109963, 2023.

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Improvements for AI systems

Bold header: Depth-Aware Path Planning Integration

The improved AI system can perform bathymetric surveying path planning by incorporating coarse prior depth information to pre-process the target region and adaptively guide path generation and sensing range configuration, ensuring a single continuous path that guarantees each subregion is visited only once.

Bold header: Elimination of Computational Overhead

The system can achieve superior scalability and robustness by utilizing a method that does not require cell decomposition, which improves scalability, simplifies implementation, and increases robustness in areas with irregular shapes or complex topography.

Bold header: Dynamic Sensor Adaptation

The improved system can dynamically adjust its sensing parameters by modifying the beam aperture based on local conditions, as described by the MDNUC modification where the opening angle of the MBES can be dynamically modified and the footprint width adjusted to the depth at each subregion, maintaining constant coverage throughout the full, single sweep.

Bold header: Enhanced Real-World Accuracy

The system will achieve significantly improved performance in real-world applications by achieving coverage reaching over 92% in realistic simulations using real bathymetric data from a coastal harbour, surpassing traditional methods with coverage rates below 65%.

Abstract

This paper introduces a novel automatic coverage path planning algorithm for bathymetry surveying with unmanned surface vehicles. The detection range of the mapping sensor employed - a multibeam echo sounder - is heavily influenced by local seafloor depths. Hence, a path designed to uniformly cover the sea surface does not guarantee uniform coverage of the seafloor. Yet this is currently the typical process for bathymetric surveys, with the simplistic boustrophedon scheme along manually selected waypoints at constant depths being the most widespread planner used. The proposed scheme incorporates coarse prior depth information to pre-process the target region and adaptively guide path generation and sensing range configuration. By explicitly accounting for depth variations, the proposed algorithm designs a coverage path with optimised spacing between survey passes that adjusts the sensing beam aperture to achieve more consistent seafloor coverage. The proposed method is shown to offer significant improvements in both synthetic and real-world scenarios. Validations in challenging synthetic terrains achieves coverage ratios beyond 99%, a marked improvement when compared with traditional boustrophedon paths revealing a maximum 75% coverage. The same trend appears in realistic simulations using real bathymetric data from a coastal harbour, with coverage reaching over 92%, and significantly surpassing boustrophedon sweeps with coverage rates below 65%. Beyond improved performance, the scheme also brings a fully automated design, suitable for autonomous marine vehicles, thus offering practical utilities for real-world applications.