Planning Coverage Paths on Bathymetric Maps for In-Detail Inspectionof the Ocean Floor

Enric Galceran and Marc Carreras

Abstract— This paper proposes a coverage path planning(CPP) method for inspection of 3D natural structures onthe ocean floor charted as 2.5D bathymetric maps. This taskis integral to many marine robotics applications, such asmicrobathymetry mapping and image photo-mosaicing. We con-sider an autonomous underwater vehicle (AUV) with hoveringcapabilities imaging the ocean floor with an orientable sensor,such as a camera or a sonar. While standard lawnmower-type surveys at constant altitude are well-suited for coveringeffectively planar areas, two major problems arise when tracingsuch paths over high-relief terrain. First, the sudden depthchanges required by such paths imply very costly motions,as moving in the vertical axis is expensive for most AUVs.Second, some time is required to adjust the vehicle depth aftera sudden change in the relief, resulting in a varying distancefrom the target surface which deteriorates the overall qualityof the collected imaging data. The method proposed in thispaper accounts for these facts and generates different coveragepatterns according to terrain’s relief, resulting in a well-suitedcoverage path for imaging tasks. The proposed CPP method isfast and easy to implement, and provides a valuable tool forplanning coverage paths in marine environments. We tested theproposed method on a real-world bathymetric dataset of a lavatongue obtained during recent sea trials in the Santorini calderain Greece and compares favorably to a standard lawnmower-type survey path.

I. INTRODUCTION

Coverage path planning (CPP) is the task of determininga path that passes a robot or a sensor over all points of atarget space while avoiding obstacles. This task is integral tomany robotic applications, such as vacuum cleaning robots,painter robots, lawn mowers and automated harvesters, just toname a few. A large body of research has investigated CPPin 2D [1], [2], 2.5D [3], [4], [5] and 3D [6], [7] environ-ments. Applications of CPP in domains such as agriculturalrobotics [8] and unmanned aerial vehicles (UAVs) [9], [10]have been reported in the literature. However, while manyunderwater robotics applications, such as microbathymetrymapping, habitat monitoring or image photo-mosaicing, canbenefit greatly from the complete coverage guarantees androbustness of CPP methods, their application to underwaterenvironments up to date has been limited. Especially, re-search on 3D path planning for underwater vehicles so far

This research was sponsored by the Spanish government (COMAROBProject, DPI2011-27977-C03-02) and the MORPH EU FP7-Project underthe Grant agreement FP7-ICT-2011-7-288704. We are grateful for thissupport.

Enric Galceran and Marc Carreras are with the UnderwaterRobotics Research Center (CIRS), University of Girona,Girona, Spain enricgalceran at eia.udg.edu,marc.carreras@udg.edu

often only deals with abstract scenarios based on very sim-ple simulations. Examples include sets of randomly placedspheres of different sizes [11] and randomly occupied cellsin a grid [12]. Notable exceptions are the recent work inCPP for ship hull inspection tasks presented in [13] andthe 6 DOF 3D path planning approach presented in [14].In general, however, few research has studied CPP in theunderwater domain (see Sec. II below for further review ofrelated work).

In this paper, we address the problem of planning acoverage path for in-detail inspection of 3D natural structureson the ocean floor charted as 2.5D bathymetric∗ maps.This is a realistic situation arising in many marine roboticsapplications, such as seabed image photo-mosaicing, micro-bathymetry mapping or geological activity characterization.Consider, for example, an area of the ocean floor mappednavigating at a safe distance from the bottom using abathymetry sonar. A typical task is to select a region ofinterest (ROI) on the mapped area and inspect it in closerdetail, for instance by means of image photo-mosaicing. Toaccomplish this task autonomously, an automated method toplan an in-detail inspection coverage path on the selectedarea is required.

To this aim, we propose a 3D CPP method for coverageof bathymetric surfaces. The proposed method is particularlytargeted for Autonomous Underwater Vehicles (AUVs) withhovering capabilities. The planned paths lay at a user-provided constant offset distance from the target surface,which allows for sensor imaging. Classical bottom cover-age at constant altitude in high relief environments impliessudden adjustments of the AUV’s depth in order to followthe vertical profile. This results in two major problems. First,the frequent sudden depth changes imply a very inefficientmotion, as moving in the vertical direction is expensivefor most AUVs (due to their design characteristics, amongwhich torpedo shapes are common). Second, some time isrequired to adjust the vehicle depth after a sudden changein the relief, resulting in a varying distance from the targetsurface which deteriorates the overall quality of the collectedimaging data due to varying resolution. The proposed methodaccounts for these facts in the planning process and, inhigh relief areas, it generates a coverage path which followsconstant-depth horizontal contours on the target surface.Therefore, the resulting path avoids sudden depth changes.

∗Bathymetry is the study of underwater depth of lake or ocean floors.In other words, bathymetry is the underwater equivalent to hypsometry (themeasurement of land elevation relative to sea level). A bathymetric map isan elevation map of the mapped area.

On the other hand, low-relief, effectively planar regions arecovered using a classical lawnmower-type survey at constantaltitude, for which the design characteristics of most AUVsavailable today are optimized for. Specifically, our methodidentifies high-slope regions and effectively planar regionsin the bathymetric map. To cover the high-slope regions,we provide a slicing algorithm which plans coverage pathsfollowing constant-depth horizontal bathymetric contours atsequentially increasing depths. The resulting coverage pathsprovide a fair view angle on the target surface. For coverageof the effectively planar regions, we propose a cellular de-composition approach which generates standard lawnmower-type survey paths at constant altitude. By linking together thepaths planned in each region, a full coverage path for thetarget bathymetric surface is obtained. The proposed methodis fast and easy to implement.

We tested the proposed method on a real-world bathymet-ric dataset of a lava tongue obtained during recent sea trialsin the Santorini caldera in Greece. We execute the path insimulation using and compare it to a standard lawnmower-type survey path, showing the benefits of the proposedmethod. The results obtained in simulation provide valuableinformation, as the coverage paths generated in this workwill be executed by an AUV at sea in scientific missionstaking place in the near future.

The remainder of this paper is organized as follows. Sec. IIbriefly reviews several related CPP methods reported inthe literature. The proposed CPP method for bathymetricsurfaces is described in Sec. III. Sec. IV introduces thereal-world bathymetric dataset obtained in recent sea trialsupon which we test the proposed method. The method isthen applied to the dataset and results of the simulatedpath execution are reported in Sec. V, comparing them toa lawnmower-type survey path. Finally, concluding remarksand directions for further research are given in Sec. VI.

II. RELATED WORK

An extensive body of research has addressed the CPPproblem in planar areas (see [1] for a survey). However,there are fewer approaches in the literature which addresscoverage of 3D spaces.

Atkar et al. [6] presented a sensor-based coverage algo-rithm for 3-dimensional surfaces. This algorithm is provencomplete under the assumption that the robot is equippedwith a 360 range sensor. In a later work, they proposed anoff-line CPP method specifically targeted for spray-paintingof automotive parts [7]. The algorithm accounts for thefact that the target surface not only needs to be completelycovered, but also the resulting paint deposition must meetcertain uniformity requirements. To achieve uniform cov-erage, their proposed method takes a CAD model of thetarget automotive parts segments it into topologically simpleregions of similar curvature. Then, individual coverage pathsare generated for each region.

Cheng et al. presented an off-line approach for planningtime-optimal trajectories for UAVs performing 3D coverageof urban structures presenting 2.5D features [4]. First, they

simplify the structures to be covered, namely buildings, intohemispheres and cylinders. Then, trajectories are planned tocover these simpler surfaces. Their proposal is validated inhardware-in-the-loop simulations using a fixed-wing aircraft.

In the underwater domain, CPP research on planar en-vironments has addressed mainly in the context of minecountermeasure applications [15], [16]. Regarding 3D en-vironments, Hert et al. presented an AUV-targeted algorithmwhich allows for coverage of 2.5D environments [3]. Thepaths generated by the algorithm cover completely the watercolumn, which is not desired in most applications. In thissense, Lee et al. proposed an extension of this algorithm forcovering only areas close to the seabed (that is, avoiding cov-erage of the water column) [5]. However, motion constraintsof the vehicle were not taken into account in these works.Recently, Englot et al. introduced an off-line, sampling-basedalgorithm to achieve probabilistically complete coverage ofcomplex, 3-dimensional structures [13]. Their target applica-tion is autonomous ship hull inspection. While this algorithmcan handle surfaces of unprecedented complexity, it requiresan accurate 3D model of the target surface and time in theorder of several minutes to plan the coverage path.

III. COVERAGE PATH PLANNING ONBATHYMETRIC MAPS

Our proposed CPP method operates on a bathymetric map,B(x, y), provided as input. For every point (x, y) on themapped area, B(x, y) returns its depth. The proposed CPPmethod is a three-step process. First, high-slope regions areidentified on the the bathymetric map. Next, a constant-depthhorizontal-pattern coverage path is generated in the identifiedhigh-slope regions using a slicing algorithm. Finally, a cov-erage path is planned for the remaining effectively planarregions of the target surface. This later coverage path isgenerated using a cellular decomposition approach where thealready processed high-slope regions are treated as obstacles.

A. Identifying High-Slope Regions

First, we identify high-slope regions where a horizontalcoverage pattern is desired. To that aim, a “slope map”,S(x, y), is calculated for the mapped area as the norm ofthe gradient of B, that is:

S(x, y) = ||∇B|| =∣∣∣∣∣∣∣∣∂B∂x~i+

∂B∂y~j

∣∣∣∣∣∣∣∣ ,

where ~i,~j are the standard unit vectors in the X and Yaxis, respectively.

Then, we apply a user-defined slope threshold, δs, to S toobtain a binarized map

T (x, y) =

1 if S(x, y) ≥ δs0 if S(x, y) < δs

.

In order to filter out small regions, we apply the dilateand erode morphological operations [17] to T using anappropriate structuring element. Finally, the bounding boxesof the connected components of T are calculated. Eachbounding box will be treated as a high-slope region.

B. Covering High-Slope Regions using the Slicing Algorithm

We propose a slicing algorithm to generate an in-detailcoverage path for each identified high-slope region. Theproposed algorithm draws inspiration from the algorithmproposed in [6]. The main idea is to intersect a horizontalslice plane with the target surface at incremental depths, andthen link these intersections.

Consider a point-mass robot equipped with a limited field-of-view (FOV) sensor. The sensor FOV is determined by anaperture angle, α, and a maximum range rmax, as shownin Fig. 1. The sensor FOV can be oriented towards a givenpoint in the target surface by means of a pan and tilt unit. Toimage the target surface with the sensor, the robot navigatesat a user-defined fixed offset distance, Ω < rmax, from thetarget surface. Note that Ω can be chosen to accommodate arobot modeled as a sphere with non-zero radius.

Robot

α

rmax

Ω Δλ

Fig. 1: Sensor FOV of a point-mass robot located at anoffset distance Ω from the target surface. The sensor footprintdetermines the distance between slice planes, ∆λ.

The sensor footprint on the target surface determines thespacing between successive slice planes, ∆λ (where λ is thecurrent slice plane depth), as shown in Fig. 2 (top). Note thatthe footprint extent depends on the curvature of the targetsurface on the imaged area. We approximate the footprintextent as a circle of radius r = Ω tan α

2 , and therefore ∆λ =2r.

The slicing algorithm is detailed in Algorithm 1. Thealgorithm is applied to each identified high-slope regionof the bathymetric map. For each high-slope region, thealgorithm takes as input the corresponding subset of thebathymetric map B, Br, the offset distance, Ω, and the sliceplane spacing, ∆λ. First, it initializes the coverage path, p,as empty (line 1) and the current slice plane depth, λ, asthe minimum depth in Br plus the slice plane spacing (line2). The algorithm runs at incremental values of λ until λsurpasses the maximum depth in Br (line 3). At each depthlevel, a horizontal plane is intersected with the bathymetricsurface (line 4). The function INTERSECT() returns the listof closed edges composing the intersection, as illustrated inFig. 2. Next, a coverage path for the current slice plane isgenerated by linking each edge in the list to the next (functionLINK EDGES(), line 5). The function LINK EDGES() usesthe function LINK() to generate the “link paths”. LINK()traces a straight line path between two given points. If thestraight line intersects the bathymetric surface, it traces the

projection of the line on the bathymetric surface. Finally,the path generated at the current depth level is linked andconcatenated to the global path (line 6). The value of λ isincreased (line 7) and the process continues. Notice that,when the while loop exits, the path generated so far laysexactly on the bathymetric surface. The path is then projectedonto the offset surface by OFFSET PATH(), which projectsall points in the path along the bathymetric surface normalby an offset distance Ω. The result is a coverage path on thedesired offset surface. Using this very same surface normal,the orientation of the robot and the sensor pan and tilt anglesare set for the sensor to point normally to the target surfacealong all points in the path in order to maximize imagingquality.

Algorithm 1: Slicing AlgorithmInput: High-slope region of a bathymetric map, B(x, y)Parameters: Offset distance, Ω. Slice plane spacing,

∆λ.p← ∅;1

λ← minx,y B(x, y) + ∆λ;2

while λ < maxx,y B(x, y) do3

E ← INTERSECT(λ,B);4

l← LINK EDGES(E) ;5

p← p ∪ LINK(p.end, l.start) ∪ l;6

λ← λ+ ∆λ7

p← OFFSET PATH(p,Ω);8

return p9

C. Covering the Effectively Planar Regions using the Recti-linear Decomposition Algorithm

We propose a rectilinear cell decomposition algorithm tocover the remaining effectively planar areas. The idea ofthe algorithm is to decompose the space outside the high-slope areas into rectilinear cells. Then, individual coveragepaths are generated within each cell. Each individual pathwithin a cell consists of a lawnmower-type motion at a fixedoffset distance above the target surface. This algorithm wepropose bears similarity with other CPP algorithms for planarenvironments, such as the trapezoidal decomposition [18],the boustrophedon decomposition [19] or the CCR algorithm[20].

Consider a horizontal plane above the target bathymetricsurface where the bounding boxes of the high-slope regionsdiscussed above represent obstacles. The rectilinear decom-position is generated by sweeping a vertical slice segmentfrom left to right through this plane. Whenever the slice seg-ment encounters the boundary of high-slope region boundingbox, a vertical cell division along the current slice segmentis placed. The cell division extends upwards and downwardsuntil it encounters the boundary of another obstacle regionor until the boundary of the mapped area is reached. Onceconstructed, the decomposition is encoded as an adjacencygraph. In the adjacency graph, each node represents a recti-linear cell, and an edge represents an adjacency relationship

Δλ λ1

λ2

Δλ

λ1

λ2

e1,1

e2,1 e2,2

l1

l2

e1,1

e2,1

e2,2l2

l1

e2,2

e2,1

e1,1

Fig. 2: 3D view (top), top view (middle) and side view(bottom) of the slicing algorithm applied at two differentdepth levels (λ1, λ2) on an example target surface. At levelλ1, the intersection comprises one single closed edge, eλ1,1.Path l1 links the partial path at λ1 with the partial path atλ2. At λ2, the intersection comprises two closed edges, eλ2,1

and eλ2,2. Those two edges are linked by l2 to form the finalpath.

between two cells (i.e., cells that share a common boundary).Then, an exhaustive walk through the graph (i.e., a path thatvisits all the nodes in the graph) is computed to determinethe order in which the cells will be covered. Once the order isdetermined, individual lawnmower-type paths are generatedwithin each cell. Generation of such lawnmower-type mo-tions, also called seed spreader motions, is well documentedin the literature [19], [2]. The individual paths within the cellsare then linked in the order determined by the exhaustivewalk using straight line paths. The generated path is thenprojected onto the target surface, i.e., for each point (x, y)in the path, its depth value becomes B(x, y). From the targetsurface, the path is finally projected onto the offset surfaceusing the OFFSET PATH() function of Algorithm 1. Fig. 3illustrates the application of the rectilinear decompositionto an example workspace and its corresponding adjacencygraph.

IV. THE CALDERA 2012 DATASET AND THEGIRONA 500 AUV

We now introduce the real-world lava tongue bathymetricmap and the AUV we use to test our CPP scheme. The lavatongue bathymetric map was obtained during the Caldera2012 sea trials, which took place from July 13th to July 23rdwithin the caldera of Santorini (Greece). These sea trialswere part of a joint project involving an international andmultidisciplinary team, formed by the Institut de Physique duGlobe de Paris (France), the University of Girona (Spain), theWoods Hole Oceanographic Institute (USA), the Universityof Athens with the infrastructure support of Hellenic Centre

C1

C2

C3

C5

C4

C6

C7

e12

e13

e34

e35

e26

e67

e57

e46

Fig. 3: Rectilinear decomposition of an example workspace.Cells are labeled C1, ..., C7. Each curved line eij rep-resents adjacency graph edge between cells Ci and Cj .Dashed vertical lines represent cell boundaries. An exhaus-tive walk through the depicted adjacency graph could beC1, C2, C6, C7, C5, C3, C4.

of Marine Research (Greece). During the Caldera 2012 trials,the GIRONA 500 AUV [21] was used for characterization ofhydrothermal activity within the caldera via optical mappingand for collection of other oceanographic data. The GIRONA500 AUV, shown in Fig. 4, is a reconfigurable vehicle ratedfor depths up to 500 m. It is equipped with a complete sensorsuite including cameras and bathymetry sonar.

Fig. 4: The GIRONA 500 AUV during the Caldera 2012 seatrials.

In one of the missions carried out during the Caldera 2012trials, the GIRONA 500 AUV gathered bathymetric data on alava tongue in the vicinity of the caldera. The vehicle mappedthe area navigating at a safe altitude of 15 m from the bottom.The mapped area is 427.5 m by 406.5 m, with depths rangingfrom 284 m to 363 m.

A 100 m by 250 m ROI on the mapped area was selectedfor further in-detail inspection. The selected ROI comprisesthe boundary of the lava tongue, and is therefore of highgeological interest. Fig. 5 shows the bathymetric maps ofthe entire mapped area and of the selected ROI.

V. EXPERIMENTAL RESULTSWe apply our proposed CPP scheme to the selected ROI

of the bathymetric map introduced above. The objective is to

(a)

Y X

Z

(b)

Fig. 5: Bathymetric map of a lava tongue near the calderaof Santorini with the ROI approximately indicated by therectangle (a). Bathymetric map of the selected ROI (b).

obtain a coverage path on the ROI at a 2 m offset distancefrom the target surface to collect imaging data with theGIRONA 500 AUV. A 60 aperture angle camera is used.

Values in the slope map, S(x, y) of the ROI range between0.001 and 0.622. A threshold δs = 0.5 is applied to the slopemap. Fig. 6 shows the slope map and the single identifiedhigh-slope region after applying the described morphologicaloperations. The resulting rectilinear decomposition of theremaining space is comprised of two cells, laying to the leftand above the high-slope region.

The slicing and rectilinear decomposition algorithms arethen applied to the corresponding regions. The resultingpath is shown in Fig. 7. The algorithms are implemented inunoptimized MATLAB and generate the full coverage pathin less than 5 seconds on a standard PC.

We next simulate the execution of the planned trajectorywith UWSim [22], an underwater robotics simulation pack-age. The very same software architecture which runs onthe GIRONA 500 during sea trials is used in conjunctionwith UWSim to carry out the simulation, thus allowing forimmediate transition from simulation to real-world missions.A dynamic model of the vehicle is used in the simulation.The robot can navigate at a maximum speed of 1.5 m/s.

We compare the path obtained using our bathymetric CPPscheme and a standard constant-altitude lawnmower-typesurvey path in Table ??, where the path lengths and execution

Y

X

(a)

Y

X

(b)

Fig. 6: Slope map of the Caldera 2012 bathymetric dataset(a) and the high-slope region thresholding (b). The boundingboxes in both subfigures indicate the single identified high-slope region.

(a)

(b)

Fig. 7: Resulting in-detail coverage path for the Caldera 2012dataset. Point of view in (a) is the same as in Fig. 5(b). Alateral point of view is provided in (b), showing in moredetail the horizontal contours on the high-slope region.

times for each region, for the full coverage path and for thelawnmower survey path are shown.

Note that, although the classical survey path is shorter,it takes almost as long to execute. This is mainly dueto the sudden depth changes which are difficult for theAUV to accommodate. While we have not quantified thevertical/lateral energy cost ratio of our vehicle, this difficultyis clearly observable in the simulation. It can be qualitativelyobserved that our method better accommodates these motionconstraints of the AUV. The method might be less beneficialfor an AUV with a lower vertical/lateral energy cost ratio,such as a spherical vehicle. However, such AUV designs arenot common nowadays.

Finally, we note that the constant-depth horizontal edgestraced by our method provide a fair, normal-to-target viewangle for imaging tasks, whereas the sudden depth changes ofthe classic survey path bring about steep view angles whichnegatively affect imaging quality.

Dataset Max. unc. Final unc. Avg. unc. Path length

TABLE I: Maximum, final and average uncertainty (SSE)and path length for a path planned using a standardlawnmower-type path with two arbitrarily selected cross-tracks.

VI. CONCLUSION AND FURTHER WORK

We presented a CPP method including two algorithms forcoverage of bathymetric surfaces. The method takes intoaccount the slope of the areas on the bathymetric surfaceand generates paths suiting the characteristics of effectivelyplanar regions and high-slope regions. We demonstrated thefeasibility of the method by planning a coverage path on areal world bathymetric dataset.

Execution of the planned paths will take place in sea trialsin the near future. A map-based localization approach willbe used together with a standard PI path following controllerto carry out the execution. We plan to use this methodintensively as a standard tool to obtain valuable scientificdata in our future sea trials, especially in the context of theongoing MORPH European research project, which includesmapping and inspection of structures such as coral reefs.A more detailed study of the benefits of the proposed CPPmethod with respect to the vehicle vertical/lateral energycost ratio will be conducted in the near future. Further workwill include incorporating localization uncertainty into theplanning phase in order to improve path quality. Generat-ing coverage paths for marine environments such as thoseaddressed in this paper using only sensor information, thatis, without an a priori bathymetric map, is also part of ourfuture research roadmap.

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