Virtual Planning and Testing of AUV Paths for Underwater

Photogrammetry

Amy Lewis

, Kolton Yager

, Mitchell Keller

, Bonita Galvan

, Russell C. Bingham

Samantha Ting

, Jane Wu

, Timmy Gambin

, Christopher Clark

and Zo

e J. Wood

Computer Science Department, Cal Poly, San Luis Obispo, U.S.A.

Engineering Department, Harvey Mudd College, Claremont, U.S.A.

Department of Archaeology, University of Malta, Malta

Keywords:

Photogrammetry, AUV Path Planning, Viewpoint Planning, 3D Reconstruction.

Abstract:

We introduce a system for automatically generating paths for autonomous underwater vehicles which optimize

views of a site of interest. These paths can then be used to survey and map underwater sites of interest using

photogrammetry. Paths are generated in a virtual world by a single-query probabilistic roadmap algorithm that

quickly covers the conﬁguration space and generates small maps with good coverage. The objective function

used to compute the paths measures an approximate view coverage by casting rays from the virtual view to

test for intersections with the region of interest, with added weight for views with high information gain.

The motion planning algorithm was implemented in a virtual world that includes the ability to test paths and

acquire views of the virtual scene for evaluation prior to real world deployment. To measure the effectiveness

of our paths versus the commonly used pre-packaged lawnmower paths, photogrammetry reconstructions were

compared using CloudCompare. The 3D reconstructions created from the views along the paths generated by

our algorithm were more detailed and showed better coverage, creating point clouds with a mean distance

between points ranging from 1.5 to 2.3 times better than that of the lawnmower pattern.

1 INTRODUCTION

Searching for archaeological sites underwater in-

volves time consuming ﬁeld work and expensive

equipment. A common approach is to select a large

area to explore then conduct a survey, for example us-

ing a towﬁsh for sonar mapping from a boat. Sonar

data is then analyzed by experts (or intelligent sys-

tems (Rutledge et al., 2018)) which rank potential

sites of interest. The sites are revisited, for example,

by an accomplished human dive team or remotely op-

erated vehicles (ROVs).

A potentially safer and less expensive solution is

the use of Autonomous Underwater Vehicles (AUVs)

for both survey and site mapping. The work presented

here focuses on the problem of developing good paths

for the AUV to map a site for photogrammetry recon-

structions using an on-board goPro camera. The goal

is to acquire good camera views of the site of inter-

est for reconstructions. Building from an initial sonar

scan which is used to determine the extents of the site

of interest, our algorithm creates paths for the AUV

to map the site. A set of the video image frames is

then used for photogrammetry to create a 3D recon-

struction which can be used for educational and site

monitoring purposes.

In general, determining the path for an au-

tonomous vehicle has applications to many ﬁelds.

Our speciﬁc path planning algorithm prioritizes col-

lecting images of all sides of a region of interest with

good coverage by using a probabilistic roadmap algo-

rithm. The path planning algorithm takes into account

the geometry of the site of interest and general physi-

cal constraints of the AUVs movement. The objective

function weights potential positions based on the view

of the on-board camera of the region of interest.

We present our path planning algorithm and a vir-

tual world testbed, where various paths can be tested

and compared. A virtual camera collects images

along the automatically generated paths and those im-

ages are then used to create 3D models and point

clouds using photogrammetry. Most AUVs include

easy to use motion planning for surveys in the form of

‘lawnmower’ patterns. To measure the effectiveness

of our paths versus the commonly used pre-packaged

lawnmower paths, the 3D models and point clouds

Lewis, A., Yager, K., Keller, M., Galvan, B., Bingham, R., Ting, S., Wu, J., Gambin, T., Clark, C. and Wood, Z.

Virtual Planning and Testing of AUV Paths for Underwater Photogrammetry.

DOI: 10.5220/0008943300930101

In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 1: GRAPP, pages

93-101

ISBN: 978-989-758-402-2; ISSN: 2184-4321

created from the different paths were compared. The

paths generated by our algorithm captured images re-

sulting in 3D reconstruction which were more de-

tailed and showed better coverage of the site of inter-

est than those from the lawnmower pattern. Our work

is primarily focused on underwater shipwrecks, thus,

our testbed includes a simple boat model. A com-

parison of the side proﬁles of an original virtual boat

model, the 3D model created from images captured

along the lawnmower pattern, and the 3D model gen-

erated from images along the path computed by our

algorithm is shown in Figure 6.

1.1 Field Work and Motivation

This path planning work arose from extensive ﬁeld

work in the coastal waters of Malta (Wu et al., 2019;

Rutledge et al., 2018; von Fock et al., 2017a). Ini-

tial work using a 2D bounding box, seen in Figure 1

on real sonar data, showed promising results for re-

constructions. See Figure 2 for a reconstruction of a

World War 2 shipwreck created from the initial 2D

bounding box paths. Due to time, weather and cost

limitations to deployments, this virtual testbed was

developed to test and evaluate further motion plan-

ning.

Figure 1: An example of the 2D bounding box of a region

of interest produced from ﬁeld deployments (see (Wu et al.,

2019; Rutledge et al., 2018; von Fock et al., 2017a) for more

information).

2 RELATED WORKS

Motion planning for robots is well studied (Dudek

and Jenkin, 2010; Demofox, 2015; Alcazar et al.,

2011) with this work building on many of the prior

algorithms. Garau, Alvarez, and Oliver introduce

a heuristic cost function that estimates the time the

AUV would need to travel from one grid point to the

next (Garau et al., 2006). Rao and Williams present

a rapidly-exploring random tree (RRT) algorithm to

plan collision-free paths for an underwater glider in

3D space (Rao and Williams, 2009). Tan, Sutton,

and Chudley also propose a RRT algorithm to plan

Figure 2: Example model reconstruction from images ac-

quired along a 2D bounding box motion planned deploy-

ment.

collision-free paths in three-dimensions while also ac-

counting for vehicle dynamics (Tan et al., 2017).

There is likewise a rich body of work address-

ing the ﬁeld of photogrammetry (Yamafune et al.,

2016), and AUV path planning (Rantanen, 2014; Li

and Shie, 2002; Dale and Amato, 2001; Poppinga

et al., 2011; Candeloro et al., 2015; Wu et al., 2019).

Viswanathan et al. implemented a motion planner

with an RRT with a goal similar to ours (Viswanathan

et al., 2017). Our work was also inﬂuenced by a

probabilistic roadmap planning algorithm to gener-

ate virtual camera paths for ﬂy-throughs of a digital

scene (Davis, 2017). And related later work (Clark

et al., 2017), which aimed to create good cinemato-

graphic and geometric views. However, in this prior

work, rotation is only free around one axis instead of

two as in our algorithm.

Yamafune et al. share the same goal in their work

as our own - to survey shipwrecks for the purpose of

reconstruction (Yamafune et al., 2016), however, they

use a team of professional human divers to capture

their video data. It is worth noting that they recom-

mend that divers capture many circular views for opti-

mal reconstructions and the proposed paths look very

much like a lawnmower pattern.

Dunn et al. present a path planner for autonomous

vehicles with a goal of creating detailed 3D recon-

structions (Dunn et al., 2009). Computer vision is

used to obtain the geometric structure of the scene be-

ing reconstructed and a path with ‘the next best view’

is determined by their novel cost function that “quan-

tiﬁes the expected contribution of future viewing con-

ﬁgurations”. In addition, related work includes recent

work for drone trajectory optimization (Hepp et al.,

2018) for an aerial path to capture data for photogram-

metry.

Within the context of related work, our algorithm

GRAPP 2020 - 15th International Conference on Computer Graphics Theory and Applications

is novel in its algorithmic computation of view cov-

erage to weight roadmap nodes, tuned for the task of

capturing images of all sides of a site of interest for

an underwater vehicle, thereby improving coverage.

3 ALGORITHM

To generate AUV paths, this system uses a robotics

motion planning algorithm - single-query probabilis-

tic roadmaps (PRM). This algorithm quickly cov-

ers the conﬁguration space and generates small maps

with good coverage. In order to create a viable 3D

reconstruction of a site of interest, it is important for

the camera to capture good views of all regions. Our

path planning algorithm seeks to ensure that for the

discrete nodes along the path that the AUV visits, the

camera is viewing signiﬁcant portions of the site of

interest as well as ensuring all regions of the site have

been viewed. Geometric principles, primarily an ap-

proximation of how much of the main site of inter-

est is in view of the camera, are used to set node

weights and select nodes to include in the path for

the AUV. Speciﬁcally, the objective function used in

our algorithm measures an approximate view cover-

age by casting rays from the camera and intersecting

them with the region of interest.

For our path planning, the algorithm solves for

the motion within a virtual representation of a gen-

eral volume of space (in our case, sea) surrounding

the region of interest. This region of interest is identi-

ﬁed from low resolution side scan sonar data obtained

from a high altitude scan by the AUV (Rutledge et al.,

2018). A bounding box is computed based on an

automatically detected region of interest (Wu et al.,

2019), deﬁning both the site to be mapped as well as

a no ‘ﬂy’ zone (to prevent collisions). Assuming a

mapping between real-world GPS and sonar coordi-

nates and the virtual world, ultimately, the conﬁgura-

tion space is the x,y,z position and pitch-yaw of the

camera (relative to the AUV) within the extents of the

virtual world. Constraints are used to model the pos-

sible AUV turning radius between nodes and the fact

that the camera is ﬁxed to the AUV while traveling

along a path. From the bounding box, a starting po-

sition for the AUV is chosen and a roadmap is built,

expanding nodes branching from the prior node until

a path which visits all visible sides of the bounding

box has been found.

Our algorithm uses a discrete representation of the

camera’s frustum and computes an intersection quan-

tity for possible views (derived from potential vehicle

positions). Using this metric, a path can be planned

that maximizes camera coverage of all of the sides

of the site of interest. Figure 3 illustrates an inter-

section between the camera’s view frustum and the

site of interest’s bounding box. After a path has been

found, discrete images from the perspective of the vir-

tual camera travelling the planned path can be used to

create a reconstruction of the site. The reconstruc-

tion can then be compared to the original 3D model

or other reconstructions to measure the overall path

viability.

We solve for a vehicle path considering nodes in

the conﬁguration space. Physical considerations such

as the camera being oriented 90 degrees orthogonal

to the vehicle, allow the camera frame to be derived

from the vehicle velocity. Velocity is what determines

the magnitude and the direction in which the robot

moves towards the next node in the path. Other values

stored in each node for the algorithm include weights

determined by the objective function and parent in-

formation. For each node, we also keep track of a

lightweight representation of the sides of the region of

interest which have, so far, been seen in an unsigned

integer using 5 bits.

The basic algorithm is as follows:

while bboxSideCoverage < desiredCoverage

// select node n to expand from

if declustering then

n ← node from voxel with least

nodes;

end

else

if even iteration of loop then

n ← random node in

highWeightNodes;

end

else

n ← random node in

roadmap;

while n < weightThreshold;

end

randomly generate n’ from n;

calculate edge e from n to n’;

Roadmap.add(n’, e);

bboxSideCoverage ← n’.bBoxcoverage;

n’.weight ← calculateWeight(n’);

if n’.weight > highWeightThreshold then

highWeightNodes.add(n’);

end

Virtual Planning and Testing of AUV Paths for Underwater Photogrammetry

Figure 3: Visualization of the camera view frustum, in this

case intersecting with the bounding boxes representing the

region of interest.

Node Selection. The algorithm starts with the selec-

tion of a root note, which is added to the roadmap and

the algorithm proceeds with the node selection step.

For node selection, we must choose a node n from the

roadmap to expand from.

All nodes in the roadmap are stored in a 3D uni-

form spatial grid. The 3D grid is represented as

C = c

i jk

|i = 1,...,m; j = 1,...,n; k = 1,...o. The three

dimensions of C refer to discretized values of the x, y,

and z coordinates of the virtual world. Each newly

created node is inserted into the spatial data struc-

ture by its x,y,z location. The i, j,k space is twice

the magnitude of the original bounding box acquired

from a high altitude sonar scan, but this scaling is con-

ﬁgurable.

For all nodes, n, a weight measuring the node’s

viewpoint is computed. To compute n.weight, three

main criteria are used:

• Viewpoint quality: the view frustum for this node,

(where n includes x,y, z and pitch and yaw) is dis-

cretized as a matrix of 200 rays. These rays are

intersected with the bounding box of the region of

interest. Any ray that intersects with a side of the

bounding box contributes towards the total weight

for the current node,

n.weight =

∑

(RayHits)/totalRays (1)

• Information gain via new side coverage: If a node

offers a view of a side of the bounding box of

the region of interest that has not previously been

seen, the weight of the node is signiﬁcantly in-

creased, +c. The algorithm is able to distinguish

that a side is newly seen by keeping a record

of viewed sides for each node, n. To reduce

the memory footprint of nodes in the complete

roadmap, each node holds an unsigned int with

ﬁve bits used to encode which sides of the region

of interest have been seen (via ray intersections

with sides of the bounding box denoted with a

unique bit). This encoding can be compared to

the prior node to distinguish the viewing of a new

side.

• Viewpoint gain: If the current node has a higher

weight than its parent, an additional contribution,

+delta, is added to promote expansion towards

promising directions.

Node weights are used in the selection step of the al-

gorithm to balance both exploration and targeted se-

lection.

Node selection alternates to optimize various mo-

tion planning goals.

• For declustering, to promote expansion in all di-

rections, the voxel i, j,k that contains the least

number of nodes is selected for expansion every

other expansion

• For pruning, on every other step we alternate be-

tween selecting:

1. a node from the list of “high weight” nodes.

Weights for an initial 440 nodes are placed in a

discrete grid around the region of interest. The

high weight threshold is then initialized to the

average weight plus the standard deviation of

these initial nodes:

highWeightT hresh =

∑

i=1

.weight/m + σ (2)

These nodes have better then average view-

points.

2. a random node with a weight above a signif-

icantly lower minimum threshold value. This

minimum threshold decreases with each iter-

ation to promote node selection even if the

roadmap only contains low quality nodes.

The declustering step prevents the roadmap from

producing too many nodes in a single area that offers

high weight views of the region of interest, encour-

aging exploration and coverage of the conﬁguration

space. By selecting higher weight nodes, the algo-

rithm effectively prunes low quality directions and de-

creases the potential size of the roadmap.

Node Generation. In order to cover the entire

scene, the roadmap must expand to a new node, n

Once a node to expand from has been selected as de-

scribed above, a new node is generated based off the

prior node. The velocity of the prior node is taken and

a new velocity with a randomly perturbed pitch and

yaw is added to it. A delta value, within a range of

0 and π of the prior node’s pitch is randomly chosen.

The new delta value is then added to phi. The same

process happens for yaw with a delta added to theta.

GRAPP 2020 - 15th International Conference on Computer Graphics Theory and Applications

The new, perturbed pitch and yaw are then used to cal-

culate the new velocity. The new velocity is added to

the previous position, creating the position of the new

node, n

. If that is, in fact, a valid position and not col-

liding with the region of interest, then the orientation

for the robot at that position is calculated.

Path Completion. Our algorithm terminates when

all sides of the region of interest have been seen. Each

time a node is added to the roadmap, the algorithm

evaluates if all sides of the bounding box around the

region of interest have been seen. After the ﬁnal side

has been seen, the algorithm runs for a ﬁnite amount

of time. The time limit is an experimental choice and

other methods to ensure further coverage of the ﬁnal

side of the region of interest could be explored. The

ﬁnal path is generated from the roadmap by follow-

ing parent nodes from the ﬁnal node to the root node.

The nodes along this path can then be used to replay a

virtual path to gather images for reconstruction in our

virtual testbed. Future work includes mapping these

points from the virtual space back to real world GPS

coordinates which can then be used as way points for

an AUV trajectory around the real site of interest.

Using Paths in the Testbed. As underwater vehi-

cle deployments can be challenging (in terms of cost,

weather, etc.), we sought to design a virtual platform

to plan and test AUV paths and camera views. The

virtual world used in our testbed is an OpenGL appli-

cation which, in its current implementation, includes

simple geometric models. The ground plane repre-

sents the seaﬂoor and is textured with an image of

a sandy seaﬂoor like that of the Mediterranean. To

generate motion between the nodes, the positions is

interpolated using a cubic Hermite interpolation func-

tion creating a spline (Demofox, 2015). An image is

captured every third frame by the virtual camera as it

follows the generated spline. Building off the work of

(von Fock et al., 2017b), we use the frames from the

paths to construct a model of the target of interest.

4 RESULTS

We present a probabilistic roadmap algorithm for the

generation of paths for an AUV to travel in order to

capture multiple views of a region of interest with

good coverage. In addition, we present an applica-

tion to test these paths in a virtual environment which

uses simple geometry but allows for virtual frames to

be written out and then used with a photogrammetry

application for path evaluation.

Figure 4: Each node (blue sphere) represents a conﬁgura-

tion of the AUV while following the path. A path is made

by moving between these nodes.

Figure 5: Image showing the example images and subse-

quent reconstruction from aligned input images captured

from a virtual path for one side of the model.

To measure the effectiveness of our paths, the

3D models and point clouds created from our algo-

rithm were compared to those generated from running

a standard pre-packaged lawnmower pattern. The

paths generated by our algorithm captured images that

could be used in a 3D reconstruction, that were more

detailed and that showed better coverage of the region

of interest than those from the lawnmower pattern.

Point clouds of each reconstruction are also compared

to determine the level of detail of each.

4.1 Measures

To test the quality of images generated by the various

paths, we used Agisoft Photoscan



for photogram-

metry. We selected a set of twelve paths created by

our algorithm to consider for comparisons. In ad-

dition, image frames from three lawnmower pattern

paths were also captured for comparison. While one

set of lawnmower path images led to a good recon-

struction, the other two, including an attempt to run

Virtual Planning and Testing of AUV Paths for Underwater Photogrammetry

the pattern created by Yamafune et al. (Yamafune

et al., 2016), failed to produce usable models at all.

For the one lawnmower path that was able to produce

a reconstruction, the 3D model and point clouds are

compared to the original 3D model of the shipwreck

(i.e., the site of interest).

One of the key steps in photogrammetry is image

alignment (see Figure 5) and the number of aligned

images directly corresponds to the amount of data us-

able in the reconstruction. The percentage of aligned

images for the comparison paths are shown in Table 1.

On average, at least 57% of the images from our paths

are aligned. Reconstructions were created for three of

our paths, PRM 1 and PRM 6 and PRM 11. While

PRM 1 has very good image alignment, the the later

two paths are more average and are included to show

that even average paths created by our algorithm can

produce better results than a reconstruction following

the lawnmower pattern.

Table 1: Summary of Paths with Good Potential. Includes

the images aligned, the percent of those actually aligned,

and the average weight of each path.

Path Images Percent Average

Aligned Aligned Weight

1 599/608 98.52 0.54

2 121/666 18.17 0.52

3 468/551 84.94 0.58

4 198/614 32.25 0.51

5 296/641 46.18 0.57

6 790/1322 59.76 0.57

7 476/988 48.18 0.56

8 429/743 57.74 0.54

9 544/646 84.21 0.57

10 83/268 30.97 0.56

11 295/573 51.48 0.57

12 478/592 80.74 0.55

Figure 6 shows the side proﬁles of the reconstruc-

tions for PRM 6 and the lawnmower pattern along-

side the original 3D model. It is clear that the recon-

struction generated from images from our paths in-

clude much more complete model information, while

the model reconstructed from a lawnmower pattern is

missing the sides of the model. One limitation of the

current work is that given the small scale of our cur-

rent virtual testbed, both our paths and lawnmower

produced good reconstructions of the top of the ship-

wreck as shown in Figure 8 and Figure 7.

Point clouds of all of the reconstructed 3D models

were compared using CloudCompare. In general, the

denser the point cloud, the more detailed the recon-

struction. One measure of the density is the mean dis-

tance between points, with smaller distances between

Figure 6: Comparison of a 3D Model and two point cloud

reconstructions, one from images captured from a standard

‘lawnmower pattern’, and the much more complete recon-

struction from images using a path created with our algo-

rithm.

points indicating greater density. Figure 8 and Figure

9 show point clouds in blue created from our paths,

over the gray point cloud created from the original

model. As shown in the images and reinforced in the

data displayed in Table 2, the point clouds created by

our paths are signiﬁcantly more dense than the point

clouds created by the lawnmower pattern. The mean

distance of the point clouds produced by our paths

range from being 1.5 to 2.3 times better than that of

the lawnmower pattern.

Table 2: Point Cloud data for PRM and lawnmower paths.

Path Mean Distance Std Deviation

PRM 3 0.15 0.19

PRM 6 0.12 0.39

PRM 11 0.23 0.59

Lawnmower 0.34 0.43

When comparing the paths, it is worth noting that

the total distance of each path does not correlate to

the quality of the reconstruction. Table 3 shows the

distance each path covered in the virtual world. The

lawnmower pattern covers a distance of almost twice

as far as path PRM 11, but PRM 11 is a better recon-

struction overall.

GRAPP 2020 - 15th International Conference on Computer Graphics Theory and Applications

Figure 7: Additional views of the 3D Models created by

images captured along paths using our algorithm (PRM 11

and PRM 6).

Table 3: Total distance by the selected paths in virtual world

units.

Path Total Distance

PRM 3 1678.94

PRM 6 2270.19

PRM 11 664.24

Lawnmower 1128.49

Performance. All work was executed for testing on

a 2019 MSI GS63 Stealth with an Intel 8th Genera-

tion Core i7-8750H processor. The computer also has

a dedicated graphics card - NVIDIA Geforce GTX

1060. The code was written in C++14 along with the

Open Graphics Library (OpenGL) version 4.6. The

OpenGL Mathematics library, GLM, version 0.9.8.5

and GLFW3 version 3.2 were also used.

The objective function has a signiﬁcant effect on

performance. Initially, the algorithm was allowed

Figure 8: Point cloud produced from reconstruction using

images from following a lawnmower pattern path. Note the

mismatch on the sideview.

Figure 9: Top and side view of the point clouds produced

from reconstruction using images from our paths (3 and 11

speciﬁcally).

to expand by choosing a node completely randomly

from the roadmap. On multiple occasions, the algo-

rithm was left to run overnight without generating a

complete path because it either never saw all sides of

the region of interest or the computer ran out of mem-

ory. When the high weight threshold was added to

the node selection process, path generation went from

taking hours to minutes.

An important optimization to performance for this

project was the use of a hash map to represent the

spatial data structure, allowing the algorithm to look

up the voxel with the least amount of nodes rapidly.

As shown in Table 4, all of the generated paths took

between 10 and 27 seconds of computation. Table

4 shows a summary of the generated paths including

Virtual Planning and Testing of AUV Paths for Underwater Photogrammetry

the length of each path, the number of nodes in each

respective roadmap, and the time it took to generate

them. The larger the roadmap, the more time the algo-

rithm took to create a path, however, even the largest

roadmap with 538 nodes took only 27 seconds to gen-

erate a path.

Table 4: Summary of generated paths. Includes the number

of nodes of each path, the number of nodes in each roadmap,

and the time to generate each path in seconds.

Path Path Roadmap Time

Size Size (s)

1 20 36 10

2 62 99 15

3 160 261 23

4 87 193 17

5 33 48 11

6 207 407 26

7 76 178 16

8 118 189 20

9 92 137 20

10 155 234 22

11 61 100 14

12 189 538 27

5 CONCLUSIONS

We have presented a virtual path planning and testing

system to help plan paths for underwater vehicles to

map underwater sites of interest. The 3D models cre-

ated by the paths computed using our algorithm are

more detailed and show better coverage of all sides

than those created by the lawnmower pattern. The

images gathered along our paths also created signiﬁ-

cantly denser point clouds than the lawnmower paths,

with a mean distance between points that ranges from

1.5 to 2.3 times better than that of the lawnmower pat-

tern.

This project represents the culmination of a large

amount of experience in ﬁeld work focused on map-

ping underwater sites of interest (Wu et al., 2019; Rut-

ledge et al., 2018; von Fock et al., 2017a), however,

there are many areas for future work including: test-

ing the paths in a real world setting and expanding the

algorithm to account for multiple bounding boxes.

For real world AUV paths, while underwater the

AUV’s location accumulates error as time goes on (an

acoustic underwater positioning system would give

measurements with bounded error, but these systems

are not always in place). Therefore, in order to con-

vert the automatically generated paths to ones that

could be accurately used with the AUV, additional

way-points (nodes) will be added. Pairs of nodes with

similar velocities would be selected and correspond-

ing surface way-points would be appropriately spaced

to reach the correct depth for each node before and

after the node pairs are added to the ﬁnal path. This

process would be repeated until all nodes are paired

and associated with surface way-points. The AUV

would then travel to each way-point until the path is

complete. We hope to complete ﬁeld testing of our

system in the upcoming year. Additional future work

includes deeper exploration and comparisons to other

motion planning algorithms.

ACKNOWLEDGEMENTS

We would like to acknowledge the entire 2017 and

2018 ICEX teams. This material is based upon work

supported by the National Science Foundation under

Grant No. 1460153.

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