Evaluating the Beneﬁt of Using Multiple Low-Cost Forward-Looking Sonar Beams for Collision Avoidance in Small AUVs Christopher Morency and Daniel J. Stilwell

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Evaluating the Beneﬁt of Using Multiple Low-Cost Forward-Looking

Sonar Beams for Collision Avoidance in Small AUVs

Christopher Morency and Daniel J. Stilwell

Abstract— We seek to rigorously evaluate the beneﬁt of using

a few beams rather than a single beam for a low-cost obstacle

avoidance sonar for small AUVs. For a small low-cost AUV, the

complexity, cost, and volume required for a multi-beam forward

looking sonar are prohibitive. In contrast, a single-beam system

is relatively easy to integrate into a small AUV, but does not

provide the performance of a multi-beam solution. To better

understand this trade-off, we seek to rigorously quantify the

improvement with respect to obstacle avoidance performance

of adding just a few beams to a single-beam forward looking

sonar relative to the performance of the single-beam system.

Our work fundamentally supports the goal of using small low-

cost AUV systems in cluttered and unstructured environments.

Speciﬁcally, we investigate the beneﬁt of incorporating a port

and starboard beam to a single-beam sonar system for collision

avoidance. A methodology for collision avoidance is developed

to obtain a fair comparison between a single-beam and multi-

beam system, explicitly incorporating the geometry of the beam

patterns from forward-looking sonars with large beam angles,

and simulated using a high-ﬁdelity representation of acoustic

signal propagation.

I. INTRODUCTION

We address the problem of collision avoidance for an

autonomous underwater vehicle (AUV) using noisy sensor

data in an unknown environment using an array of inexpen-

sive single-beam sonars. Forward-looking sonar systems for

smaller AUVs usually consist of either a single-beam, such

as in [1], or many beams, such as in [2]. The performance

of the former is necessarily limited, and the cost and power

required for the latter may be prohibitive for small AUVs. We

rigorously evaluate what beneﬁt, if any, arises from choosing

a middle-ground solution that consists of a few sonar beams.

Through a rigorous fundamental evaluation of the beneﬁt of

additional beams, we seek to aid in the development of a

robust collision avoidance system feasible for small AUVs.

In this work, we speciﬁcally address the obstacle avoid-

ance problem by proposing a method for detecting obstacles

and selecting avoidance maneuvers that provides a fair

comparison for a forward-looking sonar system with only

a few beams. We explicitly compare obstacle avoidance

performance in the horizontal plane for the case of adding

two additional forward-looking beams to a single-beam sonar

through simulation using a high-ﬁdelity environmental model

from [3]. The performance of the single-beam and multi-

beam sonars are evaluated in environments with various

object densities and sizes, at various depths and heights

above the seaﬂoor, and at varying levels of uncertainty in the

The authors are with the Bradley Department of Electrical and Computer

Engineering, Virginia Polytechnic Institute and State University, Blacksburg,

VA 24060, USA {cmorency, stilwell}@vt.edu

dynamics of the AUV. Simulations of obstacle avoidance are

in the horizontal plane in order to simplify, yet make rigor-

ous, the comparison between the sonar systems. We present

a method for obstacle mapping which explicitly incorporates

sensor geometry and a reactive obstacle avoidance method

using Bayesian expected loss, providing the optimal decision

function for obstacle avoidance given the costs of collision

and deviation from the original path.

A sonar with a low number of beams serves as a middle

ground between single-beam sonars, such as the mechani-

cally steered Imagenex 881L Proﬁling Sonar [4] or a station-

ary sonar [5], and forward-looking imaging sonars such as

DIDSON [6] or the Blueview P450-15E [7], which use many

ﬁxed beams to build an extensive map of the surroundings.

Several approaches to mapping and collision avoidance such

as in [8] and [9] exist for multi-beam imaging sonars. These

solutions are not practical for a system with a few beams due

to the large uncertainty in object location and low resolution

of sonar images.

Underwater detection and obstacle avoidance methods for

AUVs is a challenging task since the system needs to be

robust to the high levels of uncertainty present underwater.

Several approaches to the mapping and detection problem

have been presented in the literature, many of which are

developed using ultrasonic sensors for indoor mobile robots

such as in [10], [11], [12]. These approaches have limited

utility to our application due to the dynamics of an AUV

since most AUVs must maintain a minimum forward velocity

for depth control and have high levels of uncertainty in

the dynamics. In contrast to many of the methods using

ultrasonic sensors in the literature, we rigorously incorporate

a physics-based sonar model to try to address some of these

limitations [3].

A popular approach to collision avoidance in the literature

is the artiﬁcial potential ﬁeld [13], for which obstacles are

associated with repulsive forces. The forces are summed and

the resultant force determines the resulting action of the

AUV. The limitation of potential ﬁelds is that they require

complete knowledge of the obstacles in the environment.

Modiﬁcations to the potential ﬁeld have been proposed by

Borenstein and Koren in [14] which can react to unexpected

obstacles. However, potential ﬁelds can result in the robot

becoming trapped at local minimas and oscillations, and are

not practical for robots with dynamic constraints, such as

AUVs. Vector ﬁeld histograms [11] reportedly solve some of

these issues, however, most artiﬁcial potential ﬁeld methods

remain difﬁcult to implement on vehicles with a restrictive

turn radius [10].

arXiv:2210.06537v1 [cs.RO] 12 Oct 2022

Our approach to the mapping problem uses a variation of

an occupancy grid [15]. Occupancy grids are probabilistic

representations of the environment for which the environ-

ment is partitioned into cells. For each measurement, cells are

updated by a recursive Bayesian update. Several variations to

the standard occupancy grid [16], [17] have been proposed

to improve some of the limitations of the method. Ganesan

et al. [16] approach the mapping problem using a local

n×moccupancy grid and a motion model to propagate the

grid. Using a local map improves obstacle localization by

eliminating the AUV’s positional error growth. The motion

model is able to incorporate motion uncertainty of the

obstacles relative to the AUV. In contrast, our approach uses

a local occupancy grid with cells speciﬁcally constructed to

match the volume ensoniﬁed by the sonar, leading to reduced

computational complexity and a more accurate representation

of sonar returns. Fulgenzi et al. [17] present a method

using velocity obstacles based on the Bayesian Occupancy

Filter proposed by Cou´

e et al. in [18]. Due to the large

uncertainty and beam widths of our system, using the sonar

for characterizing the velocity of an object is impractical.

A robust collision avoidance approach must be able to

minimize the effect of inaccurate sensor data which can

reduce the performance of a collision avoidance system.

Jansson and Gustafsson [19] present an approach to collision

avoidance using Bayes’ risk for a collision mitigation system

on a ground vehicle. Hu and Brady [10] approach the colli-

sion avoidance problem from decision theory, obtaining the

optimal decision rule by minimizing the Bayesian expected

loss to select a minimum cost action for an industrial robot.

A ground vehicle and industrial robot have the advantage of

being able to stop, whereas an AUV does not. To overcome

the challenges caused by dynamic constraints of an AUV, our

approach utilizes Bayesian expected loss by incorporating

the uncertainty in vehicle dynamics and incorporating the

probability that a collision is unavoidable if no action is

taken.

The remainder of the paper is organized as follows. The

detection model for mapping the environment relative to the

AUV is presented in Section II. Our approach to reactive

collision avoidance is outlined in Section III. Discussion of

the simulator and results from Monte Carlo simulations are

presented in Section IV.

II. DETECTION MODEL

A detection model is constructed to identify potential

obstacles in the ﬁeld of view of the AUV. The model maps

measurements from the sonar to the probability of an obstacle

at a discretized set of distances ahead of the AUV.

A. Polar Map

A polar map is constructed using the returns of a single-

beam forward-looking sonar for which sound energy is

returned to the sonar from reﬂections at a discrete set of times

or equivalently, discrete distances. In this work, we consider

a map in R2for simplicity. Extending the framework into R3

would require additional considerations for the continuous

nature of the sea ﬂoor and surface. The map is similar to

the occupancy grid proposed in [15], however, we explicitly

adapt the cells to our sensor instead of using an m×n

rectangular grid of cells. The beam pattern loss for a single-

beam sonar is shown in Figure 1. Cut-off angles are selected

such that an object between the cut-off angles is detectable

50 meters ahead of the sonar and are shown as red dotted

lines at -5 and 5 degrees in Figure 1.

Fig. 1. Beam pattern loss in dB (solid blue line) and cutoff angles (dashed

red line) for a single-beam forward-looking sonar

To characterize the returns from each beam at each of the

discretized distances, a map M ∈ R2comprised of n×m

cells ci,j is constructed such that each cell represents the

probability that an obstacle is present within the bounds of

the cell. The cells are constructed such that the area of each

cell is the 5 dB area for a single return from the sonar for a

5 dB beam pattern loss, such that

ci,j =x∈R2:i−1

<x< i

, x ∈θj, θj+1

where lcis the length of the cell in meters deﬁned by the

return from the sonar. The map is in the vehicle frame, and

each cell ci,j comprises the area (i−1

lc,i

lc]meters away from

the vehicle and within (θj, θj+1]degrees from the centerline.

Figure 2 shows an example of the discretized map using three

beams where c5,2corresponds to the shaded cell.

The probability of an obstacle in each cell is initially

assumed to be uniform since the system has no information

about the environment prior to the ﬁrst sensor return. Each

cell is assumed to be independent of every other cell so that

the computations are tractable.

B. Measurement Model

The measurement model is used to update the map when

the sensor measurements are received. The sensor receives

a set of measurements zt∈ Z, where tdenotes the time at

which the measurement is received. The measurements are

stochastic in nature, and the probability of a measurement

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EvaluatingtheBenetofUsingMultipleLow-CostForward-LookingSonarBeamsforCollisionAvoidanceinSmallAUVsChristopherMorencyandDanielJ.StilwellAbstractWeseektorigorouslyevaluatethebenetofusingafewbeamsratherthanasinglebeamforalow-costobstacleavoidancesonarforsmallAUVs.Forasmalllow-costAUV,thecomplexity,c...

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Evaluating the Beneﬁt of Using Multiple Low-Cost Forward-Looking Sonar Beams for Collision Avoidance in Small AUVs Christopher Morency and Daniel J. Stilwell

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