MPC-based Collision Avoidance Strategy for Existing Marine Vessel
Guidance Systems
∗
I. B. Hagen, D. K. M. Kufoalor, E. F. Brekke, T. A. Johansen
Abstract— This paper presents a viable approach for incor-
porating collision avoidance strategies into existing guidance
and control systems on marine vessels. We propose a method
that facilitates the use of simulation-based Model Predictive
Control (MPC) for collision avoidance (COLAV) on marine
vessels. Any COLAV strategy to be applied in real traffic
must adhere to the international regulations for preventing
collisions at sea (COLREGS). The proposed MPC COLAV
method does not rely on an accurate model of the guidance
system to achieve vessel behaviors that are compliant with
the COLREGS. Rather, it depends on transitional costs in the
MPC objective for collision avoidance maneuvers that are being
executed by the marine vessel. Hence, it is straightforward
to implement the MPC COLAV on different vessels without
specific knowledge of the vessel’s guidance strategy. Moreover,
it offers the possibility to switch between different (possibly
application specific) guidance strategies on the same vessel
while running the same MPC COLAV algorithm. We present
results from full scale experiments that show the viability of
our method in different collision avoidance scenarios.
I. INTRODUCTION
The existing matured technology platforms on marine
vessels form an essential part of the emerging autonomous
surface vehicles (ASVs). Such platforms include mission
planning systems, guidance, navigation and control systems,
which have several advanced capabilities such as path and
trajectory tracking, dynamic weather routing, dynamic posi-
tioning (see e.g. [1]).
Important aspects of ASVs that are still at early devel-
opment stages are automatic obstacle tracking and collision
avoidance (COLAV). The COLAV aspect requires the ca-
pability to make safe and reliable decisions in hazardous
situations, and its success may depend immensely on how
well the collision avoidance strategy incorporates the relevant
components and functionalities mentioned above.
Much research has been done in the field of COLAV
and a number of different approaches for solving this type
of problems have emerged. Methods especially relevant for
comparison are in this case velocity obstacle (VO) [2] and
dynamic window (DW) [3], [4]. Other strategies include set-
based methods [5], potential fields [6] and inevitable collision
states (ICS) [7]. With many methods there is a limitation to
the extent to which the dynamics of the ASV and the effect of
other essential components can be incorporated into COLAV
All authors are with the Center for Autonomous Marine Operations and
Systems (AMOS), Department of Engineering Cybernetics, NTNU - Norwe-
gian University of Science and Technology, O.S. Bragstads plass 2D N-7491
Trondheim, Norway. {inger.b.hagen, kwame.kufoalor,
tor.arne.johansen, edmund.brekke}@ntnu.no
* This work was supported by the Research Council of Norway (NFR)
through the projects 223254 and 244116/O70.
algorithms. The use of Model Predictive Control (MPC)
allows the possibility to explicitly include models of relevant
components that influences the ASV’s dynamics [8]. Within
this framework it is also possible to include models of the
obstacles’ motion, the evolution of the dynamic environment,
and different operational constraints. This introduces a design
flexibility (and possibly performance gains) superior to other
approaches explored in the collision avoidance literature.
A considerable amount of literature has been published
on the use of MPC for collision avoidance within a range of
fields: ground vehicles [9]–[11], aircrafts [12] and underwa-
ter vehicles [13]. Recently it has also been employed in the
case of marine crafts [8], [14], [15]. MPC is a general and
powerful method that can compute optimal trajectories and
employ nonlinear vehicle models. Environmental forces are
easily included, and risk, hazard and operational constraints
along with mission objectives can be formalized in the cost
function. However, computational complexity and conver-
gence issues is a challenge for real time implementation.
To evade these issues, one approach is to reduce the search
space to a finite number of control behaviors. Optimization
can then be reduced to evaluating the cost associated with
each behavior and comparing these [10].
Although accurate vessel models can be used in predicting
the effect of the autopilot, steering and propulsion systems
within the MPC framework, it may neither be feasible nor
convenient to replicate the numerous capabilities of exist-
ing advanced guidance systems in the COLAV algorithm.
Moreover, discrepancies between the predicted and actual
maneuvering commands generated by the guidance system
may lead to an undesired behavior of the ASV. In an attempt
to avoid these issues, this work investigates the option of
excluding the underlying decision methods of the guidance
system from the prediction model of the simulation-based
MPC scheme proposed in [8]. We therefore look at the
collision avoidance system as an extension to the guidance
system where the decisions of the latter are used as desired
setpoints to the MPC COLAV method.
In addition to this, we propose and discuss the use of
transitional costs as part of the MPC objective for collision
avoidance maneuvers that are in progress. The discussion
is supported by results from a simulation study [15], where
comparisons with the Velocity Obstacles (VO) method pro-
vide further insight into the performance and capabilities of
our approach. To conclude the work and to verify the viabil-
ity of our approach full scale experiments were conducted,
and results from four key scenarios are presented.
Mission
Planning
Guidance
Steering &
Propulsion
System
Marine
Vessel
Sensor
System
Collision
Avoidance
System
Obstacle
Tracking
System
Autopilot
χ
d
,
u
d
χ
m
,
u
m
χ
c
,
u
c
W P s,
u
p
δ
r
,
δ
p
τ
FIG. 1. Information flow for guidance and motion control with
collision avoidance (proposed architecture and parameterization).
II. COLLISION AVOIDANCE SYSTEM ARCHITECTURE
The architectural components of the proposed collision
avoidance system are shown in Fig. 1. The architecture
focuses on information flow between the collision avoidance
system and the other components. We consider a mission
planning system that generates a path in terms of a desired
forward speed (u
p
) and a set of waypoints (WPs) for the
ASV to visit. These are the inputs to the guidance system that
provides the necessary course (χ
c
) and speed (u
c
) commands
to the autopilot in order to reach the waypoints and desired
speed. The autopilot determines the steering and propulsion
control commands (δ
r
and δ
p
, respectively). The result of
the steering and propulsion system are forces and moments
(τ) that determine the vessel’s motion.
Due to disturbances and obstacles that may be detected
along the vessel’s planned path, re-planning and updates to
motion control may be necessary. Such updates depend on
information available from the sensor system and the capa-
bilities of the obstacle tracking system. This work focuses
on the collision avoidance system as an extension to the
guidance system, and we propose the use of the guidance
decisions (χ
d
, u
d
) as desired reference to the collision avoid-
ance system. The task of the collision avoidance system is
therefore to determine the amount of modification (χ
m
, u
m
)
required in order to ensure compliance with COLREGS and
thereby avoid collision.
III. MPC COLLISION AVOIDANCE STRATEGY
The MPC COLAV scheme presented in this paper is
based on the simulation-based control behavior selection
approach of [8]. The MPC is designed according to the
architecture proposed in Section II. Note that the COLAV
has been separated from the guidance module. This implies
that the simple internal simulation model of the MPC does
not include the known guidance behavior as was assumed in
[8].
The main objective of the MPC is to compute modifica-
tions to the desired course (χ
d
) and speed (u
d
) that lead to
a COLREGS-compliant ASV trajectory (cf. Fig. 2). In this
work, an obstacle’s future motion is predicted as a straight-
line trajectory, and we focus on a hazard minimization cri-
terion (i.e. a cost function) that considers dynamic obstacles
and COLREGS compliance. Including static obstacles is
straightforward [8].
A scenario in the MPC is defined by the current state of
the ASV, the trajectories of obstacles, and a control behavior
FIG. 2. Main COLREGS scenarios and correct vessel behavior. The
ASV is marked in gray and obstacle vessel in red. From left: head-
on, crossing from right, crossing from left, overtaking. Furthermore,
any action taken to avoid collision must be significant enough to
be readily apparent to other vessels (cf. COLREGS, Rule 8). For a
comprehensive guide to steering and sailing rules, see [16].
candidate [8]. The set of control behaviors are chosen so
that the resulting maneuvers are easily observable from other
vessels (cf. COLREGS). The following set of alternative
control behaviors are evaluated and assumed to be fixed on
the prediction horizon:
• Course offset in degrees (χ
m
):
-90, -75, -60, -45, -30, -15, 0, 15, 30, 45, 60, 75, 90.
• Speed factor (u
m
): 1, 0.5, 0
i.e. ‘keep speed’, ‘slow down’, ‘stop’
The modifications are in turn applied to the desired decisions
(χ
d
, u
d
) from the guidance system to obtain a course and
speed command (i.e. χ
c
= χ
d
+ χ
m
, and u
c
= u
d
· u
m
).
Therefore, choosing χ
m
= 0 and u
m
= 1 simply recovers the
desired course χ
d
and speed u
d
. This parametrization leads
to a total of 13 · 3 = 39 possible scenarios to be simulated
and evaluated. Trajectories for the obstacles must also be
predicted. The computational complexity thus depend on the
number of scenarios, the number of obstacles and the chosen
prediction horizon. The internal model and cost function are
described next.
A. Internal simulation model
A model of the ASV is necessary to generate the tra-
jectories to be evaluated by the cost function. The limited
computational resources of the target platform in our exper-
iments require a much simpler model than the 3-degrees of
freedom model used in [8]. In the experiments the ASV is
only expected to perform long-range, deliberate maneuvers,
this along with its relatively fast dynamics, makes the time
the ASV needs to change its course/speed negligible. We
therefore argue that a sufficiently accurate trajectory can be
achieved using only the kinematic equation
˙η = R(χ)υ, (1)
where η = (x, y, χ) denotes the position and course in the
earth-fixed frame, υ = (υ
x
, υ
y
, r) denotes the velocities in
surge, sway, and yaw, decomposed in the body-fixed frame,
and R(χ) is the rotation matrix from body-fixed to earth-
fixed frame. The prediction of the ASV’s trajectory is made
by inserting the desired values from scenario k into the
equation (1), ie. υ = (υ
x
= u
d
· u
k
m
, υ
y
= 0, r = 0)
and R(χ = χ
d
+ χ
k
m
). This model implies an instant turn
and it also assumes no drift due to wind and ocean current.
This is clearly a very simplified model but its applicability
for our experiments is confirmed by [15], where both the
kinematic equation (1) and the full 3-DOF model were tested,
producing only minor differences in the simulation results.
B. Cost function components
The cost function specifies the hazard evaluation criterion
used in the collision avoidance strategy. We adopt the main
components proposed in [8]. Specifically,
• a cost associated with collision with an obstacle,
• a cost for violating COLREGS,
• and a cost for the choice of maneuvering effort.
In addition, we introduce a new cost component:
• a COLREGS-transitional cost,
which penalizes control behaviors that abort a COLREGS-
compliant maneuver. The new cost makes it possible to
use decisions from a guidance strategy as reference to the
MPC COLAV scheme, without including the same guidance
strategy in the MPC’s internal model (cf. Fig. 1).
With the guidance strategy included in the MPC COLAV,
as in [8], a cost penalizing the change of control behavior
is sufficient to deter the abortion of COLREGS-compliant
maneuvers, provided that an adequate prediction horizon
has been chosen. Not including the guidance strategy in
the MPC COLAV results in a chattering behavior appearing
in overtaking and crossing scenarios, as can be seen in the
simulations of [15].
The problem arises because the modification to the guid-
ance decision is made under the assumption that the desired
guidance decision is constant on the prediction horizon.
Using a LOS guidance strategy as an example, i.e. χ
d
=
χ
LOS
. When a COLAV maneuver is initiated by a modifi-
cation to the course command, the ASV will deviate from
the desired path. At the next run of the MPC, χ
LOS
points
back towards the desired path. Setting χ
c
= χ
LOS
(χ
m
= 0)
will cause the ASV to cross the desired path and pass the
obstacle on the side opposite to what was initially predicted.
If this new path is collision free and COLREGS-compliant,
this scenario has the lowest cost and will be chosen. This
process repeats itself until another crossing would lead to
a violation of the requirement of keeping well clear (cf.
COLREGS, Rule 16).
Note that the complex decision process outlined above
may not be straightforward to address using a simple im-
plementation of hysteresis (see e.g. [2]) that is merely
dependent on the rate at which COLAV decisions switch.
The transitional cost systematically addresses this issue by
penalizing control behaviors that will cause the ASV to
pass an obstacle on a different side than what is predicted
with the current control behavior. Furthermore, by ensuring
that the cost of collision with an obstacle dominates the
corresponding transitional cost, a change in decision that is
necessary due to a high cost of collision will still be allowed.
C. Cost function details
The MPC COLAV objective is to evaluate the scenar-
ios k ∈ {1, 2, . . . , N
s
} for each obstacle vessel i ∈
{1, 2, . . . , N
o
} at time t
0
and select the control behavior that
minimizes the cost H
k
(t
0
). Specifically,
k
∗
(t
0
) = arg min
k
H
k
(t
0
), (2)
where
H
k
(t
0
) = max
i
max
t∈D(t
0
)
C
k
i
(t)R
k
i
(t) + κ
i
M
k
i
(t) + λ
i
T
k
i
(t)
+ f(u
k
m
, χ
k
m
)
The terms of the above cost function will now be defined.
For the following, the definitions are as proposed in [8]:
• the cost associated with collision with obstacle i at
time t in scenario k, i.e. C
k
i
(t), and the corresponding
collision risk factor, R
k
i
(t),
• the cost for violating COLREGS, κ
i
M
k
i
(t), were κ
i
is
a tuning parameter.
• and the cost of maneuvering effort associated with
scenario k, i.e. f(u
k
m
, χ
k
m
).
Each scenario is evaluated at discrete sample times along the
horizon T using the discretization interval T
s
, i.e. D(t
0
) =
{t
0
, t
0
+ T
s
, . . . , t
0
+ T }. The costs at a given time t
are calculated based on the position, speed and course of
the ASV and the obstacles at time t, obtained from the
simulations of their respective trajectories (cf. Section III-
A).
The COLREGS-transitional cost λ
i
T
k
i
(t) is formulated
using the binary indicator T
k
i
∈ {0, 1} and weight λ
i
, which
is a tuning parameter. The indicator value is specified using
T
k
i
(t) = O
k
i
(t) ∨ Q
k
i
(t) ∨ X
k
i
(t),
where the binary indicators O
k
i
(t) = 1 , Q
k
i
(t) = 1 and
X
k
i
(t) = 1 indicate the type of situation at time t, (the
ASV is overtaking a vessel, the ASV is being overtaken
and a crossing situation, respectively) and that the control
behavior of scenario k will at time t cause the vessels to
pass each other on the side opposite to what is predicted
with the current control behavior. The following paragraphs
define the indicator for each situation type.
Overtaking:
If the ASV is currently overtaking obstacle i, a control
behavior in scenario k at a future time t is associated with
a transitional cost if the predicted location of obstacle i at
time t is not on the same side of the ASV as observed at the
current time t
0
. That is, for t ∈ {t
0
+ T
s
, . . . , t
0
+ T },
O
k
i
(t) =
(
O
i
(t
0
) ∧ S
k
i
(t) if ¬S
i
(t
0
)
O
i
(t
0
) ∧ ¬S
k
i
(t) if S
i
(t
0
)
where S
i
(t
0
) = 1 indicates that obstacle i is currently on
the ASV’s starboard side, whereas S
k
i
(t) = 1 indicates
that obstacle i appears on the ASV’s starboard side at the
future time t in scenario k. The ASV is currently overtaking
obstacle i, i.e. O
i
(t
0
) = 1, if the obstacle is considered close,
ahead, and traveling at a lower speed. If the obstacle’s speed
|~υ
i
(t
0
)| is not close to zero, the following condition must also
hold:
~υ(t
0
) · ~υ
i
(t
0
) > cos(φ
ot
)|~υ(t
0
)||~υ
i
(t
0
)|,
FIG. 3. The Polar Circle 845 Sport vessel Telemetron.
where φ
ot
is a suitable angle according to COLREGS,
~υ(t
0
) is the current velocity of the ASV, and ~υ
i
(t
0
) is
the current velocity of obstacle i. In the situation where
the ASV is being overtaken by the obstacle, the binary
indicators defined above are appropriately adapted from the
perspective of the obstacle.
Crossing:
If obstacle i is currently crossing the path of the ASV
from starboard side, a COLREGS-compliant maneuver to
starboard should result in the obstacle appearing on port side
when the crossing situation is over. Therefore, an alternative
control behavior in scenario k at a future time t is associated
with a transitional cost if the obstacle is on starboard side
at time t and the control behavior suggests a change in
maneuver to port side. That is, for t = t
0
+ T
s
, . . . , t
0
+ T ,
X
k
i
(t) = X
i
(t
0
) ∧ S
i
(t
0
) ∧ S
k
i
(t) ∧ turn to port.
The ASV is said to be currently in a crossing situation with
obstacle i if the obstacle is ahead and
~υ(t
0
) · ~υ
i
(t
0
) < cos(φ
cr
)|~υ(t
0
)||~υ
i
(t
0
)| ∧ ¬O
i
(t
0
) ∧ ¬Q
i
(t
0
),
where φ
cr
is a suitable angle according to COLREGS.
IV. EXPERIMENTS
A. Test setup and objectives
Experiments were performed in the Trondheimsfjord to
test the performance of the proposed MPC COLAV scheme
in realistic situations where deliberate COLREGS-compliant
maneuvers are expected, more than 1 nautical mile away
from a dynamic obstacle.
The ASV used is Maritime Robotics’ Polar Circle 845
Sport vessel called Telemetron (Fig. 3). Telemetron is a
relatively small Rigid Bouyancy Boat (RBB) with a V-shaped
hull, making it both stable and highly maneuverable. We
used the Trondheim Port Authority’s Munkholmen II tugboat
as the obstacle vessel. Some technical specifications of the
vessels are provided in Table I.
The MPC COLAV scheme was implemented in C++
and installed on the embedded computer of the Telemetron
vessel. In addition, the interface between the COLAV system
and the existing systems was implemented according to
the proposed architecture shown in Fig. 1. We used the
TABLE I. Vessel specifications
Parameter Telemetron (ASV) Munkholmen II (obstacle)
Length [m] 8.0 14.0
Width [m] 3.0 6.0
Weight [kg] ∼ 2000 –
Power [hp] 225 520
Max. speed [kn] ∼ 34 ∼ 10
Automatic Identification System (AIS) as the sensor for
tracking the motion of the obstacle vessel. The accuracy of
AIS depends on the GPS system of the target vessel and is
not a tool for precision navigation. It is however sufficient
for our purposes.
Both the guidance system and the MPC COLAV extension
installed on the ASV were run at a rate of 0.5Hz. However,
since the AIS data received is updated at least once in 10 s,
a linear prediction is used until new information about the
obstacle is received. Moreover, the predicted position of the
obstacle vessel is considered close to that of the ASV when
it is 1000 m away, the safety distance used in computing
the collision risk factor R
k
i
(defined in [8]) was 200 m, and
the prediction horizon T was set to 400 s, with T
s
= 5 s
discretization interval.
The experiments were performed in weather conditions
that introduced significant disturbances into the dynamics
of the ASV. Although no measurements of the weather
condition were available during the experiments, updated
weather forecast close to the time of the experiments reflect
the conditions experienced: wind speeds up to 15 m/s, wave
height of about 1 m, and up to 0.5 m/s currents.
B. Results
The results from different collision avoidance scenarios
are shown in Fig. 5–8. The figures show snap shots of the
trajectories and the main variables that describe the behavior
of the ASV and the obstacle vessel. An aerial photo taken
during the experiments can be seen in Fig. 4. In Fig. 5 the
ASV is the give-way vessel, and it performs a COLREGS-
compliant maneuver in order to avoid collision. A clear
deviation from the desired course from the guidance system
can be seen in Fig. 5b. The next results represent cases
where both the ASV and the obstacle vessel are expected to
perform COLREGS-compliant maneuvers in order to avoid
collision. We examine the ASV’s behavior in the case where
the obstacle vessel ‘stays on’ (Fig. 6) and in cases where
the obstacle vessel either performs a COLREGS-compliant
maneuver (Fig. 7) or makes the situation worse through a
more dangerous maneuver (Fig. 8).
The snap shots in Fig. 8a reveal an important property of
the MPC COLAV method. That is, the capability to abort
a COLREGS-compliant maneuver when a drastic change in
situation is detected. Moreover, the COLAV scheme does not
prevent the ASV from making necessary reactive maneuvers
to its port side when in a close range situation as observed
in the second snap shot of Fig. 8a and the corresponding
course modification in Fig. 8b (between samples 220 and
FIG. 4. Head-on situation: Planned path of ASV ( ) and actual
trajectories of ASV ( ) and obstacle vessel ( ). This image
is a snapshot from the video accompanying the article.
(a) Trajectories of the ASV ( ) and the obstacle vessel ( )
(b) Desired value from guidance ( ), COLAV modification ( ), and
measured value ( )
(c) Obstacle course and speed values from AIS
FIG. 5. Obstacle vessel crossing from starboard.
280). Although the control behavior parameterization and
tuning prioritize course modification, the speed is reduced
in critical situations (cf. Fig. 8b).
Although the environmental disturbances are not explicitly
accounted for in the COLAV implementation, the results con-
firm the viability of the MPC COLAV method. An important
observation is that an acceptable level of robustness to distur-
bances is achieved due to the choice of parameterization of
alternative control behaviors (χ
m
, u
m
) and the cost function
components (see Section III) that ensure that the control
behavior remains unchanged unless an alternative behavior
provides a significant reduction in the collision hazard.
Considering the weight and design of the ASV, the weather
conditions also introduce significant uncertainty into the
guidance system. Although the obstacle vessel is much
heavier, it is less maneuverable at low speeds and therefore
(a) Trajectories of the ASV ( ) and the obstacle vessel ( )
(b) Desired value from guidance ( ), COLAV modification ( ), and
measured value ( )
(c) Obstacle course and speed values from AIS
FIG. 6. Obstacle vessel approaching head-on.The ASV performs a
COLREGS compliant avoidance maneuver, before returning to its
planned path.
(a) Trajectories of the ASV ( ) and the obstacle vessel ( )
(b) Desired value from guidance ( ), COLAV modification ( ), and
measured value ( )
(c) Obstacle course and speed values from AIS
FIG. 7. Obstacle vessel approaching head-on and turns to star-
board. In this situation both vessels act according to COLREGS.
