WO2023073164A1

WO2023073164A1 - Collision avoidance for marine vessels

Info

Publication number: WO2023073164A1
Application number: PCT/EP2022/080183
Authority: WO
Inventors: Emil Hjelseth THYRI
Original assignee: Norwegian University Of Science And Technology
Priority date: 2021-10-28
Filing date: 2022-10-28
Publication date: 2023-05-04
Also published as: GB202115538D0

Abstract

A collision avoidance system for a marine vessel comprises: a tracker unit configured to track target vessels within an area around the marine vessel by determining a position and velocity of the tracked target vessels; an encounter determination unit configured to determine an encounter type associated with each target vessel based on its position and velocity; a manoeuvrable space determination unit configured to determine the manoeuvrable space around each target vessel, wherein the manoeuvrable space depends on a distance between the target vessel and a static object; a target vessel domain determination unit configured to use the determined encounter type and manoeuvrable space around each target vessel to determine a domain of the target vessel within which the marine vessel cannot pass to avoid collision.

Description

COLLISION AVOIDANCE FOR MARINE VESSELS

TECHNICAL FIELD

The present disclosure concerns a collision avoidance system and method for marine vessels.

BACKGROUND

A majority of the world's large urban areas are located around waterways, where the water bore a majority of the transport for centuries until the construction of roads and railways. The recent development in technology enabling autonomous maritime operations, has again made maritime transportation in urban waterways a competitive option, and several cities have taken an interest in renewed utilization of their waterways. There already exist several initiatives on this with the goal of increasing efficiency and flexibility while reducing the strain on existing infrastructure both in cargo transport and passenger transport.

While the potential benefits are many, so are the challenges. Manoeuvring in urban waterways is no trivial task for human or machine, due to the long list of considerations that has to be taken into account. For example, some factors that should be considered are traffic from commercial vessels and leisure-craft, risk of grounding, global and local rules of manoeuvring and navigation, traffic regulations, and weather and sea current. Not only should these aspects be considered in the autonomous planning, guidance, navigation and vessel control system, but the information itself needs to be acquired through situational awareness systems consisting of sensors and algorithms for interpretation and comprehension to produce reliable information that can be applied by the planners.

A collision avoidance (COLAV) module may consider the Convention on the International Regulations for Preventing Collisions at Sea (COLREG) rules in vessel-to- vessel (V2V) encounters, and make adjustments to the nominal path or trajectory to comply with the relevant regulations. The COLREGs is the result of a convention developed over several decades to prevent collision between two or more vessels at sea, which in 1972 was revised and given its current name. The convention is continuously tested and revised to be unambiguous as new technology and maritime applications occur. The COLREGs apply to all vessels upon the high seas and all waters connected to the high seas and navigable by seagoing vessels.

Part B of the convention concerns steering and sailing. Rules 8, and 13 to 17 may be most relevant for COLAV and are listed below.

• Rule 8 Any action to avoid collision shall, if circumstances of the case admit, be positive, made in ample time, and with due regard to good seamanship.

• Rule 13 Any vessel overtaking another vessel shall keep out of the way of the vessel being overtaken. A vessel approaching another vessel from a direction of more than 22:5 deg abaft her beam is an overtaking vessel. Any subsequent alternation of bearing between the two vessels shall not relieve the overtaking vessel of the duty of keeping clear of the overtaken vessel until she is finally past and clear.

• Rule 14 When two power-driven vessels are meeting on reciprocal or nearly reciprocal courses so as to involve risk of collision each shall alter her course to starboard so that each shall pass on the port side of the other.

• Rule 15 When two power-driven vessels are crossing so as to involve risk of collision, the vessel which has the other on her own starboard side shall keep out of the way and shall, if the circumstances of the case admit, avoid crossing ahead of the other vessel.

• Rule 16 Every vessel which is directed to keep out of the way of another vessel shall, so far as possible, take early and substantial action to keep well clear.

• Rule 17 Where one of two vessels is to keep out of the way, the other shall keep her course and speed. The latter vessel may take action to prevent collision if it is apparent that the vessel required to keep out of the way is not taking appropriate action. Figure 1 provides illustrations of situations where the COLREG rules apply, as seen from the own ship (OS) 1 in a V2V encounter with a target ship (TS) 2.

For a substantial review of COLAV algorithms see Vagale et al., “Path planning and collision avoidance for autonomous surface vehicles I: A review”, Journal of Marine Science and Technology, 2021, pages 1-15, for a review of the field of path planning and COLAV for ASVs, Vagale et al., “Path planning and collision avoidance for autonomous surface vehicles II: A comparative study of algorithms”, Journal of Marine Science and Technology, 2021, pages 1-17, and for a comparative study of existing COLAV algorithms, and (Huang et al., “Ship collision avoidance methods: State-of-the- art”, Safety Science 121 , 2020, pages 451-473) for a structured breakdown of the techniques that go into maritime COLAV, and a discussion of state-of-the-art approaches to each sub-problem of maritime COLAV.

Benjamin et al., “A method for protocol-based collision avoidance between autonomous marine surface craft”, Journal of Field Robotics, 25(5), 2006, pages 333-346 provides a demonstration of an autonomous partial protocol compliant COLAV system tested on a marine platform. Inclusion of COLAV is encoded by a reduction in utility based on the estimated closest point of approach (CPA). COLREGs considerations for rules 14-16 as well as parts of Rule 8, are included by further reduction in utility for non-readily apparent manoeuvres, manoeuvres that pass in front of crossing vessels and starboard to starboard in head-on encounters.

Kuwata et al., “Safe maritime autonomous navigation with COLREGs, using velocity obstacles”, IEEE Journal of Oceanic Engineering, 39(1), 2014, pages 110-119 describes a version of a velocity obstacle (VO) algorithm and assigns a domain to the target ship that includes both the extension of the ownship (OS), which is the vessel that is controlled, and the target ship. COLREG rules 14-15 of are directly encoded into the velocity space by considering at what side of the target ship the own ship should pass.

Thyri, E. H., Basso, E. A., Breivik, M., Pettersen, K. Y., Skjetne, R., and Lekkas, A. M., “Reactive collision avoidance for ASVs based on control barrier functions”, In Proceedings of the 2020 4th IEEE Conference on Control Technology and Applications (CCTA), (2020), pages 380-387, Montreal, QC, Canada, describes a target ship domain for substantially complying with COLREG rules 13 to 15 in V2V encounters. The domain splits the horizontal plane in two, which constrains the own ship to pass the target ship on a particular side.

SUMMARY

While some of the current methods consider COLAV with some regard to COLREGs in open waters, they do not consider or are less effective in regards to COLAV in confined waters. In confined waters, the presence of static obstacles should be taken into account when considering manoeuvres also with respect to dynamic obstacles. For example, the acceptable distance at CPA, which varies with the available manoeuvrable space, should be taken into account in the domain design when providing target ship domains.

To at least partly solve this problem there is provided according to a first aspect of the present disclosure a collision avoidance system for a marine vessel (e.g. an autonomous ship) comprising a tracker unit configured to track target vessels within an area around the marine vessel by determining a position and velocity of the tracked target vessels (typically other ships). The tracker unit may receive various sensor input from e.g. LIDAR sensors in order to track other vessels within the field of view of the marine vessel (also referred to as the “own ship”). The system comprises an encounter determination unit configured to determine an encounter type associated with each target vessel based on its position and velocity. The encounter type is typically one of overtaking, head on, give way, stand on, and safe. The system further comprises a manoeuvrable space determination unit configured to determine the manoeuvrable space around each target vessel, wherein the manoeuvrable space depends on a distance between the target vessel and a static object, and a target vessel domain determination unit configured to use the determined encounter type and manoeuvrable space around each target vessel to determine a domain of the target vessel within which the marine vessel cannot pass to avoid collision.

The target vessel domain determination unit can be configured to determine the domain so that it splits at least the area around the marine vessel in two by a domain line, wherein the domain line is a straight line with the marine vessel located on one side of the line and the target vessel located inside the domain on the other side of the line. The domain line can then be updated in real time as the vessels approach each other until the encounter is “resolved”.

The shortest distance between the domain line and the target vessel is determined by the manoeuvrable space of the target vessel. By taking the manoeuvrable space into account, an improved target vessel domain can be determined that can allow the system to operate better in confined waters (e.g. in a canal, harbour or on a river).

The manoeuvrable space can be calculated to equal to a minimum distance from the target vessel to the static object minus a minimum distance to the static object at which no collision will occur and minus a minimum distance to the target vessel at which no collision will occur, wherein the target vessel domain determination unit is configured to determine the domain so that the shortest distance between the domain line and the target vessel is equal to the minimum distance to the target vessel at which no collision will occur, when the manoeuvrable space is less than or equal to zero, equal to the minimum distance to the target vessel at which no collision will occur plus the manoeuvrable space multiplied by an adjustment factor between 0 and 1 , when the manoeuvrable space is greater than zero and smaller than a threshold distance, and equal to the minimum distance to the target vessel at which no collision will occur plus the threshold distance multiplied by the adjustment factor, when the manoeuvrable space is greater than or equal to the threshold distance. The minimum distance where no collision occurs may typically depend on the physical shape and size of the target vessel and static object/obstacle.

The system may further comprise a split angle determination unit for determining a split angle from each target vessel, wherein a bearing of the marine vessel from the target vessel relative to the split angle determines a target side, and the target vessel domain determination unit is configured to set the domain so that the marine vessel passes the target vessel on the target side by avoiding the domain. While the encounter type alone could be used to determine the side on which to pass the marine vessel, this can be problematic in some circumstances. The split angle determination unit can allow for an improved manoeuvring. For example, the split angle may depend on a relative velocity vector between the marine vessel and the target vessel as well as on the encounter type. The split angle may be equal to an angle of the relative velocity vector plus a bias angle, wherein the bias angle depends on the encounter type. The split angle determination unit can be configured to determine a magnitude of the relative velocity vector, and then set the split angle to equal an angle of the relative velocity vector plus a bias angle, wherein the bias angle depends on the encounter type, when the magnitude is greater than or equal to a threshold speed, and equal to a weighted average of the angle of the relative velocity vector and a bearing of the marine vessel from the target vessel plus the bias angle when the magnitude is smaller than the speed threshold. By using the weighted average, large fluctuations due to noise at low relative speeds may be mitigated.

An angle of a normal vector to the domain pointing away from the target vessel may depend on the bearing of the marine vessel from the target vessel, the split angle, and a deflection angle which depends on the encounter type. The target vessel domain determination unit can be configured to determine the angle of the normal vector by calculating and adding a saturation angle to the split angle, wherein saturation is applied to the saturation angle when calculated so that the saturation angle falls within predefined limits. The saturation limits can help ensure that the marine vessel maintains a give-way manoeuvre until it past and clear, which can prevent the vessel from moving into the path of the target vessel at close range after an overtaking manoeuvre. The predefined limits typically depend on the encounter type.

The collision avoidance system can further comprise a constraint formulation unit configured to provide constraints that prevent domain violation. The constraints may be usable for determining a thrust vector for controlling the marine vessel to avoid the domain and thereby collision. The constraint formulation unit can be configured to provide control barrier functions based on a position and velocity of the domain relative to the marine vessel. The control barrier functions may be used in a quadratic optimisation problem in order to provide the constraints. Alternatively, the constraint formulation unit can be configured to eliminate a discrete set of manoeuvre options.

The collision avoidance system may further comprise a detection system for providing sensor output to the tracker unit, wherein the detection unit comprises one or more of a LIDAR sensor, a radar sensor, and a camera. The sensor can allow one or more target vessels within the field of view of the marine vessel from being tracked. The system can further comprise a vessel motion control system configured to control one or more thrusters of the marine vessel so as to avoid the domain of each target vessel. The vessel motion control system can use the constraints provided based on the target vessel domain to control the vessel and thereby avoid domain violation.

While the system and method described herein have referred to “target vessels” or “target ships”, the system may be further configured to track and avoid other dynamic objects (e.g. a floating log).

According to a second aspect of the present disclosure there is provided a marine vessel comprising a collision avoidance system according to the first aspect. For example, the collision avoidance system may be incorporated in an onboard computing device.

According to a third aspect of the present disclosure there is provided a method of collision avoidance for a marine vessel in an encounter with a target vessel. The method comprises determining a position and velocity of the target vessel, determining an encounter type associated with the target vessel based on its position and velocity, and determining a manoeuvrable space around the target vessel, wherein the manoeuvrable space depends on a distance between the target vessel and a static object. The method further comprises, based on the encounter type and manoeuvrable space around the target vessel, determining a domain of the target vessel within which the marine vessel cannot pass to avoid collision. The method may be implemented using the collision avoidance system of the first aspect.

The step of determining the domain may comprise splitting at least an area around the marine vessel in two by a domain line, wherein the domain line is a straight line with the marine vessel located on one side of the line and the target vessel located inside the domain on the other side of the line. The shortest distance between the domain line and the target vessel can be determined by the manoeuvrable space around the target vessel. The manoeuvrable space can be set equal to a minimum distance from the target vessel to the static object minus a minimum distance to the static object at which no collision will occur and minus a minimum distance to the target vessel at which no collision will occur, wherein the target vessel domain determination unit is configured to determine the domain so that the shortest distance between the domain line and the target vessel is equal to the minimum distance to the target vessel at which no collision will occur, when the manoeuvrable space is less than or equal to zero, equal to the minimum distance to the target vessel at which no collision will occur plus the manoeuvrable space multiplied by an adjustment factor between 0 and 1 , when the manoeuvrable space is greater than zero and smaller than a threshold distance, and equal to the minimum distance to the target vessel at which no collision will occur plus the threshold distance multiplied by the adjustment factor, when the manoeuvrable space is greater than or equal to the threshold distance.

The method may further comprise determining a split angle from the target vessel, wherein a bearing of the marine vessel from the target vessel relative to the split angle determines a target side, and wherein the domain is configured so that the marine vessel passes the target vessel on the target side by avoiding the domain. The split angle can depend on a relative velocity vector between the marine vessel and the target vessel and on the encounter type. For example, the split angle can be set equal to an angle of the relative velocity vector plus a bias angle, wherein the bias angle depends on the encounter type.

The method may comprise determining a magnitude of the relative velocity vector, and setting the split angle equal to an angle of the relative velocity vector plus a bias angle, wherein the bias angle depends on the encounter type, when the magnitude is greater than or equal to a threshold speed, and equal to a weighted average of the angle of the relative velocity vector and a bearing of the marine vessel from the target vessel plus the bias angle when the magnitude is smaller than the speed threshold.

An angle of a normal vector to the domain pointing away from the target vessel can depend on the bearing of the marine vessel from the target vessel, the split angle, and a deflection angle which depends on the encounter type. The method may comprise determining the angle of the normal vector by calculating and adding a saturation angle to the split angle, wherein saturation is applied to the saturation angle when calculated so that the saturation angle falls within predefined limits. The predefined limits typically depend on the encounter type.

The method may further comprise providing constraints that prevent domain violation. The constraints can be used to eliminate manoeuvre options that would cause the marine vessel to enter the target vessel domain. The step of providing constraints may comprise providing control barrier functions based on a position and velocity of the domain relative to the marine vessel. A thrust vector of the marine vessel for avoiding the domain may be determined based on the control barrier functions. The method may comprise eliminating a discrete set of manoeuvre options that do not fall within the constraints.

The method may further comprise controlling the marine vessel to avoid the domain and thereby avoid collision with the target vessel.

According to a fourth aspect of the present disclosure there is provided a computing device comprising one or more processors and one or more memories comprising computer readable instructions. The one or more processors are configured to read the computer readable instructions to cause the computing device to perform the method according to the third aspect.

According to a fifth aspect of the present disclosure there is provided a computer program that, when read by a computer, causes the computer to perform the method of the third aspect.

According to a sixth aspect of the present disclosure there is provided a non-transitory computer readable storage medium comprising computer readable instructions that, when read by a computer, cause the computer to perform the method of the third aspect.

BRIEF DESCRIPTION OF DRAWINGS

Figure 1 shows a schematic diagram of different encounter types and related COLREGs rules;

Figure 2 shows a target vessel and associated domain;

Figure 3 shows a collision avoidance system according to an embodiment;

Figure 4 shows a collision avoidance system according to another embodiment;

Figure 5 shows a collision avoidance system according to a further embodiment; Figure 6 shows a geometric representation of an algorithm for determining an encounter type;

Figure 7 shows the encounter type determined for a number of target vessels relative to the own ship;

Figure 8 shows the manoeuvrable space around a target vessel in confined waters;

Figure 9 shows the split angle from a target vessel relative to two instances of the own ship;

Figure 10 shows the split angle from a target vessel relative to two instances of the own ship;

Figure 11 shows the target ship domain of a target vessel relative to two instances of the own ship;

Figure 12 shows a vector field of normal vectors to the target vessel domain for different encounter types;

Figure 13 shows a schematic diagram of a collision avoidance system according to an embodiment; and

Figure 14 shows a flow diagram of a method of collision avoidance according to an embodiment.

DETAILED DESCRIPTION

Figure 2 shows a schematic top view diagram of a target ship 2 at prs with a domain 3 provided according to an embodiment. The domain 3 can be defined by three variables: The position (P_TS) of the target ship 2, the angle (a) of the normal vector to the domain pointing away from the target ship, and the shortest distance (/) from the target ship 2 to the domain 3. The angle (a) and the distance (/) are functions of the states of the two involved vessels, the static obstacles (not shown), and encounterspecific parameters (e.g. head-on, overtaking etc.). The domain 3 splits the area around the vessels in two by a domain line 4. The domain line 4 is a straight line with the own ship (not shown) located on one side of the line 4 and the target ship 2 located inside the domain 3 on the other side of the line 4. The collision avoidance system of the own ship determines the domain 3 of the target ship 2 and facilitates controlling of the own ship to avoid the domain 3, thereby inherently complying with the COLREG rules in the V2V encounter. Figure 3 shows a collision avoidance system 5 according to an embodiment. Due to the task complexity of autonomous maritime operations, and in particular the collision avoidance (COLAV) objective, autonomous guidance navigation and control (GNC) systems are often composed of multiple layers of planners in a hybrid structure. In such structures, the effectiveness of several planners can be exploited by distributing the planning responsibility to match each planner's capacity. Figure 3 illustrates a threelayered structure with several examples of situational awareness modules 6 that one or more of the planners might apply.

The high-level COLAV module 7 can perform long-term or global path or trajectory planning with respect to e.g. map data from electronic nautical charts (ENC), weather and ocean current data, departure and arrival time, and traffic regulations such as allocated fairways or traffic separation schemes. The high-level module 7 may run once at the start of a transit or periodically with a relatively long period between each iteration.

The mid-level COLAV module 8 considers COLREGs in vessel-to-vessel (V2V) encounters, and makes adjustments to the nominal path or trajectory from the high- level module 7 to comply with the relevant regulations. The planning can be performed based on target data from an AIS and/or a target tracking system based on exteroceptive sensors. The planning horizon of the mid-level COLAV module 8 can be from several seconds to several minutes, with a planning period suitable for the rate of change of the relevant features in the environment.

The low-level COLAV module 9 should have a short planning horizon relative to the dynamics of the operational environment, and for several applications, it can be purely reactive, where it reacts to current states without deliberation. The task of the low-level planner is to resolve immediate situations in a safe manner. For autonomous surface vessels (ASVs), that is mainly avoiding collision with all obstacles, both static and dynamic, while adhering to the relevant protocol.

The target ship domain determination unit would typically be applied in the mid-level COLAV module 8, and low-level COLAV module 9 to facilitate adherence to the COLREGs manoeuvring regulations, and improve compatibility between the long-term and short-term COLAV.

Figure 4 shows another collision avoidance system 5 comprising a tracking unit 10 for tracking target vessels in e.g. the field of view of a marine vessel (the own ship) and a target domain and constraint formulation unit 11 configured to provide constraints for avoiding the domain of the target vessel. The system further comprises a PID controller 12 as part of a vessel motion control system. The PID controller provides a target thrust/force vector (τ_d) based on the nominal (high-level) path of the marine vessel. The target thrust vector (τ_d) and constraints (Aτ ≤ b) are provided to a QP solver 13, which generates a thrust/force vector (τ), which is as close to the target (τ_d) as possible while not violating the constraints. The thrust vector (τ) is provided to a thrust allocation unit 14, which in turn controls the thrust drivers 15.

Figure 5 illustrates a collision avoidance system 5, which may be the collision avoidance system of Figure 4 or a different embodiment. The system 5 comprises an encounter determination unit 16, a manoeuvrable space determination unit 17, a split angle determination unit 18, and a target ship domain determination unit 19. The system further comprises a tracking unit 10, for providing the position and velocity of any target vessels. The system 5 also comprises a static obstacle domain determination unit 20, for determining the domain of static objects, which can be used to provide additional constraints in order to avoid collisions with static objects. The system 5 further comprises a constraint formulation unit 21 configured to provide CBFs for each determined target ship domain in order to provide constraints. The constraints are usable by the vessel motion control system 22 for controlling the own ship 1 so as to avoid any target ship domains (while following as close as possible to a target path).

Figure 6 illustrates an example classification algorithm implemented by an encounter determination unit. The position of the own ship is at the centre of the middle circle 23. The encounter type is determined by the relative bearing between the own ship and target ship. In situation sectors with two encounter classifications, the outer classification is chosen when the involved vessels have a closing range, while the inner one is chosen for increasing range. The different encounter types are listed in Table 1. Table 1

Figure 7 illustrates classification examples for an arbitrary set of target ships in the outer circles, and a central own ship. Classification is made by selecting the encounter type of the sector that the target ship course vector lies within.

The encounter type may be determined as follow: In a first step, the relative bearing sector (RBS) is determined based on φ and the sector angles [-θ₂, -θ₁, θ₂, θ₂], wherein φ = atan2((E_TS - E), (N_TS - N)) - X, (1) wherein χ is the course of the own ship, and N and E, and N_TS and E_TS are the north and east position of the own ship and target ship, respectively. The RBS is chosen based on which sector φ lies within. The angles (θ) are the sector angles as illustrated in Figure 6. This will put the target ship in one of the four RBS: R1 , R2, R3 or R4.

The course of the target ship relative to the own ship is calculated as:

X_rel = X_TS - X. (2)

In a second step, the situation sector is determined by χ_rel, with a set of rotated sector angles [-θ'₂, -θ'₁, θ'₁, θ'₂], where θ'₁ = θ₁ - φ_TS and θ'₂ = θ₂ - φ_TS, and where φ_TS = atan2((E_TS - E), (N_TS - N)). (3) Figure 8 is a schematic diagram of a target ship 2 close to a static obstacle 24 being the coast line or canal side in this example. The Figure illustrates how the manoeuvrable space around the target ship can be determined, taking the static obstacle into account. The manoeuvrable space can later be used when determining the target ship domain.

Close quarters, risk of collision, ample time, and close proximity are all relative terms. Yet they are applied in the COLREGs formulation of how and when vessels in sight of one another are obliged to manoeuvre. A quantitative interpretation of these terms may depend on the surroundings. For two vessels moving in confined waters, e.g. in a harbour, canal or an area where the vessel draft is restricting manoeuvrability, passing at 30, 20 or even 10 meters can be considered acceptable, while doing this at open waters would be considered misconduct, and in violation of the COLREGs. For vessels moving in confined waters, the accepted distance at closest point of approach (DCPA) is therefore highly dependent on the available manoeuvrable space, and it is important that this should be considered when determining the shortest allowable DCPA in an encounter.

The manoeuvrable space around a target ship is denoted r_free, and is usable for determining the size of the target ship domain. According to an embodiment r_free for a V2V encounter is calculated by first determining a pass sector being the sector around the target ship where the own ship should pass. The pass sector is given by the encounter classification. The shortest distance from the target ship to any static obstacle in the pass sector is determined. The pass sector can be denoted by two angles,

and , where the pass sector is the sector swiped by a line

starting at p_TS and swiping the sector , Figure 8 shows the pass sector

shaded in for a target ship 2 located at p_TS. The smallest distance to the static obstacle 24 within the pass sector, r_{mi n} is indicated by the dashed line at right angles to the obstacle 24. The free range is given by r_free = r_min - r_dyn - r_stat, (4) wherein r_dyn = ½ (l_{O S} + l_TS) + δ_dyn , (5) is the minimum DCPA to a dynamic obstacle at which no collision will occur, and r_stat = ½ l_{O S} + δ_stat (6) is the minimum distance to a static obstacle at which no collision will occur, /_OS and I_TS are the lengths of the own ship and target ship, respectively. The distances δ_dyn and δ_stat are additional tolerances to dynamic and static obstacles, respectively. The tolerance can be used to account for uncertainties in map data, target tracking and navigation. To calculate r_free a priori knowledge of the area in the form of map data can be used. Map data is typically available for ASV operations, in which it is also used for long-term path or trajectory planning. Such data is often readily available from online map services.

In a V2V encounter where risk of collision exist, at least one vessel is obliged by the COLREGs to take action to avoid collision. The manoeuvring guidelines are in large focused on what is the preferred side of the own ship the target ship should be when passing. For most encounters, if the circumstances admit, it is the port side, except for overtaking encounters, where the manoeuvring choice is dependent on other factors. At the same time, some close quarters encounters can be resolved by passing with the target ship on the starboard side with little or no manoeuvring effort, while passing with the target ship on the port side would require extensive manoeuvring effort, either due to the encounter geometry or the velocity of the vessels. Hence, the COLAV system described herein may comprise a split angle determination unit, which is configured to determine on which side to pass the target ship. The split angle determination unit can determine which side to pass the target ship considering one or more of the encounter classification, the geometry of the encounter, and the relative velocity vector (U_rel) between the two vessels. The distinction is made based on the bearing of the own ship from the target ship relative to a port-starboard split angle.

Figure 9 illustrates determination of the split angle (α_s) according to an embodiment. The split angle, which is used to determine whether to pass the target ship 2 on the port side or starboard side, can be calculated as:

wherein is the angle of the relative velocity vector 25,

with and

as the north and east components of the relative velocity vector U_rel respectively, and is a bias angle, that creates a bias towards passing on the

COLREGs compliant side. The bias angle can be a classification specific offset that will facilitate protocol compliant manoeuvres.

Figure 10 illustrates calculating of the split angle for two positions (p and p') of the own ship 1 relative to the target ship 2 (the relative velocity 25 being the same in each case). The angle to the relative bearing from the target ship 2 to the own ship 1 is φ_TS and φ'_TS for the two positions of the own ship 1 respectively. The target ship domain determination unit can be configured to determine the domain so that the own ship 1 passes with the target ship 2 on its starboard side when φ_TS > α_s and to determine the domain so that the own ship 1 passes with the target ship 2 on its port side when φ_TS ≤ α_s.

For low relative velocities, the angle

to the relative velocity vector is prone to noise, and for zero relative velocity the angle is undefined. In order to reliably determine the split angle for low velocities a weighted average between the angle to the relative velocity vector and the angle (φ_TS) to the relative bearing from

the target ship 2 to the own ship 1 can be used. For example, the split angle determination unit can be configured to apply the weighted average when the magnitude of the relative velocity vector (U_rel) is below a threshold value (U_lim). Hence, in this embodiment the split angle can be defined as

The split angle can also reduce the chance of oscillating behaviour that can result from noise or uncertainty in the position and velocity estimates for the own ship 1 and target ship 2 when the angle (φ_TS) to the relative bearing is close to the split angle (α_s), since the absolute difference between the angles, |α_s - φ_TS|, will increase once a manoeuvre is initiated due to the resulting changes in the relative velocity vector, effectively increasing the commitment to the manoeuvre. The same is true for manoeuvres by the target ship 2.

The target ship domain can be determined based on the encounter type, the available manoeuvrable space, and the side on which the target ship should be when the own ship passes.

As shown in Figure 2, the domain is defined by a straight line dividing the North-East (or x-y) plane into two halves. The half plane containing the target ship is the target ship domain. The domain can be defined by the position of the target ship, and the two variables:

• I ≥ r_dyn being the shortest distance from the target ship to the domain line; and

• α ∈ [π, -π] being the angle to the normal vector to the domain pointing away from the target ship.

The target ship domain can be considered as an unsafe set, denoted for target

ship i, where i ∈ [1, N_TS] and N_TS is the number of tracked target ships. The safe set regarding all dynamic obstacles can be defined as the complement set of the sum of the unsafe sets. That is

with

The distance I to the domain line is determined based on the manoeuvrable space around the target ship. In an embodiment, I is given by

wherein r_free is the manoeuvrable space, k_l ∈ [0,1] is a design parameter that splits the free manoeuvrable space between the target ship and a potential static obstacle, and is a threshold distance beyond which static obstacles may be neglected (e.g.

at open sea).

The angle (a) of the normal vector to the domain can be defined as α := α_s + α_D , (13) where

Here is the deflection angle, which is used to alter the deflection of the

own ship on the target ship domain to avoid stagnation when the own ship approaches the target ship at near right angle, and to facilitate passing the target ship with a geometry that complies with the relevant rules. α_D may be saturated to be within classification specific limits, i.e.

. The saturation limits on α_D are applied to ensure that the own ship maintains a give- way manoeuvre until it is finally past and clear, in particular to prevent the own ship from moving into the path of the target ship at close range after an overtaking manoeuvre. Additionally, the use of a high deflection angle, in combination with effective saturation limits, can provide extended effective target ship domain in desired directions.

Two points on the target ship domain can be defined as the point (P_D) on the domain closest to the target ship and the point (P_B) on the domain closest to the own ship,

and

respectively, where

is the tangent unit vector to the target ship domain.

Figure 11 illustrates examples of the target ship domain for two instances of the own ship 1 , denoted OS and OS', one located on each side of the split angle (α_s). The Figure shows the parameters for the target ship domain for a target ship 2 located at P_TS with course X_TS, and the two instances of the own ship 1, located at p and p’ on either side of the port-starboard split line defined by the split angle (α_s), with bearing from the target ship φ_TS and φ'_TS respectively. The target ship domain is given by the dashed line 4 passing through P_D and P’_D at a distance I > r_dyn from the center of the target ship. All angles are positive in the clockwise direction.

Figure 12 shows a grid with normal vectors to the target ship domain for an own ship located at the base of each normal vector. The own ship has its heading aligned with its course at χ = 0 and speed of 1 m/s. The line from the centre of the target ship indicates the port-starboard split angle and the contour around the target ship indicates the shortest allowable range to the target ship at any approach angle. Due to the saturation of α_D, the target ship domain extends aft of the target ship in overtaking encounters, in front of the target ship in head-on encounters and to the front and either side of the target ship in give-way crossing encounters, without ineffective extensions of the target ship domain that only contribute to restricting the manoeuvrable space. The effect of the saturation of α_D is also apparent from the unidirectional vector-field in the top right and top left parts of the overtaking, head-on and give-way vector fields. Confined waters operations do not only require consideration of the available manoeuvrable space when moving in vicinity to other vessels, but also active COLAV regarding static obstacles. Unexpected manoeuvres by a target ship during a close quarter passing can move the target ship domain closer to the own ship, and hence push the own ship towards static obstacles. Additionally, the position and size of the static obstacles in the map might differ from the real obstacles due to quasi-static features such as docked or stationary vessels, or floating harbours that change position as a result of periodic water movements or other external forces.

Embodiments described herein may handle static obstacles in a similar way to dynamic obstacles, where a domain is assigned to each relevant static obstacle. To assign the domains for static obstacles, a general approach that is applicable for most map data is used. It may also be easily unifiable with real-time lidar data, which can be applied in to mitigate the effects of imprecise map data as well as estimation errors in the vessel's navigation system.

First, the area around the own ship is split into n_sect equally sized sectors, with the own ship as the centre. Subsequently, the closest point on any of the map-entries and the closest point for a lidar measurement within each sector is found. The point closest to the vessel is considered the relevant static obstacle in that sector. For sector i, this point is denoted .

A domain for each point is determined. The domain has the same form as for

dynamic obstacles, with a straight line that divides the North-East plane into two halves. When determining the orientation, and hence a normal vector to the domain line, a method is applied that calculates the tangent vector to the domain line for each point so that it is tangent to an ellipse around the own ship, where the major axis of the ellipse is aligned with the desired own ship course from the guidance system. The safe set regarding static obstacles is defined as the complement set of the unsafe set, that is

with

where is the unsafe set to the point . The set Cstat is by design a convex

set in .

The safe operating set of the own ship can be defined as

where the vessel is safe from collision and manoeuvring in compliance with the relevant COLREG rules when inside this set. To ensure forward invariance of C embodiments may use control barrier functions (CBFs). CBFs can be formulated for both the dynamic and static obstacles such that the combined set of CBFs ensure that p stays in C by restricting control inputs. To formulate the CBFs the 3DOF vessel model described in Fossen, T.I., “Handbook of Marine Craft Hydrodynamics and Motion Control” John Wiley & Sons, (2011) can be applied, wherein

where M is the inertia matrix including hydrodynamic added mass, C(v) is the Coriolis centripetal matrix, D(v) is the damping matrix, are the generalised forces

produced by the actuators, and

The CBFs for dynamic obstacles are formulated with respect to each target ship domain at the current time. In the formulation, the dynamics of the domain do not have to be considered. The domain can therefore be considered as a straight line moving in with constant velocity and a constant rate of rotation about the point P_TS. Hence, the effect on the domain dynamics from accelerations of the own ship can be omitted. The CBF can be defined with respect to the point (p_B) on the domain closest to the target ship as

where

and

is the unit vector of . The first and second term in equation 24 are the Euclidean

distance to and the relative velocity towards the target ship domain respectively, where the parameter C_dyn > 0 mitigates between the distance to the domain and the velocity at which the own ship is allowed to approach the domain. The parameter C_dyn serves as a direct method of setting a threshold for how early the own ship should start to manoeuvre in an encounter. The parameter C_dyn can also reflect the physical aspect of the vessel.

To apply the CBF as an inequality constraint in a quadratic program (QP) the time derivative of equation 24 is taken:

with , where is the north-east velocity of the own ship, and

Further,

where

and

is the derivative of equation 15. In the CBF formulation it is assumed that the target ship keeps a constant course and speed, and hence

with

where denotes the relative velocity between the two vessels, and

From equation 27 the double time derivative of is taken. The acceleration of the point

p_B is set to , since the acceleration of the target ship domain is omitted. This can

improve behaviour close to the domain. By setting the resulting gradient of the

CBF is rotated in the direction of the deflection angle, and hence facilitate the own ship to traverse in that direction. This gives , where

with

and

By inserting equation 35 into equation 27 the CBF derivative takes the form

with

and

which is affine in the control input τ. From equation 38 an inequality constraint can be formulated as

which can be applied as an inequality constraint in an optimisation problem of the form

A_τ ≤ b, with

The constraints are usable by the vessel motion control system to control the vessel so as to avoid the target ship domain(s). CBFs for any static obstacles can be similarly formulated. CBFs provide one useful way of converting the target ship domain to usable constraints on the vessel motion control system. However, other methods may also be used with the same target ship domain and with the same technical benefits.

There are two types of methods for providing constraints from the target ship domain.

One type of method is based on continuous optimization, as described above using CBFs, where an optimization problem finds an optimal manoeuvre (e.g. a generalised force), from a continuous set of generalised forces. While CBFs can provide a good set of theoretical safety properties, in an alternative embodiment a linear constraint that requires the distance to the domain to be positive can be formulated instead.

The other type of method is discrete, such as the velocity obstacle (VO) and the dynamic window (DW) methods. In such methods, a discrete set of manoeuvres is considered, for example a set of speeds and yaw rates that can be applied for a given duration. Each potential manoeuvre from the set of manoeuvres is checked if it will lead to conflict/collision with target-ship domain, and any manoeuvre that causes conflict/collision is removed from the set. From the conflict/collision free manoeuvres left in the set, an optimal manoeuvre is chosen based on some cost function (for example the manoeuvre that is closest to some desired transit velocity).

In both types of methods, the proposed target-ship domain is used to "eliminate" the manoeuvres that lead to domain violation. Then, an objective function can be applied to find the preferred manoeuvre from the remaining options.

In Table 2 some examples of encounter specific parameters are provided.

Table 2

Figure 13 shows a schematic diagram of an anti-collision system 5 for a marine vessel. The system 5 comprises a tracker unit 10 configured to track target vessels within an area around the marine vessel, an encounter determination unit 16 configured to determine an encounter type associated with each target vessel, and a manoeuvrable space determination unit 17 configured to determine the manoeuvrable space around each target vessel. The system 5 further comprises a target vessel domain determination unit 19 configured to use the determined encounter type and manoeuvrable space around each target vessel to determine a domain of the target vessel within which the marine vessel cannot pass to avoid collision. Each of the units of the anti-collision system 5 may be implemented by one or more processors of a computing device.

Figure 14 is a flow diagram illustrating the steps of a method according to an embodiment. The method comprises determining a position and velocity of the target vessel (step S1), determining an encounter type associated with the target vessel based on its position and velocity (step S2), determining the manoeuvrable space around the target vessel (step S3), and based on the encounter type and manoeuvrable space around the target vessel, determining a domain of the target vessel within which the marine vessel cannot pass to avoid collision (step S4). The method further comprises using the target vessel domain to provide constraints (step S5), and using the constraints to control the vessel to avoid domain violation and thereby collision with the target vessel (step S6).

Although specific embodiments have been described above, the claims are not limited to those embodiments. Each feature disclosed may be incorporated in any of the described embodiments, alone or in an appropriate combination with other features disclosed herein.

Claims

CLAIMS:

1. A collision avoidance system for a marine vessel comprising: a tracker unit configured to track target vessels within an area around the marine vessel by determining a position and velocity of the tracked target vessels; an encounter determination unit configured to determine an encounter type associated with each target vessel based on its position and velocity; a manoeuvrable space determination unit configured to determine the manoeuvrable space around each target vessel, wherein the manoeuvrable space depends on a distance between the target vessel and a static object; a target vessel domain determination unit configured to use the determined encounter type and manoeuvrable space around each target vessel to determine a domain of the target vessel within which the marine vessel cannot pass to avoid collision.

2. A collision avoidance system according to claim 1, wherein target vessel domain determination unit is configured to determine the domain so that it splits at least the area around the marine vessel in two by a domain line, wherein the domain line is a straight line with the marine vessel located on one side of the line and the target vessel located inside the domain on the other side of the line.

3. A collision avoidance system according to claim 2, wherein the shortest distance between the domain line and the target vessel is determined by the manoeuvrable space of the target vessel.

4. A collision avoidance system according to claim 1 , 2, or 3, wherein the manoeuvrable space is equal to a minimum distance from the target vessel to the static object minus a minimum distance to the static object at which no collision will occur and minus a minimum distance to the target vessel at which no collision will occur, wherein the target vessel domain determination unit is configured to determine the domain so that the shortest distance between the domain line and the target vessel is equal to the minimum distance to the target vessel at which no collision will occur, when the manoeuvrable space is less than or equal to zero, equal to the minimum distance to the target vessel at which no collision will occur plus the manoeuvrable space multiplied by an adjustment factor between 0 and 1 , when the manoeuvrable space is greater than zero and smaller than a threshold distance, and equal to the minimum distance to the target vessel at which no collision will occur plus the threshold distance multiplied by the adjustment factor, when the manoeuvrable space is greater than or equal to the threshold distance.

5. A collision avoidance system according to any one of the preceding claims, further comprising a split angle determination unit for determining a split angle from each target vessel, wherein a bearing of the marine vessel from the target vessel relative to the split angle determines a target side, and the target vessel domain determination unit is configured to set the domain so that the marine vessel passes the target vessel on the target side by avoiding the domain.

6. A collision avoidance system according to claim 5, wherein the split angle depends on a relative velocity vector between the marine vessel and the target vessel and on the encounter type.

7. A collision avoidance system according to claim 6, wherein the split angle is equal to an angle of the relative velocity vector plus a bias angle, wherein the bias angle depends on the encounter type.

8. A collision avoidance system according to claim 6, wherein the split angle determination unit is configured to determine a magnitude of the relative velocity vector, and then set the split angle to equal an angle of the relative velocity vector plus a bias angle, wherein the bias angle depends on the encounter type, when the magnitude is greater than or equal to a threshold speed, and equal to a weighted average of the angle of the relative velocity vector and a bearing of the marine vessel from the target vessel plus the bias angle when the magnitude is smaller than the speed threshold.

9. A collision avoidance system according to any one of claims 5 to 8, wherein an angle of a normal vector to the domain pointing away from the target vessel depends on the bearing of the marine vessel from the target vessel, the split angle, and a deflection angle which depends on the encounter type.

10. A collision avoidance system according to claim 9, wherein target vessel domain determination unit is configured to determine the angle of the normal vector by calculating and adding a saturation angle to the split angle, wherein saturation is applied to the saturation angle when calculated so that the saturation angle falls within predefined limits.

11. A collision avoidance system according to claim 10, wherein the predefined limits depend on the encounter type.

12. A collision avoidance system according to any one of the preceding claims, further comprising a constraint formulation unit configured to provide constraints that prevent domain violation.

13. A collision avoidance system according to claim 12, wherein the constraint formulation unit is configured to provide control barrier functions based on a position and velocity of the domain relative to the marine vessel.

14. A collision avoidance system according to claim 12, wherein the constraint formulation unit is configured to eliminate a discrete set of manoeuvre options.

15. A collision avoidance system according to any one of the preceding claims, wherein the encounter type is one of overtaking, head on, give way, stand on, and safe.

16. A collision avoidance system according to any one of the preceding claims, further comprising a detection system for providing sensor output to the tracker unit, wherein the detection unit comprises one or more of a LIDAR sensor, a radar sensor, and a camera.

17. A collision avoidance system according to any one of the preceding claims, further comprising a vessel motion control system configured to control one or more thrusters of the marine vessel so as to avoid the domain of each target vessel.

18. A marine vessel comprising a collision avoidance system according to any one of the preceding claims.

19. A method of collision avoidance for a marine vessel in an encounter with a target vessel, the method comprising: determining a position and velocity of the target vessel; determining an encounter type associated with the target vessel based on its position and velocity; determining a manoeuvrable space around the target vessel, wherein the manoeuvrable space depends on a distance between the target vessel and a static object; based on the encounter type and manoeuvrable space around the target vessel, determining a domain of the target vessel within which the marine vessel cannot pass to avoid collision.

20. A method according to claim 19, wherein the step of determining the domain comprises splitting at least an area around the marine vessel in two by a domain line, wherein the domain line is a straight line with the marine vessel located on one side of the line and the target vessel located inside the domain on the other side of the line.

21. A method according to claim 20, wherein the shortest distance between the domain line and the target vessel is determined by the manoeuvrable space around the target vessel.

22. A method according to claim 19, 20 or 21, wherein the manoeuvrable space is equal to a minimum distance from the target vessel to the static object minus a minimum distance to the static object at which no collision will occur and minus a minimum distance to the target vessel at which no collision will occur, wherein the target vessel domain determination unit is configured to determine the domain so that the shortest distance between the domain line and the target vessel is equal to the minimum distance to the target vessel at which no collision will occur, when the manoeuvrable space is less than or equal to zero, equal to the minimum distance to the target vessel at which no collision will occur plus the manoeuvrable space multiplied by an adjustment factor between 0 and 1, when the manoeuvrable space is greater than zero and smaller than a threshold distance, and equal to the minimum distance to the target vessel at which no collision will occur plus the threshold distance multiplied by the adjustment factor, when the manoeuvrable space is greater than or equal to the threshold distance.

23. A method according to any one of claims 19 to 22, further comprising determining a split angle from the target vessel, wherein a bearing of the marine vessel from the target vessel relative to the split angle determines a target side, and wherein the domain is configured so that the marine vessel passes the target vessel on the target side by avoiding the domain.

24. A method according to claim 23, wherein the split angle depends on a relative velocity vector between the marine vessel and the target vessel and on the encounter type.

25. A method according to claim 24, wherein the split angle is equal to an angle of the relative velocity vector plus a bias angle, wherein the bias angle depends on the encounter type.

26. A method according to claim 24, further comprising determining a magnitude of the relative velocity vector, and setting the split angle equal to an angle of the relative velocity vector plus a bias angle, wherein the bias angle depends on the encounter type, when the magnitude is greater than or equal to a threshold speed, and equal to a weighted average of the angle of the relative velocity vector and a bearing of the marine vessel from the target vessel plus the bias angle, when the magnitude is smaller than the speed threshold.

27. A method according to any one of claims 23 to 26, wherein an angle of a normal vector to the domain pointing away from the target vessel depends on the bearing of the marine vessel from the target vessel, the split angle, and a deflection angle which depends on the encounter type.

28. A method according to claim 27, further comprising determining the angle of the normal vector by calculating and adding a saturation angle to the split angle, wherein saturation is applied to the saturation angle when calculated so that the saturation angle falls within predefined limits.

29. A method according to claim 28, wherein the predefined limits depend on the encounter type.

30. A method according to any one of claims 19 to 29, further comprising providing constraints that prevent domain violation.

31. A method according to claim 30, wherein the step of providing constraints comprises providing control barrier functions based on a position and velocity of the domain relative to the marine vessel.

32. A method according to claim 31 , based on the control barrier functions, determining a thrust vector of the marine vessel for avoiding the domain.

33. A method according to claim 30, further comprising eliminating a discrete set of manoeuvre options that do not fall within the constraints.

34. A method according to any one of claims 19 to 33, further comprising controlling the marine vessel to avoid the domain and thereby avoid collision with the target vessel.

35. A computing device comprising: one or more processors; one or more memories comprising computer readable instructions; wherein the one or more processors are configured to read the computer readable instructions to cause the computing device to perform the method of any one of claims 19 to 34.

36. A computer program that, when read by a computer, causes the computer to perform the method of any one of claims 19 to 34.

37. A non-transitory computer readable storage medium comprising computer readable instructions that, when read by a computer, cause the computer to perform the method of any one of claims 19 to 34.