Extended Grid Based Collision AvoidanceConsidering COLREGs for Vessels

Michael Blaich ∗ Michael Rosenfelder ∗ Michael Schuster ∗

Oliver Bittel ∗ Johannes Reuter ∗

∗ University of Applied Sciences Konstanz, Konstanz, 78462 Germany(e-mail: mblaich@htwg-konstanz.de).

Abstract: In this work a grid based collision avoidance algorithm which considers the physicalconstrains of a vessel is presented. For this purpose a new geometry neighbourhood is introducedand explained in detail. The collision avoidance algorithm pays attention to the COLREGs andprovides a collision-free path. To find this path, Lee’s algorithm is used.

Keywords: Collision avoidance, Ship navigation, Path planning, Lee’s algorithm, COLREGs,Optimal route, Raster grid

1. INTRODUCTION

In the last decades, vessel traffic and average cursing speedhave increased, thus the collision risk for vessels is rising.Many Collision Avoidance (CA) algorithms are carried outin maritime navigation research to decrease this collisionrisk. Most research is carried out to develop supportingsystems for vessel navigators. However, most of these algo-rithms consider only other vessels but not the environmente.g., the shore line or other static obstacles. Another wayto prevent collisions is to develop systems which can au-tonomously generate manoeuvres to avoid collisions. Thesesystems have to consider both, other vessels and staticobstacles. Nowadays, collision avoidance manoeuvres con-sidering the local traffic and other obstacles are usuallysubject to the navigator’s own reaction and judgement.To adjust several avoidance manoeuvres, traffic rules arerequired. Therefore, the only specific rules for maritimenavigation are the collision regulations (COLREGs 1 ). Asreported in Perrow (1984), 56% of the maritime collisionsare caused by the violation of the COLREGs. Thus, a CAsystem which considers the COLREGs could be benefitingfor the vessel navigator.

There are several navigational advising systems to simplifythe decision finding process for the navigator, but theydo not autonomously avoid collisions. For example, theVessel Traffic Service (VTS), is a marine traffic monitoringsystem established by harbour authorities to observe themarine traffic. The idea of the system is a central unit,receiving navigation information of all vessels and sendingthe traffic situation to every connected vessel. Anothersystem is the Automatic Identification System (AIS). AISis an automated tracking system used on vessels and isincluded into VTS for identifying and locating vessels byelectronically exchanging data with other nearby vesselsand VTS stations. The Automatic Radar Plotting Aid(ARPA) is also used for tracking other objects. A radarwith ARPA capability can create tracks using radar con-tacts. The system calculates the tracked objects course,

1 The International Regulations for Preventing Collisions at Sea

speed and Closest Point of Approach (CPA). A possi-ble collision with other vessels or shore lines can so berecognised. One major drawback is, that these systems areexpensive and not suitable for small vessels like they areused on the Lake Constance.

This work focuses on a CA for small vessels in inlandwaters or ports where high traffic density and narrow envi-ronment leads to high collision risks. Thus, the close rangecollision avoidance methods have become an importantsubject. The developed algorithm can be used for a fullyautonomous collision avoidance, since it considers othervessels, static obstacles like a jetty, a bridge or the shorelines, and the COLREGs. It provides a collision free pathregarding the physical constrains of a vessel. This ensuresthat the vessel can follow the provided path. The algorithmcalculates the CPA with other vessels or static obstaclesin a local area of up to 800 m. This range corresponds tothe radar sensor range used to detect other vessels.

In general, there are two possibilities to avoid collisions.First, is to adjust the vessel’s velocity according to avoidcollisions with other vessels. The second is to dismissthe current path and continue on an alternative course.The presented Extended Grid Based Collision Avoidance(EGBCA) approach focuses on planning an alternativecollision free path. But the speed altering for collisionavoidance could also be used by calculating different tra-jectories depending on different speed. The algorithm forthe alternative path calculation is based on the approachof Szlapczynski (2005) and uses a raster grid. For the rastergrid, a variation of the maze-routing algorithm presentedby Lee (1961) is implemented to find a collision-free pathfrom the current position to a given goal. The maze-routing algorithm always finds the shortest path. Thedrawback of this path is that it could include many turnswhich lead to an unqualified vessel course. Szlapczynski(2005) extended the maze-algorithm by introducing turnpenalties to achieve more suitable path with less turnsfor vessel manoeuvres. Physical constrains like the turningrate are not considered in Szlapczynski (2005), which lim-its the algorithm. In his approach, the vessel can reach all

Fig. 1. The vessel Korona from the HTWG Konstanz usedfor dimensioning and testing the CA algorithm on theLake Constance.

neighbour cells in the grid apart from the previously usedcell. To be able to turn a real vessel about 135 degree inone cell, a large cell size is required. For our vessel Koronashown in Figure 1, the cell size would be about 40 m. Innarrow environment like ports or channels, this cell size isnot suitable for CA. Therefore, the EGBCA extends thegrid by a cell size independent model of the vessel dynamicwhich regards the physical constrains of the vessel.

To use the CA algorithm on real vessels, some furtherextensions are required. First, the algorithm has to keepthe conditions of the COLREGs. This is realized byadopting the ship domain of Goodwin et al. (1975) for theother vessels. Further, the collision-free path should havea tangential connection to the original path, in this workcalled global path. This is necessary because the CA onlyworks in a local domain of 800 m but the global path canbe much longer. Therefore, the collision-free path requiresa tangential connection to the global path to get a smoothchangeover from the local collision-free path to the globalpath.

This work is structerd in 5 sections. In section 2, simi-lar approaches for maritime collision avoidance are intro-duced. Section 3 presents a new grid based approach toovercome the limitations of the previous ones. The exper-imental results are shown in section 4. Finally, section 5concludes this work with some future prospects.

2. RELATED WORK

Collision avoidance of vessels has been first discussed bySharpey-Schafer (1955). The discussion focused on the be-haviour of marine traffic in general and optimal strategiesfor evasive manoeuvres in close range encounters. Thiswork concentrates on general issues and provides somesuggestions how to act in a possible collision situation.Collision avoidance research for vessels, nearly stoppedfor the next decades after this discussion. Because of,increasing traffic and collisions on sea in the last twodecades, research focused on theoretical and practical de-velopments of collision avoidance systems. The intensive

research started with a fuzzy set approach published byJames (1986).

Nowadays, many different approaches are carried out formaritime collision avoidance. An overview of the algo-rithms developed in the last decades is given in Statheroset al. (2007) and Tam et al. (2009). Referring to thesepublications, the CA algorithms can by divided into twogroups, the deterministic and the heuristic approaches.Deterministic approaches use mathematical models andalgorithms to find an optimal solution. Depending onthe problem complexity and the large search space, thecomputing time of these algorithms is high. Thus, most ofthese approaches are not suitable for a real CA system. Toreduce this computing time, heuristic approaches searchfor an acceptable solution in a subspace. Therefore, oftensoft-computing techniques based on Artificial Intelligence(AI) are adopted. Some typical soft-computing methodsused for CA algorithms are evolutionary algorithms, fuzzylogic, neural networks, expert systems and combinations ofthese as hybrid systems. Referring to Tam et al. (2009), themost promising algorithm is the evolutionary algorithmpublished by Smierzchalski (1999). But for this work thefocus is on a deterministic approach. Tam et al. (2009)claim that the approach of Szlapczynski (2005) is the mostpractical and the most efficient one. The approach is basedon Chang et al. (2003) which uses a raster grid and themaze-routing algorithm.

Approaches with raster grid realize the search by iteratingover predefined steps and guarantee a solution if there isone. A raster grid is an extension of an occupancy gridbut stores more then one value per cell. The grids areused to discretise the search space for a faster processing.These approaches have become more popular in the lastdecade. The reason is the increasing storage space andcomputer performance. Search algorithms like the maze-routing algorithm used in Chang et al. (2003) find anoptimal path in these grids. The grid raster of Changet al. (2003) stores in each cell if it is sea or land, if thecell is occupied by an other vessel and the arrival time ofthe own vessel. The maze-routing algorithm always findsthe shortest path. This does not have to be the optimalpath for vessel navigation if it consist of many turns.For vessel navigation, a straight path with a minimumof turns is mostly preferred by navigators. To solve thisproblem, Szlapczynski (2005) presented a modified versionof this approach and added turn penalties to each cell.This results in a path with a minimum of turns which ismore suitable for vessel navigation. Additionally, he addedthe possibility to reduce the own vessel’s speed to avoid acollision. This speed altering is only used if no collision-freepath exists for the current speed.

3. EXTENDED GRID BASED COLLISIONAVOIDANCE

The EGBCA is based on the approach of Szlapczynski(2005) who extended the approach of Chang et al. (2003)by turn-penalties. Both approaches will not be further ex-plained, it is assumed that the reader is familiar with these.The main improvements of the EGBCA regarding to theprevious approaches are a new neighbourhood geometrycalled T-neighbourhood and the tangential connection to

the global path. The T-neighbourhood is used to considerthe vessel’s physical constraints. For this purpose, a newstoring method for the orientation of the vessel in thegrid is required which leads to a new calculation of theturn penalties. This extension provides the possibility touse a smaller cell size which improves the accuracy andthe consideration of the COLREGs because of a betterapproximation of the ship domain.

Normally the vessel follows a predefined global path. Thispath is given be an autopilot system or by the vessel’snavigator and is not checked for collisions. The EGBCAchecks if collisions occur in a subsection of the path. Thissubsection is also called local area. The size of the localarea is adopted to the sensor’s range for detecting othervessels. For this work a grid size of 400 cells with a cellsize of 2 m is used. Only considering a subsection of theglobal path leads to the problem that the vessel has toreturn to the global path after a collision is avoided.To get a drivable path, the reconnection to the globalpath should be smooth. Therefore, the EGBCA uses atangential connection between the local collision-free andthe global path.

A further extension for the collision avoidance process isthe providing of supporting points of a trajectory insteadof list of visited cells as done in the previous approaches. Tofind the supporting points of the visited cells, the Douglasand Peucker (1973) algorithm is used. As presented inSchuster et al. (2012), supporting points can be directlyused for navigation systems to control the vessel.

3.1 Considering Vessel’s physical constraints

Each vessel has its own dynamic characteristics. For CA,the most important characteristic is the maximal turningrate which defines the turning circle. This turning rate isgiven in degrees per travelled meter. If the CA does notconsider this turning rate, the vessel may not be able tonavigate on the planed path. For this work the physicalconstrains of the Korona are used, with a turning rateof 0.66667◦/m. This means for a track length of 10 m ,theKorona can change the orientation of about 6.6667◦. To re-gard this performance, the T-neighbourhood is introduced.An overview of the traditional geometry neighbourhood isgiven in Chang et al. (2003). Contrary to the traditionalgeometry neighbourhoods the T-neighbourhood only con-siders the cells reachable by the vessel even for a smallcell size. This leads to a neighbourhood’s geometry whichlooks like the character T. For this work, the vertical lineis called body and the horizontal line is called head. Inthis work, the T-neighbourhood is normalized to a headof three cells. The physical constrains can be applied bymodify the length of the body. Using the Korona and a cellsize of 2 m e.g., leads to a T-neighbourhood with a headof three cells and a body of four cells which is shown inFigure 2.

Using the T-neighbourhood requires a precise orientationwhich is not reachable with the discretised orientationsused by traditional geometry neighbourhoods. They reacha maximum step size for the orientation of 11.25◦ for a16-geometry neighbourhood. This is not suitable for theT-neighbourhood. To solve this problem, the orientationof the vessel is stored in an undiscretised form in each

Fig. 2. Example of the T-neighbourhood for the boatKorona and a cell size of 2 m.

Fig. 3. The domain presented by Goodwin et al. (1975)and its basic representation (if a ship is considered asone cell) in the grid raster

cell. Therefore, the EGBCA only discretise the position ofthe vessel including the latitude and longitude coordinates.But the incoming orientation for each cell is stored as anundiscretised value. Using these undiscretised orientationvalues the turn penalties have to be calculated betweenthe incoming and outgoing orientation. This leads to newturn penalties. To adopt this turn penalties to the cell sizeof the grid, a scaling factor is added.

3.2 Considering the COLREGs

As a benefit of the T-neighbourhood a raster grid witha small cell size can be used. This provides a preciserealisation of the ship domain presented by Goodwin et al.(1975). This approach obtaines a non-symmetric ship do-main which is divided into three sectors as shown in Figure3. For each sector a different dimension is used to modelthe collision risk for the direction of this sector. Using thisship domain for other vessels and Lee’s algorithm to findthe collision-free path enabled the consideration of theCOLREGs since Lee’s algorithm finds the shortest pathto pass this domain. Therefore, the path on the stern sideis shorter than on the bow side and on the port side it isshorter then on the starboard side. In a heading situatione.g. , this leads to avoidance manoeuvre for the own vesselto the starboard side to pass the other vessel on the portside. This is conform to the COLREGs. Detailed tests withconsidering the COLREGs by the EGBCA are presentedin section 4.

3.3 Tangential Connection to the Global Path

In vessel navigation, typically a global path is planned anda CA algorithm checks in a local area if the subsection ofthe path is collision-free. A scenario with a global path

Fig. 4. Consideration of tangential connection to the globalpath.

and a local area for the CA is shown in Figure 4. Theblue line is the global path and the vessel is shown in themiddle of the red marked window which defines the localarea. The shore line and the pier are marked orange andthe vessel is highlighted in red. If the CA generates a newcollision-free path, it has to be connected tangential tothe global path. To consider this tangential connection,two new virtual circular obstacles are added to the grid.This can be seen at the right part of Figure 4. Theseobstacles are called funnel, based on their functionality.The diameter of these obstacles corresponds to the turncircle of the vessel to consider this physical constraint.These obstacles are created by a wave-front propagationalgorithm.

4. EXPERIMENTAL RESULTS

To analyse the performance of the EGBCA and theconsideration of the COLREGs, several test scenarios arecarried out. These scenarios have been verified by Perera(2010) with his fuzzy logic approach. For all tests, twovessels with different course conditions are used. The ownvessel has a speed of 1m/s and the other vessel 2m/s. Inall the scenarios, collisions have been avoided confirm toguidelines of the COLREGs.

4.1 Heading

In the heading scenario the other vessel drives straighttowards the own vessel. The result of the EGBCA is a pathpassing the other vessel parallel on port side as shown inFigure 5.

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Fig. 5. Heading scenario.

4.2 Overtaking

If the own vessel is overtaken by another vessel, normallythe own vessel stays on the course. But if the other vesselhas a higher priority as the own vessel, the own vesselhas to dismiss his path. The overtaking scenario simulatesan overtaking by a vessel with higher priority. For thisscenario the EGBCA dismisses its path and successfullyavoids a collision as shown in Figure 6.

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Fig. 6. Overtaking scenario.

4.3 Crossing Port Side

The crossing port side scenario shows the crossing byanother vessel from port side. The EGBCA plans a pathto pass the other vessel on stern side as shown in Figure 7.

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Fig. 7. Crossing port side scenario.

4.4 Crossing Port Bow Side

In this scenario, the other vessel drives towards the ownvessel from port bow side. The EGBCA plans a pathto pass the other vessel on stern side. This is shown inFigure 8.

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Fig. 8. Crossing port bow side scenario.

4.5 Crossing Port Stern Side

In this scenario, the other vessel drives towards the ownvessel from port stern side. The EGBCA plans a pathwhich first goes parallel to the other vessel and then passeson stern side. This is shown in Figure 9.

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Fig. 9. Crossing port stern side scenario.

4.6 Crossing Starboard Side

In the crossing starboard side scenario, the other vesseldrives towards the own vessel from starboard side. TheEGBCA plans a path to pass the other vessel on sternside as shown in Figure 10.

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Fig. 10. Crossing starboard side scenario.

4.7 Crossing Starboard Bow Side

In this scenario, the other vessel drives towards the ownvessel from starboard bow side. The EGBCA plans a pathto pass the other vessel on stern side. This is shown inFigure 11.

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Fig. 11. Crossing starboard bow side scenario.

4.8 Crossing Starboard Stern Side

In this scenario, the other vessel drives towards the ownvessel from starboard stern side. The EGBCA plans a pathwhich first goes parallel to the other vessel and then passeson stern side. This is shown in Figure 12.

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Fig. 12. Crossing starboard stern side scenario.

5. CONCLUSION

This work presented a grid based collision avoidance al-gorithm. The algorithm uses a special T-neighbourhoodfor the grid search algorithm to consider the physicalconstraints of the vessel. This new T-neighbourhood offersthe possibility to use a smaller cell size. Some of thedeficiencies reported by Tam et al. (2009) for the approachof Szlapczynski (2005) are eliminated by this work. Theextendability to other objectives is guaranteed by thevariability of the cell size. Smaller cell sizes also lead to animproved consideration of the COLREGs. The confirma-tion of the produced collision avoidance manoeuvres withthe COLREGs is proved in several tests.

For future work the T-neighbourhood could be modeleddynamically and asymmetric to regard external influencee.g., wind and river current.

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