Quantifying protocol evaluation for autonomous collision ...marinerobotics.mit.edu/sites/default/files/Woerner... · avoidance rules to include overtaking, head-on, crossing, give-way,

Autonomous Robotshttps://doi.org/10.1007/s10514-018-9765-y

Quantifying protocol evaluation for autonomous collision avoidance

Toward establishing COLREGS compliance metrics

Kyle Woerner1 ·Michael R. Benjamin1 ·Michael Novitzky1 · John J. Leonard1

Received: 14 November 2016 / Accepted: 2 April 2018© Springer Science+Business Media, LLC, part of Springer Nature 2018

AbstractCollision avoidance protocols such as COLREGS are written primarily for human operators resulting in a rule set thatis open to some interpretation, difficult to quantify, and challenging to evaluate. Increasing use of autonomous controlof vehicles emphasizes the need to more uniformly establish entry and exit criteria for collision avoidance rules, adopt ameans to quantitatively evaluate performance, and establish a “road test” for autonomous marine vehicle collision avoidance.This paper presents a means to quantify and subsequently evaluate the otherwise subjective nature of COLREGS thusproviding a path toward standardized evaluation and certification of protocol-constrained collision avoidance systems basedon admiralty case law and on-water experience. Notional algorithms are presented for evaluation of COLREGS collisionavoidance rules to include overtaking, head-on, crossing, give-way, and stand-on rules as well as applicable entry criteria.These rules complement and enable an autonomous collision avoidance road test as a first iteration of algorithm certificationprior to vessels operating in human-present environments. Additional COLREGS rules are discussed for future development.Both real-time and post-mission protocol evaluation tools are introduced. While the motivation of these techniques applies toimprovement of autonomousmarine collision avoidance, the concepts for protocol evaluation and certification extend naturallyto human-operated vessels. Evaluation of protocols governing other physical domains may also benefit from adapting thesetechniques to their cases.

Keywords COLREGS · Autonomous collision avoidance · Human–robot collaboration · Marine navigation

This work was supported by the U.S. Office of Naval Research (GrantNo. N00014-15-1-2213) (Code 33: Robert Brizzolara; Code 311:Behzad Kamgar-Parsi and Don Wagner) and Battelle (Mike Mellott).Portions of this paper first appeared in Woerner (2016).

B Kyle [email protected]

Michael R. [email protected]

Michael [email protected]

John J. [email protected]

1 Department of Mechanical Engineering and ComputerScience and Artificial Intelligence Laboratory, MassachusettsInstitute of Technology, 77 Massachusetts Avenue 32-220,Cambridge, MA 02139, USA

List of symbolsα Contact angleα0 Contact angle at detectionαcpa Contact angle at CPAαc Cutoff contact angle to define reward func-

tionsαcrit Critical cutoff angle for entry criteriaβ Relative bearingβ0 Relative bearing at detectionβcpa Relative bearing at CPAβc Cutoff rel. bearing to define reward func-

tionsφ Arbitrary angle for generic functionsφ0 Arbitrary steering angle for generic func-

tionsCPA Closest point of approach; point of min

ranger Current range to contactrcpa Predicted or actual CPA range (distance)

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rdetect Range at which a contact is detectedreff Effective range after adding pose compo-

nentrmaneuver Range at which vessel maneuversRcol Range that assumes physical collisionRdetect Assumed range of contact detectionRmin Minimum acceptable CPA rangeRnm Range considered a nearmiss encounterRpref Preferred CPA rangeR COLREGS rule compliance functionRmax Max possible COLREGS compliance scoreRΘ Pose component of COLREGS complianceS Safety function for an encounterSr Range component of safety functionSΘ Pose component of safety functionSmaxΘ Maximum possible pose score

tcpa Time of CPAtmaneuver Time of maneuverθ Candidate or actual course (θ ∈ [0, 360◦))|Δθ | Absolute change in courseΔθapp Apparent course deviation thresholdΔθmd Minimum detectable course deviationΘ Pose consisting of 〈α, β〉Θo Initial relative pose (determines rule set)Θcpa Relative pose at CPA (measure of safety)v Speedv0 Initial speed at time of detectionΔv Change in speed during maneuverΔvapp Apparent speed reduction thresholdΔvslow Slow down of vessel during maneuverΔvfast Speed up of vessel during maneuverΔvmax Greater of absolute speed up or slow downΔvmd Minimum detectable speed change_180

◦Angle converted to [− 180◦, 180◦)

_360◦

Angle converted to [0, 360◦)

1 Introduction

The ability to quantify and subsequently evaluate collisionavoidance performance allows society to more uniformlyassess capability and risk of the driver. In the case ofautonomous collision avoidance, a means to validate theunderlying algorithms to standards consistent with humanexpectations necessitates a first step toward quantificationof performance. Improving algorithms and their evaluationtechniques incrementally in real-world environments maythen contribute to successively increasing collision avoid-ance performance standards throughout the world.

The methods discussed in this paper are intended to be afirst step toward a more robust and standardized autonomouscollision avoidance evaluation process. These methods canfurther serve to standardize literature regarding collision

Fig. 1 Algorithms of this paper use autonomous surface vessel col-lision avoidance track data to evaluate each vehicle’s safety (top leftand bottom right) and protocol compliance (top right and bottom left)based on the COLREGS rules, at-sea experience, maritime case law,and case studies of past collisions. Evaluation algorithms may be tunedto localized requirements using a library of functions and configurationparameters.Both real-time andpost-mission analysis tools are presentedgiving evaluators and drivers a means to objectively quantify the safetyand protocol compliance using established metrics and standards. Thispaper provides the metrics necessary to complete a recently introduced“road test” for protocol-constrained collision avoidance for certifyingautonomous marine vehicles to operate at sea in the vicinity of human-operated vessels. Here, blue marker rings indicate an encounter whoseCOLREGS score fell below a threshold level. Other markers are shownwhen violations of configurable safety parameters occur includingmini-mumacceptable range atCPA (green), range atwhich a near-miss occurs(yellow), and range at which a collision is assumed (red) (Color figureonline)

avoidance compliance, especially under protocol constraintssuch as COLREGS1 (United States Coast Guard 1999;Woerner 2016). Figure 1 demonstrates example safety andprotocol compliance evaluation during on-water experimen-tation.

Government certifying agencies such as the InternationalMaritime Organization and its nation-state agents (e.g., U.S.Coast Guard, etc.) may rely on real-world performance andtrack data before issuing licenses to operate in open oceanor other environments where non-test vessels operate. Pastperformance and accident reconstruction may be objectively

1 COLREGS refers to the international rules as formalized at the Con-vention on the International Rules for Preventing Collisions at Sea,developed by the International Maritime Organization, and ratified asan international treaty by Congress. These rules were further formal-ized by the U.S. International Navigational Rules Act of 1977 (UnitedStates CoastGuard 1999), and are sometimes referred to as theCollisionRegulations outside the United States.

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evaluated using real-world track data and a standardized setof expectations quantified by the algorithms of this paper.

Insurance companies can use these performance scoreswhen issuing policies for autonomous vessels or determin-ing fault in an accident. Regulatory bodies can use thesemetrics for an autonomous or remotely operated vehicle’s“road test” before certification as presented in Woerner et al.(2016). Humans and machines alike may train with real-time feedback using measured performance of track data.Autonomous collision avoidance systems can use machinelearning to improvebehavior using aggregateddata frombothhuman-operated and autonomous vessels around the world.This may lead to specific tuning of collision avoidance sys-tems or collision avoidance evaluation standards in differentareas of the world depending on local customs or standards.

With the methods of this paper, conversations in futureliterature can be more exact in their meaning of compliancein protocol-constrained collision avoidance research. Thispaper is organized as follows:

– review of collision avoidance in the literature– introduction of collision avoidance evaluation algorithmsand function libraries addressing overtaking, head-on,give-way, and stand-on rules

– discussion of other collision avoidance rules as they relateto future development of evaluation algorithms

– introduction of real-time and post-mission analysis toolsfor overtaking, head-on, give-way, and stand-on rules

– discussion of recommendations to alter the Rules to bemore inclusive of autonomous vessels

– conclusion with remarks to support other collision avoid-ance domains such as ground and air vehicles.

A means to quantify the power driven rules is presentedto include a numeric scale of compliance (0–100%) foreach applicable rule and its subsequent contribution to theapplicable categories of rules. Detailed numeric evaluationof scenarios may accompany an overall score to provideadditional feedback and amplification of penalties assessed.Tuning of each algorithm’s parameters allows evaluators tocontrol the scores corresponding to specific performance.The scores and thus mapping of numeric values to action-able results (e.g., pass, fail, etc.) are largely dependent onthe evaluator’s tuning decisions. The assignment of scor-ing thresholds such as pass, fail, etc. are therefore reservedfor the evaluation algorithm tuner or the appropriate certify-ing agency. The tuner in a developmental stage is likely thealgorithm designer with input from standardized, publishedrequirements as set by an evaluation authority (e.g., U.S.Coast Guard). The algorithm tuner in certification phases islikely the certification organization or its designated agent.

COLREGS collision avoidance evaluation within thispaper consists of two primary metrics: safety and protocol

compliance. Safety is based on a combination of range andpose of the vessels at closest point of approach (CPA). CPAis defined as the point on ownship’s track where the distanceto the contact reaches its minimum value within the contextof an encounter. Protocol compliance is based on collisionavoidance rule-specific requirements. Pose in this contextrefers to the relative angles of two vessels with respect tothe other and is introduced in Sect. 3. Pose at CPA, specificvalues of range at CPA, complexity of simultaneous contactgeometries, and total contact picture are complicating fac-tors that are not directly quantified in the written COLREGSexcept in limited circumstances or as a consideration with-out specific definition. Each of these factors are, however,important to collision avoidance decision making.

Examination of past encounters and collisions can be usedto help train algorithms to understand safe and unsafe char-acteristics of interactions. Protocol compliance and safetyare related yet can provide additional value when observedin context of the other. For example, a sufficiently compliantmaneuver with respect to the written rules might have vary-ing degrees of safety depending on how a designer configurescertain collision avoidance configuration parameters such asacceptable range at CPA. By examining the components ofsafety and compliance to include range, speed, pose, andsimilar quantities, much insight into true performance canbe inferred. Section 2 introduces COLREGS compliance asfound in the literature. Section 3 discusses the safety met-rics of evaluation. Section 4 discusses protocol compliancemetrics and considerations for power-driven vessels underRules 13–17. Section 5 provides narrative for other COL-REGS rules that would benefit from development of similarevaluation techniques. Section 6 discusses specific COL-REGS testing and evaluation techniques including a functionlibrary and both pre- and post-mission analysis tools. Con-clusions are presented in Sect. 7.

2 COLREGS compliance in the literature

Collision avoidance protocols are prevalent in many physi-cal domains where explicit negotiation or communication iseither impractical or infeasible. In common practice, theseprotocols are often communicated simply as having “rightof way.” In ground transit, drivers are taught to yield to thedriver on the right when arriving simultaneously at an inter-section with stop signs (Commonwealth of Massachusetts2015). Airplanes use the Rules of the Air to determineright of way and appropriate maneuvers—including altitudedeviation—when not under active control of an air trafficcontroller (International Civil Aviation Organization 2005).Surface vessels similarly abide by the COLREGS to deter-mine right ofway and appropriatemaneuverswithout explicitcommunication (United States Coast Guard 1999). Special

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ruleswithin eachprotocol have evolved fromreal-world feed-back; one such example is the traffic separation schemes ofCOLREGSwhen entering or exiting a harbor (Cockcroft andLameijer 2012; Thomas 2001). While the Rules of the Airand COLREGS are largely similar, differences in the phys-ical domains manifest as differences between the collisionavoidance protocol requirements, such as maintaining alti-tude separation for aerial vehicles.

Collision avoidance using COLREGS has been incor-porated on autonomous vessels using various approachessince first demonstrated with on-water experimentation inBenjamin et al. (2006). Throughout maritime literaturediscussing COLREGS, the term “compliance” arises withvarying context and meaning. Power-driven collision avoid-ance implementations ofCOLREGS(Rules 13–18) dominatethe COLREGS-related collision avoidance literature. Othernon-collision avoidance rules of COLREGS arise as beingcompliant within the literature when discussing light config-urations (Fisher 1991).

Testing in the literature predominately fails to define theterm compliance in any quantifiable fashion with respect toCOLREGS. Several authors claim compliance with theseprotocols without specifying the degree or scope of compli-ance (Campbell et al. 2013; Kuwata et al. 2014; Shah 2014;Švec et al. 2013; Tam and Bucknall 2010a, b;Woerner 2014).InKuwata et al. (2014), the head-on rulewas shown to appro-priately eliminate all turns to port. It did not, however, appearto prefer courses that were “readily apparent” (COLREGSRule 8) when finding a turn to starboard. Case law definesapparent course maneuvers to consist of a minimum turn of35◦ while common practice often requires no less than 30◦ ofheading change (Allen 2005; Cockcroft and Lameijer 2012;United States Coast Guard 2006; United States Navy 1999).Courts have found that head-on maneuvers with insufficientturns (i.e., not readily apparent) are in fact non-compliantand, when a collision occurs, partly to blame (Allen 2005).With velocity vector cost functions that favor maintainingcourse and speed such as Kuwata et al. (2014), improperselection of costing weights may easily result in less thanapparent course changes. Other authors consider breaches ofCOLREGS that “may be in the USV’s best interest” suchas turning to port to avoid a collision when explicitly pro-hibited by the COLREGS (Shah 2014). Many authors suchas Woerner (2014) simply claimed COLREGS compliancewithout any quantification or definition of scope.

This trend in claiming unquantified compliance likelystems from a combination of three factors including:

– the vagueness of the rules as written for human usage– the unspecified scope of each author’s work with respectto the numbered COLREGS rules

– the tacit assumption that the COLREGS rules as writtenfully encompass all collision avoidance requirements.

2.1 Intentional vagueness of COLREGS

This intentional vagueness might allow the autonomous col-lision avoidance designer to assume some liberty to interpretthe vast array of complex collision avoidance scenarios with-out being overly restricted from a common sense yet safeapproach. However, case law and common practice greatlyinfluence the requirements of COLREGS despite not beingfound anywhere within the written rules. Examples of on-water collisions and case law provide relevant insight intonuances of the COLREGS and their evolution over theyears. Areas for increased scrutiny in autonomous collisionavoidance solutions can be derived from problematic pastencounters of human ship drivers. The intentional vague-ness of the COLREGS including their underlyingmeaning asderived from the evolution of protocol-constrained collisionavoidance in maritime environments, analysis of real-worldexamples, critiques of experiencedmariners, and relevant rul-ings fromCourts ofAdmiralty are presented in detail inAllen(2005), Cockcroft and Lameijer (2012), Henderson (2006),Thomas (2001) and Zhao (2010) with examples presented asappropriate in this paper.

2.2 Categories for COLREGS scope

A further complicating factor results from the disconnectbetween experienced mariners and autonomous designers:few designers of marine autonomous collision avoidancealgorithms have demonstrated significant experience usingCOLREGS in open ocean navigation for non-academic pur-poses. The varying scope of what authors claim as compliantlargely depends on the scope of interest of a particularresearcher. For example, a perception and sensing authormight claim COLREGS compliance if day shapes or vesseltypes are correctly identified using vision sensing algorithms.An acoustician might claim compliance for properly iden-tified sound signals. The notion of compliance, however,should be amplified with the applicable scope of the COL-REGS within each author’s work.

Collision avoidance compliance in the most general senseinvolves maneuvering one’s vessel to properly interact with acontact for a given initial geometry with appropriate caveatsfor vessel type, maneuvering restrictions, etc. To counter thedisparity between claims and actual performance, the scopeand requirements of COLREGS compliance were quantifiedin Woerner (2016) and Woerner et al. (2016) as part of anautonomous collision avoidance approach. The COLREGSrules were separated into categories to allow a vehicle todemonstrate compliance of appropriate COLREGS subsets.International Maritime Organization guidance, US CoastGuard’s local issuance of inland-specific requirements, andother local guidelines can be adopted as appropriate.

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Table 1 Categories of scope for COLREGS compliance evaluationfrom Woerner et al. (2016)

I General rules (Rules 1–3)

II General conduct of vessels (Rules 4–8)

III Special traffic schemes (Rules 9–10)

IV Sailing in sight of another sailing vessel (Rule 12)

V Vessel encounters in sight of one another (Rules 13–17)

VI Responsibilities in sight of one another (Rules 11, 18)

VII Restricted visibility (Rule 19)

VIII Lights and shapes (Rules 20–31)

IX Sound and light signals (Rules 32–37)

X Inter-vehicle communications

XI Cumulative performance including local customs

A few notable exceptions to this trend exist includingwork with a restricted visibility (Rule 19) compliance fac-tor in Szlapczynski (2015) to give a preliminary estimateof fitness. A traffic separation scheme compliance factor inSzlapczynski (2013) measures fitness of a reference trackwith respect to the ship’s track. A fitness scheme was used inSzlapczynski and Szlapczynska (2011) to penalize maneu-vers which grossly violated COLREGS such as maneuveringto port when turns to starboard were required.

Several categories of scope were presented in Woerner(2016) and Woerner et al. (2016) as a first pass meansof grouping similar research and subsequent evaluation.Table 1 reproduces this grouping for reference and discussionthroughout this paper. With the development of metrics andevaluation techniques within each category, performance canbe reliably demonstrated to a certifying body to a requireddegree of satisfaction. A means would then exist to prop-erly combine work of differing categories to produce morefully compliant solutions prior to achieving the next level ofoperational or testing certification.

Rule categorization allows one designer to claim compli-ance within one or more categories (for example, maneuver-ing requirements of power driven vessels) while deferringevaluation of rules related to other areas (for example, soundidentification and response) to other authors. By defining thescope of applicable rules and demonstrating quantifiable lev-els of compliancewithin each category, autonomous collisionavoidance algorithm designers can more sufficiently articu-late their contributions to the literature. It should be notedthat evaluation within the scope of one category may rely oncompliance of another category to some degree. For example,because Category II includes maintaining a lookout, deter-mining safe speed, determining risk of collision, and takingaction to avoid a collision, it heavily influences evaluationof Categories III–VII. This paper primarily focuses on Cate-goryV scenarioswhile discussing necessary aspects of futuredevelopment of the other categories.

2.3 Collision avoidance and risk

Several approaches have been taken with respect to collisionavoidance and risk in the literature. Each physical domainoffers its unique challenges with modeling and assessingrisk. In the maritime domain, collision risk assessments haveoften studied single vehicle pairs such as vessels in a trafficlane (Lee and Rhee 2001) or a vessel in a similar open oceanscenario (Lee and Kim 2004). A study of the reliability ofquantitative risk analysis through a case study of ship–shipcollision risk is presented in Goerlandt and Kujala (2014),which showed that probability and indicator based risk per-spectives do not necessarily provide the same risk picture. Aframework for measuring ship collision risk was presentedin Goerlandt et al. (2015), though no evaluation of proto-col compliance was formally considered. A methodologyfor assessing the collision risk without consideration of pro-tocol requirements in an electronic navigation environmentwith vessel state uncertainties was presented in Perera andGuedes Soares (2015). A multi-ship anti-collision decisionsupport formulation is presented using simulations in Zhanget al. (2015). A domain violation problem was presentedin Szlapczynski and Szlapczynska (2016) that consideredboth the degree of domain violation and time of domainviolation aspects. A non-linear model for risk estimationwhich attempts to capture mariners judgment was presentedin Lopez-Santander and Lawry (2017), largely based on dataanalysis from a questionnaire to experienced mariners.

3 Evaluating safety using CPA range andpose

Safety has traditionally been viewed in the collision avoid-ance literature as a measure of the number of collisionsrelative to the number of encounters. This, however, isinconsistentwith howhuman-operated shipsmake decisions,especially in scenarios of complex multi-contact collisionavoidance. By considering several quantities important tomaking collision avoidance decisions, safety performancecan be quantified in a way that is more meaningful thansimply declaring a collision or collision-free encounter. Byapproaching the evaluation problem in the same way thatships make maneuvering decisions (United States CoastGuard 2006; United States Navy 1999), closer ranges areconsidered to be higher risk even if not resulting in a colli-sion.

Within the scope of COLREGS, a collision avoidanceencounter is defined to be from first detection of a contactthat is assessed to have a risk of collision until the contactis past CPA, opening range, and no longer considered a riskof collision. Within the scope of this evaluation, vessels areassumed to commence a collision avoidance encounter once

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Fig. 2 Contact angle α represents how ownship’s (labelled “O/S”) rel-ative bearing is seen from the perspective of the contact. Contact angleis 0◦ if the contact is pointing its bow at ownship. Similarly α = 180◦ ifthe contact’s stern is facing ownship. Starboard-facing aspects assumepositive values while port-facing aspects assume negative values. Inboth of these examples, ownship is far to the left and the contact is oncourse North. In (a) ownship is pointing the contact while in (b) theships are on parallel tracks, both at the same location in 2-D space (x,y). Contact angle remains unchanged while relative bearing changes forthe two cases. a α = − 90◦, β = 0◦. b α = − 90◦, β = 90◦

the other vessel is detected. Vessels detect each other at anominal threshold range of Rdetect.

While many factors are important to the CPA vernacular,the two most important values are the range between vesselsatCPA (“CPA range”, rcpa) and the timeuntil or atwhichCPAoccurs (“time of CPA”, tcpa).2 A third value important to CPAcalculations is the pose (“pose at CPA”, Θcpa). Pose in thiscontext refers to a vectorΘcpa = 〈αcpa, βcpa〉 denoting valuesof contact angle (α) and relative bearing (β). Relative bear-ing denotes the bearing of a contact relative to ownship’s bowas 0◦. Contact angle3 refers to the relative bearing of ownshipas seen from the perspective of the contact in question andserves as a clear means to distinguish between the two rela-tive bearings: one from the perspective of ownship, the otherfrom the perspective of the contact. Consistent with on-shipconventions, relative bearing is considered on the domain[0, 360) and contact angle on the domain [− 180, 180). Agraphical representation of relative bearing and contact angleis presented in Fig. 2.

2 Range at CPA sometimes appears in the literature as distance at CPA(DCPA). Both may be used interchangeably. Similarly, tcpa sometimesappears as TCPA.3 The term originated in World War II submarine operations under thenames of “angle on the bow” and “target angle.”

3.1 Range at CPA

Maneuvers that are otherwise compliant with required turndirection and speed but maneuver in a way that resultsin unnecessarily close range at CPA are penalized in thesafety score. The resulting range and pose at closest point ofapproach are considered when penalizing unsafe maneuvers.A safety score for evaluating autonomous collision avoid-ance considers four primary configurable range thresholds asshown in Table 2 and Fig. 3. Range notation uses upper caseR to denote a threshold or nominal value and a lower caser to denote a measured or actual value. Using these rangethresholds, a collision avoidance decision is considered todesire ranges at CPA greater than some value Rpref whileaccepting a known value of risk for ranges as close as Rmin.

Table 2 Primary threshold ranges for evaluation

Range Description

Rpref Preferred range at CPA

Rmin Minimum acceptable range at CPA

Rnm Range considered as a “near miss” encounter

Rcol Range considered as a physical collision

Fig. 3 Concentric range rings represent configurable threshold rangevalues that may be used in evaluation of safety of a collision avoid-ance encounter. While vessels nominally prefer CPA ranges greaterthan Rpref, maneuvers with Rpref > rcpa > Rmin (inside the greenarea) are considered allowable if certain precautions are taken (UnitedStates Coast Guard 2006; United States Navy 1999). Maneuvers withRmin > rcpa > Rnm (inside the yellow area) should be consideredunsafe encounters and examined more closely to improve future per-formance. Any encounter violating a closer Rnm (inside the orange area)threshold is considered to be a nearmiss. Rcol denotes the range atwhichan actual collision is assumed tooccur (inside the red area). Safety scoresmay be quantified using evaluator-defined functions that map specificvalues of rcpa using these threshold values. While the range rings of thisfigure only consider rcpa, pose may be factored into the safety score tocreate shapes other than concentric circles. Evaluation ranges shownhere are not necessarily to scale (Color figure online)

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Fig. 4 Ownship (labeled “O/S”) is traveling east and first sights a con-tact at relative bearingβ with contact angleα in (a). Speed is representedby the length of the colored lines from each vessel (red for contact, bluefor ownship). From the perspective of the contact looking at ownship,α and β are simply interchanged. These two angles give great insightinto the collision avoidance picture and quickly aid in determining theapplicable protocol constraints. Combined with CPA range and time(rcpa, tcpa), pose at CPA (Θcpa = 〈αcpa, βcpa〉) gives important infor-mation as to risk of collision, collision avoidance protocol compliance,and overall safety of a maneuver. Relative bearing and contact angle atCPA are shown in (b). CPA (b) occurs when the range between contactsreaches its minimum value. a Initial pose (Θ0). bArbitrary pose at CPA(Θcpa) (Color figure online)

Ranges closer than Rmin are considered unsafe and abnormaloperating conditions. An encounter is considered to have ahigh risk of imminent collision if its range violates a “nearmiss” threshold Rnm. A physical collision is considered tooccur for any violation of the Rcol threshold.

3.2 Pose at CPA

Using contact angle, relative bearing, range, and speed, acomplete contact geometry can be realized. Contact angleassumes positive increasing values clockwise from the star-board bow and negative values counterclockwise from theport bow, such that α = 0◦ represents the contact’s bow andα = ± 180◦ represents the contact’s stern as shown in Fig. 2.Pose at CPA is therefore not a single quantity, but rather avector of two angles that give great insight into the collisionavoidance problem. The pose at time of sighting or detec-tion (Θ0) often defines which rule(s) of a protocol applies.The pose at CPAwhen combined with rcpa and relative speedgives considerable insight into the degree of risk at tcpa. Fig-ure 4 shows relative bearing and contact angle for an arbitraryinitial geometry and geometry at CPA. Figure 5 shows the

Fig. 5 Ownship (labeled “O/S” and traveling north) encounters twoscenarios of a canonical track crossing with identical ranges at CPA.The bow crossing scenario of (a) demonstrates a much more dangerousencounter than the stern crossing of (b). While many techniques treatall ranges equally, this canonical example of equivalent ranges demon-strates the necessity of incorporating pose into calculations of risk andperformance. a Bow-crossing pose at CPA. b Stern-crossing pose atCPA

importance of considering pose for two different encountersof the same range at CPA.

3.3 Safety functions

A tiered range approach allows for maneuverability con-siderations and quantification of a safety score betweenthe minimum acceptable CPA range and preferred CPArange. This technique also produces a safety score for rcpavalues closer than the minimum acceptable CPA range ina format more meaningful than standard binary evalua-tion (collision or non-collision). While any rcpa closer thanRmin is undesirable, quantifying each encounter allows morethorough insight into the overall effectiveness of a colli-sion avoidance algorithm, collision avoidance configurationparameters, performance under certain rule constraints, andsimilar considerations. User-defined safety functions mapthreshold ranges to safety scores. In a basic example, a lin-ear function maps values between each of the configurationranges with a collision having a safety score of S = 0 andany range greater than preferred CPA range having a safetyscore of S = Smax = 100%. Safety functions can be tai-lored by the evaluator to create specific results based onregulations or experience. A piecewise linear safety function(Fig. 6) demonstrates the adaptability of evaluating perfor-mance using multiple range thresholds.

Figure 5 demonstrated that two identical ranges are notnecessarily equally dangerous. For example, a ship cross-ing in front of another (ownship’s bow pointing a contact’sbeam at CPA)may be considerably more dangerous than twovessels passing at the same range in a port-to-port or stern-to-beam arrangement. For this reason, incorporation of bothpose and range at CPA may prove valuable to an evaluatorof collision avoidance algorithms.

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0 Rcol Rnm Rmin Rpref

0

20%

40%

60%

80%

100%

SRcol = 0%

SRmin

SRnm

Smax = 100%

Range at CPA (rcpa)

Safe

tySc

ore

Safety Function

Fig. 6 Safety scores map range and pose at CPA to a numeric value.This figure demonstrates a piecewise linear mapping of range at CPA(rcpa) to a range-based safety score Sr using the primary thresholdranges of Table 2. Additional penalty or reward may be assigned forpose considerations according to the evaluator’s preference of a safetyfunction. Threshold evaluation ranges give safety scores at preferredrange at CPA

(Sr (Rpref) = SRpref

), minimum acceptable range at CPA(

Sr (Rmin) = SRmin), range at which a near-miss occurs

(Sr (Rnm) =

SRnm), and the nominal range at which a physical collision is assumed(

Sr (Rcol) = SRcol)

Asafety function (S)may includeCPAvalues of both pose(Θcpa = 〈αcpa, βcpa〉) and range (rcpa) as shown in Eq. (1).While most often evaluated at CPA, the safety function con-cept may be applied at any point in a collision avoidanceencounter to achieve a real-time measurement of safety asshown in Eq. (2). The safety function may take both rangeand pose components directly or as a combination of a range-based safety function (Sr ) and a pose-based safety function(SΘ). If desired, an evaluator might consider only the range-based safety function or only the pose-based safety function.

S = S(rcpa,Θcpa) = S(Sr , SΘ) (1)

S = S(r,Θ) (2)

Equation (3) defines an example range-based safety func-tion Sr . This may take the form of a piecewise-definedfunction corresponding to each range threshold (Fig. 6) ora single function defined across the entire domain. Safetyfunctionsmight take other arbitrary shapes such as quadratic,logarithmic, or step-wise designs depending on the needs ofthe evaluator.

Sr = Sr (SRmin , SRnm , Rcol, Rnm, Rmin, Rpref) (3)

Pose-based safety functions (Eq. 4) are used to accountfor the risk associated with the degree which contacts arepointing each other. By combining a pose factor for contactangle using Eq. (5) and relative bearing using Eq. (6), an

−150 −100 −50 0 50 100 1500%

20%

40%

60%

80%

100%

αcpa [deg]

Sα Θ

[%]

Pose-based Safety Function (αc = 80◦)

Fig. 7 COLREGS pose-based safety functions can be used to givepreference to passing contacts with relative bearing and contact anglethat are least likely to increase risk of collision. This safety functionshows Sα

Θ that favors beam and stern contact angles at CPA (αcpa)

using Eq. (5). Here, a cutoff angle αc = 80◦ gives equal preference tobeam and stern aspects. Pointing the bow (0◦) results in a pose-basedsafety score of SΘ = 0

assessment may be made to reward beam or stern aspectsat CPA up to a maximum value of Smax

Θ . Contact angles atCPA aft of a configurable cutoff value αc are given a uniformreward value. Similarly, relative bearings at CPA aft of a con-figurable cutoff value βc are given a uniform reward value.Figure 7 demonstrates the pose-based safety scoring schemeof Eq. (5) that favors non-bow pointing contact angles at CPAusing αc = 80◦.

SΘ = SmaxΘ · Sα

Θ · SβΘ (4)

SαΘ =

{1−cos(αcpa)1−cos(αc)

, if |αcpa| < αc

1, if |αcpa| ≥ αc

(5)

SβΘ =

{1−cos(βcpa)1−cos(βc)

, if |βcpa| < βc

1, if |βcpa| ≥ βc

(6)

An evaluator may find particular value in one form of asafety function over others for a given use case. These safetyfunctions include range-only, pose-only, weighted summa-tion,multiplicative, reward-onlymultiplicative, and effectiverange.

The range-only method of Eq. (3) improves the precisionof standard approaches in collision avoidance:most literaturecurrentlymeasures safety performance as either a collision ora success. By approaching the evaluation problem in the sameway that ships make maneuvering decisions (United StatesCoast Guard 2006; United States Navy 1999), additional riskmay be assumed to be present at closer ranges even if theydo not result in a collision. Even without incorporating pose,this technique provides evaluators with a means to examine

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encounters with higher precision than simply determiningwhether or not a collision occurred.

The pose-only method of Eq. (4) allows for testing safeposes at the time of encounter. On its own, this method mightprove valuable to an evaluator interested only in determininghowconsistently a vessel passes in non-bowpointing aspects.Typically, the pose-based method appears with the range-based method in the form of a combined safety function.

The weighted summation method of Eq. (7) provides ameans for an evaluator to consider both range and pose. Thismethod limits the influence of the range and pose componentsusing the weights sr and sΘ , respectively. Evaluators maychose weights to emphasize the appropriate balance of rangeand pose as necessary.

S = sr · Sr + sΘ · SΘ

sr + sΘ = 1 (7)

The multiplicative safety function of Eq. (8) requires highscores for both range and pose components to have an over-all high safety score. Poor performance in either range orpose immediately results in a low safety score. An evaluator’schoice of Sr and SΘ is therefore particularly important.Whenusing a safety function such as Eq. (8) that requires both sat-isfactory performance of both range and pose, Smax

Θ ≡ 1.

S = Sr · SΘ (8)

As an alternative to the penalty nature of pose in Eq. (8), anevaluator may choose to use pose to reward vessels for pass-ing astern, for example, up to some reasonable percentagedefined by Smax

Θ using Eq. (9). Reward-only multiplicativesafety functions (Eq. 9) allow for the pose component to adda reward value to the original range-based safety score. Inthis reward case, an evaluator may choose to limit the posereward to Smax

Θ < 1 (e.g., 20% maximum reward).

S = max

(Sr · (1 + SΘ), 100%

)(9)

The effective range method of Eq. (10) directly adds somerange value to the actual rcpa based on a pose-based safetyscore SΘ . This effective range reff (Eq. 11) is then used asthe input of a range-based safety function to compute theoverall safety score at CPA for r = reff rather than r = rcpa.The true rcpa value may not be compensated more than somemaximum possible pose-reward rΘ . This technique allowsfor pose to effectively improve the rcpa which is seen bythe safety function as though range were actually at reff. Incontrast, a technique such as the reward-only multiplicativeof Eq. (9) uses a proportional reward rather than the absolutemaximum reward of the effective range method.

S = S(reff) (10)

Table 3 Summary of collision avoidance safety functions

Equations Likely use case

(3) Range-only solution desired

(4) Pose-only solution desired

(7) Preserves strong performance in either range or pose

(8) Requires high performance in both range and pose

(9) Rewards favorable pose without penalizing poor pose

(10) Rewards advantageous pose by increasing the “effec-tive” range; limits reward to an absolute quantityrather than relative increase of (9). Easy to visualizeas graph of Sr (reff)

reff = r + SΘ · rΘ (11)

Algorithm 1 demonstrates assessment of safety as a func-tion of both range and pose. Table 3 summarizes the differentmeans of computing safety scores.

Algorithm 1 General Approach of Safety Evaluation1: procedure Pseudocode for analyzeSafety()2: Input: range thresholds and associated penalty values3: Input: safety functions and shapes4: for each encounter do5: Θcpa ← pose at CPA6: rcpa ← range at CPA7: S ← S(rcpa,Θcpa)

combine range and pose components using Table 38: end for9: end procedure

4 Evaluating protocol requirements usingrule-specific algorithms andconsiderations

Standardized measures of collision avoidance algorithmperformance and effectiveness enable consistent evaluationof COLREGS for both human-operated and autonomousvessels. Creating rule categories, assigning each rule to a cat-egory, and defining metrics for each applicable rule enablesconsistent evaluation and allows for more clear scientificconversation regarding the advancement of autonomous col-lision avoidance. Incorporation of the appropriate case law,localized nuance, and knowledge of the evolution of theCOLREGS are vital to ensuring appropriate behavior innuanced situations. While the Rules give general guidance,actions generally consistent with human behavior and expec-tations must be the objective when integrating autonomoussystems into human-present environments. Appropriatelymodeling and accounting for human intuition, common prac-tice, and human expectations are among the many factors

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Algorithm 2 General Approach of Evaluation Technique1: procedure Pseudocode for EvaluateEncounter()2: Input: positions (x,y), courses (θ), and speeds (v) from track data3: Input: configurable threshold ranges and angles4: Input: configurable penalty values and functions5: for each encounter commencing at r = Rdetect do6: Calculate: initial pose (Θ0)

7: Calculate: pose at CPA (Θcpa)

8: Calculate: CPA range (rcpa)9: Calculate: changes in speed (Δv, vmin, vmax)

10: Calculate: changes in course (Δθ)

11: Determine R using Algorithm 3 entry criteria12: R ← R(Θ0,Θcpa, rcpa,Δv,Δθ)

evaluate for each contact with respect to its rule set R13: S ← S(rcpa,Θcpa)

evaluate safety for each contact using AnalyzeSafety()14: end for15: end procedure

not found on any written page of United States Coast Guard(1999). For example, the colloquial Law of Gross Tonnagestates that a small craft generally stays out of the way of alarge vessel such as an intercontinental merchant even when,strictly by the protocol requirements, the small vessel mighthave right of way. Adherence to custom and human expecta-tion must be considered and honored in order to integrateautonomous platforms into a human-dominated environ-ment.

Algorithm 2 demonstrates the general approach of eval-uating COLREGS compliance including calculation of thesafety score of Algorithm 1. Collision avoidance encoun-ters commence at a threshold detection range r = Rdetect.Protocol compliance functions take the symbol R with asuperscript denoting the applicable COLREGS rule(s) (e.g.,R14 denotes evaluation of head-on compliance). Each sub-section below presents a protocol requirement and briefdiscussionof evaluation technique andnuance as appropriate.

This section presents methods corresponding to Cate-gory V of Table 1 (vessel encounters in sight of one another(Rules 13–17)) with the understanding that other categories(e.g., I, II, VI) may additionally apply. Each collision avoid-ance rule for vessels in sight of one another except Rule 14(COLREGS Rules 11–13, 15–18) allows for entry criteriathat assign one vessel to be stand-on (maintain course andspeed4) and the other give-way (keep out of the way ofthe other) based on geometry, ship type or maneuverabilityrestrictions, and environmental (wind) conditions for the spe-cific case of two sailing vessels. Rules 13–17 are presentedwith considerations below. Rule 18 is discussed in Sect. 5.1.Openocean vessel behavior assumes thatmaneuvers aremostlikely due to collision avoidance requirements unless other-wise specified for navigational or operational necessity.

4 Maintaining course and speed gives appropriate latitude to normalactions required per case law (Allen 2005; Cockcroft and Lameijer2012; Zhao 2010).

4.1 Entry criteria

Entry criteria for Rules 13–17 largely depend on a combi-nation of relative geometry, relative speeds, and an assessedrisk of collision for two power driven vessels assuming nospecial precedence of Rule 18. While relative bearing isspecified explicitly in the COLREGS for Rule 13, ambi-guity exists for Rule 14. Contact angle offers significantinsight into the appropriate rule and helps discriminate risk ofcollision before making more computationally costly calcu-lations. Algorithm designers and evaluators evaluating entrycriteria must show due regard for the written rules of UnitedStates Coast Guard (1999), appropriate case law, and localcustom (Allen 2005; Cockcroft and Lameijer 2012).

A configurable critical contact angle (αcrit) shown in Fig. 8for Rules 13–15 helps to specify whether a vessel shouldtake action per the COLREGS. The ability to configure αcrit

gives flexibility to the evaluator. When self-evaluating forthe purposes of autonomous collision avoidance algorithmdevelopment and improvement, a designer might tune αcrit tobestmimic human ship driving practice. Algorithm 3 demon-strates entry criteria for Rules 13–17 assuming no overridingRule 18 precedence. Specific considerations of entry criteriafor each rule are presented in the following subsections.

The introduction and configuration of αcrit allows morecontext for discussion and evaluation of entry criteria com-pared to the basic consideration of range and relative bearingalone. For example, algorithms might struggle to determinethe appropriate context to assign a contact as “coming upon” within the context of Rule 13 (Allen 2005; Cockcroftand Lameijer 2012). Using α relative to αcrit as a first passfilter to determine potential applicability of Rule 13may giveinsight to appropriate values of αcrit in different regions ofthe world where local case law differs on “coming up on”with respect to Rule 13 entry criteria.

Entry criteria for Rule 14 must be carefully consideredwithin the context of the local environmental conditions.Context of a ship’s course over ground as observed by radarand its heading as observed visiblymust be reconciled withincollision avoidance algorithms to avoid inappropriate ruleentry. That is, a contact’s course as observed visually maybe quite different than that observed by relative motion onradar. Selection of entry criteria using a contact’s heading forboth collision avoidance and its subsequent evaluation mustaccount for this environmental influence.

Further research is required to determine the appropri-ate use of αcrit for edge case scenarios such as Fig. 8d.Rule 15 specifies a contact off the starboard side as beinga crossing give-way. This does not relieve the vessel of herduties to give-way if a risk of collision exists in an edge casegeometry that might not be within the canonical examplesof β ∈ [0◦, 112.5◦]. This is especially true if strong envi-

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Fig. 8 Entry criteria for Rules 13–15. All critical angles are relative toownship’s heading. Critical angles of Rules 13 and 14 represent half-angles of the shaded region. All critical contact angles are configurable

to the evaluator as they have no prescribed value in the COLREGS. aRule 13—Overtaking. b Rule 14—Head-on. c Rule 15—Crossing. dRule 15—Crossing (edge case)

ronmental conditions might dominate a slow contact speedcausing a risk of collision if no action were taken.

Entry into many of the numbered collision avoidancerules requires adherence to give-way (Rule 16) or stand-on(Rule 17) requirements. Evaluation algorithms for give-wayrequirements are presented in Sect. 4.2 with amplificationin later sections as necessary for rule-specific requirements(e.g., power-driven crossing vessels in Rule 15). Similarly,evaluation algorithms for stand-on vessel requirements arepresented in Sect. 4.3 with appropriate amplification in latersections.

4.2 Rule 16: Give-way

Give-way vessels are to take early action, to take substantialaction, and to keep well clear as shown in Algorithm 4. Thisyields three measurable criteria for all give-way vessels:

– range at time of maneuver relative to the ranges at timesof detection, determination of collision risk, and CPA(Algorithm 5)

– determination of substantial action as measured by thesize and direction of the maneuver (turn or speed changeconsistent with Rule 8) (Algorithms 6, 7, and 8)

– range and pose at CPA

It should be noted that Rule 16 does not apply exclusivelyto power-driven vessels nor does it apply exclusively to cross-ing situations (Allen 2005; Cockcroft and Lameijer 2012).Rather, Rule 16 may be invoked as a result of Rules 12, 13,15, or 18. Claims of “compliance” with Rule 16 have beenimplicitly made in autonomous collision avoidance literaturewith a scope limited to power-driven crossing give-way situ-ations (Rule 15) without discussion of its wider implications.Full Rule 16 compliance claims must, however, specify thatthey include the scope of Rule 12 (sailing vessels), Rule 13(overtaking), Rule 15 (power-driven crossing), and Rule 18(precedence) to be complete and truly compliant. Detaileddiscussion of the applicability of Rule 16 to each of thesegive-way situations is presented in the appropriate subsec-tions.

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Algorithm 3 COLREGS Entry Criteria: Determining theAppropriate Rule Set1: procedure Pseudocode for COLREGS Entry Criteria2: if rcpa > Rdetect then3: R ← Rcpa no risk of collision

Rdetect is nominal range of detection continue tracking rcpa, range-rate, and bearing-rate and evaluatesubsequent rule entry

4: return5: end if6: risk of collision assumed7: α13

crit ← overtaking tolerance default 45◦; tolerance for “coming up with” pose

also require closing range and risk of collision8: α14

crit ← head-on tolerance default 13◦ tolerance for “reciprocal or nearly reciprocal courses”

“When...in any doubt...assume...[head-on].”9: α15

crit ← crossing aspect limit default 10◦ all αcrit values are configurable by evaluator

10: α0 ← initial contact angle (α ∈ [− 180◦, 180◦)) α360◦

0 maps α0 from [− 180◦, 180◦) → [0◦, 360◦)11: β0 ← initial relative bearing (β ∈ [0◦, 360◦))

β180◦0 maps β0 from [0◦, 360◦) → [− 180◦, 180◦)

12: if (β0 > 112.5◦) && (β0 < 247.5◦) && (|α0| < α13crit) then

13: R ← R13/17 vessel is overtaken (stand-on)14: else if (α360◦

0 > 112.5◦) && (α360◦0 < 247.5◦) &&

15: (|β0|180◦< α13

crit) then16: R ← R13/16 vessel is overtaking (give-way)17: else if |β180◦

0 | < α14crit && |α0| < α14

crit then18: R ← R14

vessel is head-on; tolerance is configurable19: else if (β0 > 0) && (β0 < 112.5◦) && (α > − 112.5◦) &&

α < α15crit then

20: R ← R15/16 vessel is crossing give-way crossing aspect limit is configurable

21: else if (α360◦0 > 0◦) && (α360◦

0 < 112.5◦) &&22: (β180◦

0 − 112.5◦ && (β180◦0 < α15

crit then23: R ← R15/17 vessel is crossing stand-on

crossing aspect limit is configurable24: else25: R ← Rcpa

detectable but likely no risk of collision (not yet in a dedicatedrule) continue tracking rcpa, range-rate, and bearing-rate and evaluatesubsequent rule entry

26: end if27: end procedure

Algorithm 4 Rule 16: Give-way Vessels1: procedure Pseudocode for Give- way Vessels2: R16 ← Rmax

3: R16 ← AnalyzeSafety() (Rules 8,16,18) “keep well clear”

4: R16 ← penalize for delayed action (Algorithm 5)

5: R16 ← penalize for non-apparent maneuvers (Algorithms 6, 7, and 8)

“take early and substantial action”6: R16 ← penalize for hindrance of stand-on vessel

“keep well clear”7: end procedure

Algorithm 5 Penalize for Delayed Action1: procedure Pseudocode for PenalizeDelayedAction()2: rdetect ← range to contact at time of detection

if rdetect not explicitly known, set rdetect = Rdetect assumes collision risk assessed immediately

3: rmaneuver ← range at time of ownship’s maneuver4: rmaneuver ← min(rmaneuver, rdetect)5: Rdelay ← maximum score deduction (percent)

6: Rdelay ← Rdelay ·(

rdetect − rmaneuver

rdetect

)

7: Rrule ← Rrule · (1 − Rdelay)

8: end procedure

Algorithm 6 Penalize for Non-Readily Apparent Maneuver1: procedure Pseudocode for PenalizeNon-

ApparentManeuver()2: RΔθapp ← Non-ApparentCourseChange()

(Algorithm 7)3: RΔvapp ← Non-ApparentSpeedChange()

(Algorithm 8)4: thresh ← threshold penalty before non-apparent maneuver

deducts from score5: default 30%6: if

(RΔθapp < thresh

) || (RΔvapp < thresh

)then

7: return;8: else if

(RΔvapp < thresh

)then

9: Rrule ← Rrule · (1 − RΔθapp

)

10: else11: Rrule ← Rrule · (

1 − RΔvapp)

12: Rrule ← Rrule · (1 − RΔθapp

)

13: end if14: end procedure

Algorithm 7 Check for Non-Readily Apparent CourseChange1: procedure Pseudocode for Non- ApparentCourseChange()2: RΔθapp ← max penalty for non-apparent course maneuver3: RΔθapp ∈ [0, 1], default 50%4: |Δθ| ← absolute course deviation5: Δθapp ← apparent course deviation threshold

default 30◦6: Δθmd ← minimum detectable course deviation

default 0◦7: if |Δθ | > Δθapp then8: return

(RΔθapp ← 0

)

9: end if

10: RΔθapp ← RΔθapp ·(

Δθapp − |Δθ |Δθapp − Δθmd

)

11: end procedure

4.3 Rule 17: Stand-on

Stand-on vessels are by definition the vessel not assignedgive-way responsibilities for an encounter requiring onevessel to keep clear (i.e., Rule 16 give-way). Stand-on ves-sels are not necessarily limited to situations of a crossingencounter with two power-driven vessels. The stand-on ves-sel is required by Rule 17 to maintain course and speedas demonstrated in Algorithm 9. A penalty should thus be

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Algorithm 8 Check for Non-Readily Apparent SpeedChange1: procedure Pseudocode for Non- ApparentSpeedChange()2: RΔvapp ← max penalty for non-apparent speed maneuver3: RΔvapp ∈ [0, 1], default 50%4: Δvapp ← apparent speed reduction threshold

Δvapp ∈ [0, 1], default 50%5: v0 ← initial ownship speed at time of detection6: vmin ← speed after slowing

7: Δv ←(

v0 − vmin

v0

)

8: if (Δv ≥ Δvapp) then9: return

(RΔvapp ← 0

)

sufficiently apparent speed change10: end if

11: RΔvapp ← RΔvapp ·(

Δvapp − Δv

Δvapp

)

12: end procedure

assessed for changing course (Algorithm 10) and anotherpenalty assessed for changing speed (Algorithm 11) withsome reasonable tolerance for environmental conditions andnoise. Consideration must be given, however, to stand-on vessels maneuvering when invoking their obligation toavoid collision when in extremis under Rule 17.a.ii. Stand-on vessels failing to maneuver prior to a collision haverepeatedly been found partially (usually 25%) at fault byadmiralty courts when not invoking this clause (Allen 2005).Environmental and contact picture-specific variables heav-ily influence the determination of when to maneuver as astand-on vessel.

Further, obligations of a stand-on vessel simultaneouslyassigned responsibilities as a head-on or give-wayvesselwithanother contact must take care to understand the obligationsof case law as it applies to maintaining course and speed.Courts have repeatedly ruled that maintaining course andspeed implies those navigational maneuvers consistent witha “steady, predictable maneuver.” This includes maneuversfor avoidance of danger or other navigational requirementsthat the stand-on vessel would otherwise perform (e.g., slow-ing to take on a pilot, maneuvering for another COLREGSobligation, etc.) (Allen 2005; Zhao 2010).

Stand-on vessels that determine themselves to be inextremis are allowed by the COLREGS to take action sub-ject to certain restrictions. Reasonable and consistent criteriaare required for determination of when to take action underRule 17.a.ii. Once entry criteria are established, evaluationof stand-on vessels deemed to be in extremis should focuson safely avoiding a collision subject to the power-drivenrestriction of Rule 17.c. With the exception of Rule 17.c,evaluation of evasive action should use the safety score as aprimary metric for rule compliance of the stand-on vessel.

For stand-on vessels, a change in speed is a violationof Rule 17 within the aforementioned caveats. To quantify

Algorithm 9 Rule 17: Stand-on Vessels1: procedure Pseudocode for Stand- on Vessels2: R17 ← Rmax

3: R17 ← AnalyzeSafety() Rules 8, 17, 18 “she shall take such action as will best aid to avoid collision”

4: R17 ← penalizeCourseChange() (Algorithm 10)5: R17 ← penalizeSpeedChange() (Algorithm 11)

“shall keep her course and speed”6: R17 ← compensate formaneuvers required of normal navigation

(do not penalize a stand-on vessel for maneuvering for reasons otherthan this contact) case law Allen (2005), Cockcroft and Lameijer (2012), Thomas

(2001)7: if in extremis then8: R17 ← compensate for maneuvers required in extremis

do not penalize stand-on if rcpa < configurable value “take action to avoid collision by her maneuver alone”

9: if power-driven crossing then10: R17 ← penalize port maneuvers for port contacts

“...not alter course to port for a vessel on her own port side”11: end if12: end if13: end procedure

Algorithm 10 Penalize Course Change1: procedure Pseudocode for PenalizeCourseChange()2: if tmaneuver > tcpa then3: return;4: end if5: Rmax ← maximum penalty for changing course

default 50%6: |Δθ| ← maximum heading deviation7: Δθapp ← apparent turn threshold default 30◦8: Δθmd ← minimum detectable heading deviation

default 2◦9: if (|Δθ| < Δθmd) then10: return;11: else if

(|Δθ| > Δθapp)then

12: return(Rrule ← Rrule − Rmax

)

13: end if

14: Rrule ← Rrule − Rmax ·(

|Δθ| − Δθmd

Δθapp − Δθmd

)

15: end procedure

speed change, the speed at the declaration of entry into thestand-on obligation must be identified. A penalty can thenbe assigned for any subsequent speed up or slow down rela-tive to this initial speed value. A speed change that is likelyundetectable by the contact or insignificant to the collisionavoidance scenario should be disregarded. Speeding up orslowing down by appreciable amounts without navigationalnecessity, however, violates Rule 17 and can result in unnec-essary complication of the collision avoidance scenario.

Similarly, course changes greater than some thresholdnoise level (say, 2◦) must be penalized for stand-on ves-sels not otherwise invoking Rule 17.a.ii. Some small headingchange up to the generally accepted substantial value of 30◦must be increasingly penalized. An example metric uses alinear or quadratic mapping between minimum detectable

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Algorithm 11 Penalize Speed Change1: procedure Pseudocode for PenalizeSpeedChange()2: if tmaneuver > tcpa then3: return;4: end if5: Rmax ← max penalty for slowing default 50%6: Δvfast ← vmax − v07: Δvslow ← v0 − vmin8: Δvmax ← max(Δvfast,Δvslow)

9: Δvmd ← min detectable speed change default 0.2 m/s

10: if Δvmax < Δvmd then11: return;12: end if

13: Rrule ← Rrule ·(

v0

vmax

)2

penalize speeding up

14: Rrule ← Rrule − Rmax ·(

Δvslow

v0

)

penalize slowing down (not mutually exclusive)15: end procedure

0 2◦ 30◦0%

20%

40%

60%

80%

100% 100% Penalty →

Course Change Δθ [deg]

Pena

lty[%

]

Nominal Stand-on Vessel Course Change Penalty

Fig. 9 The stand-on vessel is required by Rule 17 to maintain courseand speed. Without a justifiable reason to alter course, a penalty maybe assessed. This figure demonstrates a linear penalty for unwarrantedcourse changes by a stand-on vessel. No penalty is assessed until aminimum detectable heading deviation is exceeded, here Δθmd = 2◦.In this example function, a linearly increasing penalty is invoked until amaximum penalty is reached at the apparent turn threshold of Δθapp =30◦

and substantial course changes (2◦−30◦) with a plateau ofpenalty outside the linear region. Several small turns resultingin a larger effective turn should also be penalized accord-ingly. Figure 9 demonstrates a stand-on vessel course changepenalty.

4.4 Rule 13: Overtaking

Collision avoidance routines for overtaking vessels (Fig. 8a)may rely on explicit entry criteria specified in the COL-REGS with respect to initial pose: a contact must be morethan 22.5◦ abaft the other vessel’s beam. Different countries

Fig. 10 Ownship’s (O/S) initial encounter geometry, closing range,and proximity at CPA require action under an overtaking scenario ofRule 13. Dotted lines indicate the blue (O/S) and red (contact) speedsand demonstrate a closing range given the initial contact pose 〈α, β〉 in(a). By appropriately altering course to starboard early in the collisionavoidance encounter (b), O/S will pass to the contact’s stern withoutcausing the stand-on vessel to maneuver for a risk of collision. a Ini-tial overtaking geometry. b Overtaking astern of contact (Color figureonline)

have interpreted the “coming up with” phrase to take differ-ent meanings including a notable admiralty case in Englandinvolving Nowy Sacz and the Olympian (Allen 2005). Mostcourts contend, however, that the overtaking rule applieswhen the appropriate encounter geometry exists, the asternvessel has a higher speed than the overtaken vessel, the ves-sels are closing range, and an expected range at CPA wouldreasonably require prudence.

The overtaking (higher speed) vessel is defined as a give-way vessel by Rule 16 (Allen 2005; Cockcroft and Lameijer2012; United States Coast Guard 1999). Pose becomes animportant aspect of measuring performance for the over-taking vessel due to both common practice and specificrequirements in the Rules including her “duty of keepingclear ... until past and clear.” Overtaking on near-paralleltracks (such as in a merchant transit lane) allows for safepose at CPA and accounts for a significant and mostly trivialcase in the absence of other collision avoidance, environ-mental, or navigational constraints. A reasonable set of entrycriteria for Rule 13 generally include a contact angle (α)

within the exclusive sternlight region, a sufficient speed andrelative bearing (β) for closing range, and a CPA range andCPA pose consistent with a risk of collision.

When the contact situation or initial geometry requiresovertaking on non-parallel tracks such as in Fig. 10, prefer-ence should be given to overtaking astern of the overtakenvessel when possible. Passing track in front of the overtakenvessel creates an encounter with higher risk and less eva-sive maneuverability for the overtaken vessel. Passing infront of the overtaken vessel within a range considered arisk of collision further degrades the overtaken vessel’s abil-ity to maintain its course and speed. Therefore, a penalty is

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assessed for overtaking vessels who cross ahead of track ofan overtaken vessel within a certain range.

The vessel being overtaken is, by the definition of Rule 17,a stand-on vessel and must keep her course and speed (Allen2005; Cockcroft and Lameijer 2012; United States CoastGuard 1999). This nuance is often unknowingly neglectedby autonomous collision avoidance authors and emphasizesthe need for incorporation of practical at-sea experience ofthose involved in designing and evaluating collision avoid-ance algorithms for autonomous vessels (Kuwata et al.2014, 2011). Vessels deemed to be overtaken must thereforedemonstrate their obligation to maintain course and speedwithin the context of their contact-free intentions (Allen2005; Zhao 2010).

Overtaking algorithms must be validated for correct con-tact angle, relative bearing, and speed considerations to verifymode entry criteria and algorithm robustness. A final neces-sary check in evaluation of overtaking collision avoidancealgorithms is to ensure that modes do not shift from over-taking to crossing. Any mode changes from overtaking tocrossing should be deemed a failure of the overtaking colli-sion avoidance algorithm, as it violates an explicit clause ofRule 13.

A general approach for evaluating overtaking vesselsunder Rules 13 and 16 is shown in Algorithm 12 as amplifiedby Algorithm 4 and includes the following attributes:

– penalize for unnecessary crossing of contact’s bow atclose ranges

– penalize for unnecessary hindrance of overtaken vessel’sdesired maneuvers

– penalize for delayed action (range ofmaneuver relative todetection range and CPA range if a maneuver is required)(Algorithm 5)

– penalize for safety violations including sufficient rangeand early action (Rules 7–8)

A general approach for evaluating overtaken vessels underRules 13 and 17 is shown in Algorithm 13 as amplified byAlgorithm 9 and includes the following attributes:

– penalize the overtaken vessel in accordance with require-ments of a stand-on vessel (Rule 17)

– penalize for safety violations resulting from neglectingto invoke Rule 17.a.ii

– compensate for changes in course or speed required as aresult of being in extremis

4.5 Rule 14: Head-on

Head-on situations (Fig. 8b) provide arguably the mostambiguous entry criteria of the rules for power-driven

Algorithm 12 Rule 13/16: Overtaking Vessels1: procedure Pseudocode for Overtaking Vessels2: R13/16 ← R16 (Algorithm 4)

overtaking vessels are give-way vessels (Rules 13 & 16) See Allen (2005), Cockcroft and Lameijer (2012), United StatesCoast Guard (1999)

3: end procedure

Algorithm 13 Rule 13/17: Overtaken Vessels1: procedure Pseudocode for Overtaken Vessels2: R13/17 ← R17 (Algorithm 9)

overtaken vessels are stand-on vessels (Rules 13 & 17) See Allen (2005), Cockcroft and Lameijer (2012), United StatesCoast Guard (1999)

3: end procedure

vessels. The definition of “reciprocal or nearly reciprocalcourses” is vague and left to interpretation. The compasscourse is required to be used when assessing course dif-ference due to the ship-fixed masthead light and sidelightdefinition of ship’s course in Rule 14. Confusion arises whenenvironmental parameters greatly affect the course-over-ground; non-visual means (e.g., radar, lidar, etc.) measurecourse-over-ground, so care must be taken in evaluatingcontact geometry for proper entry criteria and resolution ofambiguity. Similarly, a consistent entry criterion for “nearlyreciprocal course” should be configurable and set in accor-dance with local customs, case law, or certifying agencyrequirements. Environmental conditions such as sea-state,current, or fluctuating wind might also warrant a change tothe entry criteria angle (α14

crit) tolerance or use of a filter.Evaluation scenarios should incorporate sufficient set and

drift to realize an appreciable distance between course-over-ground and compass heading before certification ascompliant with Rule 14. Small sequential maneuvers shouldalso be penalized, as a single, readily apparent maneuver isrequired (Rule 8). The size of a readily apparent maneuveris not explicitly defined in the COLREGS, though turns of30◦ have been determined by custom to be sufficient (UnitedStates Coast Guard 2006). Some texts suggest a minimum of35◦ for a sufficient turn (Allen 2005). The intention of the ruleis to ensure that turns are apparent by both radar and visualobservation; the single large turn clearly communicates to theother vessel that a risk of collision has been assumed and thevessel is taking appropriate early action in accordance withthe COLREGS. This is especially important for the majorityof collision avoidance encounters that do not involve explicitcommunication but rather rely on observation of the contact’smaneuver alone.

When evaluating maneuvers for a head-on scenario, bothvessels must maneuver to starboard in an appreciable andtimely way. Maintaining course or turning to port should beviewed as a failure to maneuver in accordance with Rule 14.Rule 14 further specifics that passing pose must be port-to-

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Algorithm 14 Rule 14: Head-on Vessels1: procedure Pseudocode for Head- on Vessels2: Input: αcpa3: Input: βcpa

4: R14 ← Rmax

5: R14 ← assess non-starboard turn penalty “each shall alter her course to starboard”

6: R14 ← assess delayed action penalty “made in ample time” (Algorithm 5)

7: R14 ← assess non-apparent turn penalty “be large enough to be readily apparent” (Algorithm 7)

30◦ to 35◦ (configurable) minimum per case law (default linear penalty; configurable)

8: R14 ← assess R14Θcpa

penalty if not port-to-port “each shall pass on the port side of the other”

Equation (12); configurable per library of Sect. 6.19: end procedure

port. Pose should therefore enter into the protocol compliancemetric for head-on encounters. Equation (12) demonstratesan arbitrary Rule 14 pose function (R14

Θcpa) accounting for

both relative bearing and contact angle at CPA.

R14Θcpa

= R14αcpa

· R14βcpa

· Rmax (12)

Equation (13) uses specific pose functions for both con-tact angle and relative bearing to give large preference tonear-canonical port aspects. This example pose function usescombinations of sinusoidal functions of relative bearing (β)

and contact angle (α) at CPA. A true port-to-port passagewill be a relative bearing of β = 270◦ and a contact angle ofα = − 90◦ as seen in Fig. 11. Within an allowable tolerance,large deviations fromport-to-port passage in open-ocean sce-narios likely indicate insufficient or delayed maneuvers byone or both vessels. In Fig. 11a, a nearly canonical head-onCPA geometry gives a high pose score. In Fig. 11b, a likelylate maneuver by ownship and a subsequent narrow contactangle at CPA results in a smaller pose score.

R14Θcpa

=(

sin(αcpa) − 1

2

)2( sin(βcpa) − 1

2

)2

Rmax (13)

Algorithm 14 demonstrates an approach to evaluate head-on encounters including appropriate penalties for delayedaction (Algorithm 5) and non-apparent turns (Algorithm 7).Alternative functions to the specific R14

αcpaand R14

βcpaof

Eq. (13) are available in the evaluation library discussed inSect. 6. Figure 12 shows an example port-to-port pose func-tion while Fig. 13 shows a more severe preference to portangles. Possible scores range from 0 to the maximum possi-ble protocol compliance score (Rmax = 100%).

Fig. 11 Rule 14 requires head-on contacts tomaneuver to starboard andpass port-to-port. The geometry of a nearly canonical case (a) showsthe preferred CPA geometry including relative bearing β and contactangle α. Using Eq. (13), a nearly maximum pose score would result.In (b), a delayed maneuver from ownship (“O/S”) results in a portrelative bearing at CPA; contact angle αcpa, however, accounts for theless than ideal CPA geometry. Equation (12) would reduce the overallperformance score for the situation in (b). a Near-canonical head-ongeometry at CPA. b Head-on geometry at CPA resulting from delayedaction of ownship (O/S)

4.6 Rule 15: Power-driven crossing

Rule 15 assigns give-way and stand-on responsibilities toeach of two crossing power-driven vessels with a risk ofcollision (Fig. 8c). The geometric entry criteria are derivedfrom eliminating head-on and overtaking geometries whileretaining a risk of collision. Relative bearing therefore spans{β : (β < 112.5◦) or (β > 247.5◦)} with an appropriatecontact angle (α) such that a risk of collision exists withoutinducing head-on or overtaking obligations.

Crossing give-way vessels are specifically required to notcross ahead of the stand-on vessel; this notion has been rein-forced in admiralty courts (Allen 2005). Note that a risk ofcollision must exist for Rule 15 to apply. Therefore a riskof collision invoking crossing give-way actions requires astern crossing. Verification that a vessel crossed astern ofthe stand-on vessel is possible using Θcpa. For example, astern crossing will result in a large negative contact angle atCPA (typically αcpa < − 90◦) if the stand-on contact doesnot maneuver as shown in Fig. 14. If aggressively regain-ing course after a stern crossing, the give-way vessel mayreach CPA at a large positive value of contact angle (e.g.,α > 165◦) though this would be an exception to the norm.

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Autonomous Robots

−150 −100 −50 0 50 100 1500%

20%

40%

60%

80%

100%

Angle of Interest φ [deg]

Pro

toco

lSco

re[%

]Example Protocol Function (sin(φ)−1

2 )2

a

b

Fig. 12 The example protocol evaluation function( sin(φ)−1

2

)2 allowsstrong reinforcement of port-to-port passagewhen substituting both rel-ative bearing and contact angle forφ as shown inEq. (13). The plot of theRule 14 cost function (a) demonstrates high reward for near-port angles.The polar plot representation (b) demonstrates the same reward func-tion in a top-down viewmore natural to a collision avoidance encounter.The radius of the polar plot indicates the percentage ofRmax; the origincorresponds to zero while the outer ring corresponds toRmax = 100%.a Example protocol function

( sin(φ)−12

)2. b Polar plot of( sin(φ)−1

2

)2

If the stand-on vessel determines that an in extremis situa-tion exists and maneuvers to starboard, the give-way vesselshould similarly be penalized for failure to act in accordancewith the COLREGS.

A general approach to evaluating a crossing give-waypower-driven vessel under Rule 15 can be seen in Algo-rithms 4 and 15 and includes the following attributes:

−150 −100 −50 0 50 100 1500%

20%

40%

60%

80%

100%

Angle of Interest φ [deg]

Pro

toco

lSco

re[%

]

Example Protocol Function (sin(φ)−12 )4

a

b

Fig. 13 A function such as this fourth-order sinusoidal function allowsfor more severe penalties than those of Fig. 12. a Example protocol

function

(sin(φ)−1

2

)4

. b Polar plot of

(sin(φ)−1

2

)4

– penalize crossing ahead (e.g., − 80◦ < αcpa < 165◦(configurable) where αcpa is the stand-on vessel’s contactangle if no action is taken under Rule 17.a.ii)

– penalize forcing an in extremis maneuver by the stand-onvessel in accordance with Rule 17.a.ii

– penalize give-way requirements of Rule 16 (Sect. 4.2)– include safety penalty for early and substantial actionclause of Rule 16

Requirements of the stand-on vessel in a power-driven cross-ing situation are discussed in Sect. 4.3 and Algorithm 9.

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a b

c d

Fig. 14 Crossing astern is required of a crossing give-way vessel witha risk of collision (Allen 2005). For an initial Rule 15 crossing sce-nario (a), a give-way contact might slow considerably (b) resulting ina contact angle at CPA near αcpa = − 90◦. In (c), the give-way contacthas maneuvered to starboard and maintained speed likely resulting in acontact angle at CPA near αcpa = − 135◦. In (d), the give-way contacthas turned and is about to cross the stern of the stand-on vessel. Becauseof the forward velocity of the stand-on vessel, CPA has likely alreadyoccurred near a contact angle αcpa = − 165◦. a Initial Crossing Geom-etry. b Slowed give-way. c Stern-pointing give-way. d Stern-crossinggive-way

Algorithm 15 Rule 15: Power-driven Crossing1: procedure Pseudocode for Power- driven Crossing Ves-

sels2: if crossing give-way vessel then3: R15/16 ← R16 (Algorithm 4)

crossing give-way vessel must obey Rule 164: R15/16 ← assess pass-ahead penalty

penalize for crossing bow of contact “avoid crossing ahead of the other vessel”

see case law (Allen 2005; Cockcroft and Lameijer 2012; Thomas2001)

5: else if crossing stand-on vessel then6: R15/17 ← R17 (Algorithm 9)

“crossing stand-on vessel must obey Rule 17”7: end if8: end procedure

5 Discussion of COLREGS rules requiringfurther development of evaluationalgorithms

While Sect. 4 presented algorithms for initial evaluation ofRules 13–17, this section presents narratives of other ruleswithin the protocol that require future development. Sec-tion 5.1 presents amplification of methods for Category VIof Table 1. Section 5.2 presents Category I considerations,Sect. 5.3 presents Category II, Sect. 5.4 presents Category IV,

Sect. 5.5 presentsCategoryVI, Sect. 5.6 presentsCategoryX,and Sect. 5.7 presents Category IX all of Table 1.

5.1 Responsibilities of vessels within sight: Rules 11,18

Identification of the contact’s type (e.g., power-driven, sail-ing, etc.) gives necessary knowledge for determining prece-dence under Rule 18. Certain vessels yield right-of-way toothers by the nature of their vessel type; similarly, other ves-sels expect and are afforded right-of-way. To be compliantwith Rule 18, autonomous vessels must be able to correctlyclassify vessel types and properly assign give-way hierarchy.

Detection of another vessel being under sail is insuffi-cient for some scenarios involving multiple sailing craft inthe vicinity of a power-driven autonomous vessel. In orderto anticipate the likely movements of a sailing give-way toavoid a sailing stand-on, each autonomous vessel should beable to identify which sailing vessel is stand-on and whichis give-way to the other. By determining environmental con-ditions such as wind, a power-driven autonomous vessel cananticipate a likely maneuver of a sailing give-way vessel thatmight interfere with ownship’s intentions to give-way to bothsailing vessels.

5.2 General rules (Rules 1–3)

Much debate exists as towhether an autonomous vessel with-out a human physically present constitutes a “vessel” underinternational law. This paper assumes that the definitionaccorded in Rules 1–3 apply equally to any floating struc-ture (or “watercraft”) as if a human were physically presentand operating it. Rule 3 defines the scope of COLREGS toinclude any “vessel” without specification of control, be ithuman, machine, or some combination thereof. The only dis-tinctions drawn by the COLREGS are related to propulsion(e.g., sail, power-driven, etc.) andmaneuverability (e.g., fish-ing, not under command, etc.) constraints. This is consistentwith case law dating back to the nineteenth century (Hen-derson 2006; U.S. Supreme Court 2005; Woerner 2014). Asrecently as 2013, the U.S. Supreme Court rejected a per-manently moored house boat meeting the definition of avessel. In doing so, the court affirmed that the definition ofa vessel is met if a reasonable observer would consider itdesigned to a practical degree for carrying people or thingsover water citing the house boat’s absence of a rudder orsteering mechanism as well as a lack of capacity to generateor store electricity (U.S. Supreme Court 2013).

Accordingly, COLREGS must apply to autonomous ves-sels as though they were human controlled and performingthe same tasks. Rule 3 further stipulates that “Vessels shallbe deemed to be in sight of one another only when one can beobserved visually from the other.” Various work to emulate

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a human lookout by use of on-board sensors and sensor pro-cessing enables “sight,” including cameras, infra-red sensors,and other similar technologies. The COLREGS deliberatelyaddress a visual requirement when two vessels are in “sight”of each other, though this does not exclude non-sight sensors(e.g., radar, lidar, sonar) from assisting with initial detec-tion, classification, or queuing of sight sensors. Similarly, the“restricted visibility” definition of Rule 3 must consider thelimitations of human-operated vessels especially as it relatesto the human-visible spectrum of light; the inherent safetyimplications of entering a restricted visibility constraint evenif an autonomous vessel’s sensors allow greater detectionrange than that of a human operator must be considered.

The intention of the restricted visibility sections of COL-REGS are two-fold:

1. increase detectability to other contacts to maximizedetection range

2. reduce allowable speed while further limiting maneuverdirections to account for and partially mitigate limiteddetection distances.

Autonomous designers require clarification from the inter-national governing bodies as to what officially constitutes“sight” of a non-human controlled vessel.

5.3 General conduct of vessels and special trafficschemes (Rules 4–10)

Rules 4–10 address the requirements of all vessels includingthe stationing of a look-out, use of safe speed, determin-ing risk of collision, the action required to avoid collision,behavior in narrow channels, and behavior in traffic separa-tion schemes (United States Coast Guard 1999). One pointof contention is the requirements of Rule 5 to maintain alook-out. Several boards have been formed in the interna-tional community to address the perceived discrepancy inwhat, if any, non-human means may constitute a look-outin accordance with the COLREGS. This paper assumes thatanymeans of “sight and hearing” whether human or machinemay constitute a look-out so long as it sufficiently functionswithin the spirit of the COLREGS and to the standards of aqualified human lookout.

5.3.1 Rule 5: Lookout

Rule 5 requires a look-out to be stationed “by sight andhearing as well as by all available means appropriate in theprevailing circumstances.” Evaluation should prefer coordi-nation between sight and hearing algorithms consistentwith areasonably trained human look-out. Metrics for Rule 5 underthe assumption of machine-based lookout include:

– listeningwith on-board auditory sensors at all timeswhileunderway.Above-waterline sensorsmust always be func-tional. Sonar may supplement if installed but must neverreplace a surface vessel’s above-waterline auditory sen-sor requirement

– observing with a sufficient combination of on-board non-auditory (visual, radar, lidar, infrared, etc.) sensors at alltimes when underway

– conditionally supplementing with additional on-boardsensors (e.g., radar), off-board sensors (e.g., accompa-nying aerial vehicle), and externally provided data (e.g.,AIS) as necessary.

5.3.2 Rule 6: Safe speed

Environmental factors and ship dynamics predominantlyenter with Rule 6. Rule 6 specifically identifies 12 areas—assuming that the autonomous vessel has radar—requiringevaluation when determining a safe speed. The state of visi-bility, contact density, stopping distance, turning ability, seastate, and draft are just some of the parameters identifiedwhen determining a safe speed. Autonomous vessels must beable to independently determine their effective time-distancecapabilities, turning kinematics and dynamics, and effects ofcontact density when selecting a maximum allowable speedto be fully compliant with Rule 6.

5.3.3 Rule 7: Risk of collision

As in human-operated ship driving, autonomousmarine vehi-cles enjoy widely varying interpretation of what a “risk ofcollision”means based on operating style and design. Severalfactors allow mariners to make assumptions about the othervessel’s level of tolerance when assessing a risk of collisionincluding vessel type, cargo, primary mission, maneuver-ability, and pose. For example, merchant vessels often havesimilar desired ranges at CPA based on common training,similar ship maneuverability characteristics, and maritimecustoms. A liquid Nitrogen gas tanker might have a ten-dency for larger, more conservative ranges at CPA than saya transiting fishing trawler who is more accustomed to highcontact density environments with greater maneuverability.Pose becomes a highly relevant consideration for determina-tion of collision risk. Both pose at CPA and initial pose mustbe considered in conjunction with speed and range whenassessing risk of collision.

Another consideration is the underlying flexibility of thecollision avoidance algorithms. Human operators often usemultiple CPA range thresholds to determine risk of collisionand necessary actions. To determine risk of collision, onemust know the conditions present in the decision space ofthe vessel as well as the vessel’s current capabilities. Forexample, certain crew members offer greater levels of expe-

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Autonomous Robots

rience, while certain machinery conditions or watch-standerconfigurations allow for greater maneuverability or perfor-mance. Requiring the vessel’s Captain or additional watchofficers on the bridge for certain encounter scenarios is oneexample of a modified watch-stander configuration (UnitedStates Navy 1999). These factors directly contribute to thelevel of conservativeness of the subsequent maneuver.

A vessel master’s policy often dictates that certain pre-cautionary measures must be in place before taking contactscloser than certain ranges (United States Coast Guard 2006;United States Navy 1999). This might include certain quali-fied watch-standers present on the bridge, certain machineryconfigurations, or certain environmental conditions. Simi-larly, restricted visibility and other detectability consider-ations must be considered in the determination of risk ofcollision.

Two considerations are specifically required as compo-nents of determination of collision risk, namely, (1) contactswith constant compass bearing with corresponding decreas-ing range, and (2) approaching large vessels, tows, or closerange contacts. If either of these two areas are not explicitlyconsidered in risk determination, an immediate failure scoreis warranted for Rule 7. Additional metrics should includethe appropriate configuration of range thresholds, the tol-erance for determining a constant bearing/decreasing rangescenario, early warning capabilities, and analysis of “scantyinformation”. Such scanty information (United States CoastGuard 1999) might be considered with appropriate weightbased on radar return strength, fusion of other sensor data,and sensor filter settings.

5.3.4 Traffic separation schemes (Rule 10)

Traffic separation schemes comprise a special subset of ves-sel interactions similar to those of driving on a highway witha car. The most prominent solution to driving in this schemeis Szlapczynski (2013). Development of an evaluation algo-rithm for protocol compliance using only track data in futurework would be well served to consider the approaches ofalgorithms such as this.

5.4 Sailing in sight of another sailing vessel (Rule 12)

Sailing vessels must be properly identified in order to dis-criminate precedence per Rule 18 and, in the case of ownshipalso being a sailing vessel, determine stand-on and give-waystatus per Rule 12. In the case of both vessels being undersail, proper identification of the windward side of both ves-sels is required (both wind direction as well as the locationof the mainsail or the largest fore-and-aft sail). Failure toproperly identify other sailing vessels must result in a fail-ure of Rule 12. Further evaluation using the requirements ofRules 16 and 17 applies as appropriate.

5.5 Restricted visibility (Rule 19)

In addition to the discussion of Sect. 5.2, Rule 19 addressessituations of reduced visibility, i.e., when vessels cannot seethe other due to the environmental reasons prescribed inRule 3. Specific checks should be made during algorithmtesting to ensure restrictions are in place to limit speed con-sistent with Rules 6 and 19. The two specific cases addressedin Rule 19.d should be explicitly tested in conditions emu-lating restricted visibility, including:

– ensuring a vessel does not alter course to port for a vesselforward of the beam, except in cases of overtaking

– ensuring a vessel does not alter course toward a vesselabeam or abaft the beam

Testing should also consider the cases of auditory detectionof fog signals ahead of the beam to ensure invocation of thebare-steerage clause of Rule 19.e.

5.6 Lights and shapes (Rules 20–31)

There are two main areas of scope in the lights and shapessection of the COLREGS. First, designers must properly dis-play the required lights and shapes on ownship accordingto certain ship characteristics. This requires self-awarenessof whether a particular section of the COLREGS whichrequires special lights and shapes applies. In addition, theability to actually transmit the appropriate signal for the cor-rect duration of time is required. Second, a vehicle must beable to properly identify lights and shapes of other vesselsincluding assignment of proper meaning. This recognitionand application to the contact directly complements Rule 18requirements of precedence with respect to ownship’s colli-sion avoidance role viz stand-on or give-way. Special lightsand shapes may be necessary for autonomously operatedvessels to display. The community would be well servedby international governing bodies issuing guidance statingwhether a special day shape or light signal is required toidentify autonomously operated vehicles, and if so, makingsuch display or signal standard across the world.5

5.7 Sound and light signals (Rules 32–37)

Quite similarly to the lights and shapes requirements ofSect. 5.6, vesselsmust be able to properly communicate usingsound and light signals in accordance with the COLREGS.Autonomous vessels are in need of clarification of any spe-cial sound or light signals required for autonomous vessels.

5 Submarines operating on the surface are currently the only specialsignal not contained as a requirement within the numbered internationalrules.

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Autonomous Robots

To avoid ad hoc signals intended to indicate an autonomousvessel encountering a human vessel, international governingbodies should provide articulated guidance. Advances in thefield within the scope of this section would focus on multipleareas including:

– receiving a contact’s light and sound signals– interpreting these light and sound signals then influenc-ing ownship’s autonomous collision avoidance behaviorsappropriately

– transmitting light and sound signals to a contact whenownship autonomously determines necessity in accor-dance with the COLREGS.

6 COLREGS testing and evaluation

A COLREGS testing and evaluation software program wasdesigned to be used from a third party neutral “shoreside”observer with assumed perfect sensing data of the vesselsunder observation in Woerner (2016). The purpose of thetesting and evaluation program is to act as a neutral graderof a ship’s performance in complying with the COLREGS,especially in the absence of human intervention. Third partyperfect sensing represents a reasonable assumption for a roadtest or other evaluator entity, as the vessel autonomy couldbe evaluated in a well-sensored testing range with verifiedGPS-based location data recorded for all vessels. A posi-tion reporting protocol such as AIS may prove satisfactory ifreports can be deemed trustworthy.

Futurework could incorporate sensor fusion and imperfectsensing scenarios that would enable this concept to be usedoutside the realm of certification-focused testing and evalua-tion. Scope of the testing and evaluation programwas limitedto power-driven vessel rules, specifically Rules 13–18. Alibrary was developed to allow for both real-time (Sect. 6.3)and post-mission analysis (Sect. 6.4). Complexmulti-vehicleencounters such as the one shown in Fig. 15 are capable ofreal-time or post-mission analysis.

The testing and evaluation program for a multi-contactpower-driven scenario includes the ability to:

– identify that the geometry of two vehicles requires actionper the COLREGS

– identify the specific rules assigned to each vessel– quantify the actions of each vessel with respect to theidentified rules

– generate a report of eachvessel’s actions at the conclusionof the encounter

– populate a scoring system for each vehicle and a cumula-tive performance assessment based on various scenariosand interactions over a specified duration

Fig. 15 COLREGS evaluation will be capable of evaluating complexscenarios such as this non-canonical geometry, multi-rule encounter.Note that multiple collision avoidance rules exist simultaneouslybetween these power-driven vessels

– provide quantified data to support determination of a ves-sel’s scope of COLREGS compliance after performingspecified encounters. Sufficient interactions in variousmulti-vessel, multi-rule scenarios are necessary as partof the “road test” described in Sect. 6.5 and presented inWoerner et al. (2016).

Multi-contact scenarios often involve sets of rules thatrequire differing action. Priority must be assigned as to whataction should be takengiven the larger scopeof the navigationand collision avoidance pictures. Evaluation algorithmsmustaccount for the requirements of individual rules while alsoconsidering the larger contact picture and more overarchingrules of the protocol.

6.1 Library

The protocol-constrained collision avoidance evaluationlibrary allows a common repository for evaluation algo-rithms. The library enables expansion of functionality tomultiple programs using a common set of algorithms whilemaintaining standardized configuration of collision avoid-ance parameters and adaptability to other protocol rule sets.This allows real-time and post-mission analysis programsto use equivalent means of evaluation; however, it alsoallows post-mission evaluation using different penalty func-tions or configuration settings according to the evaluator’spreference. The library of algorithms allows configurationparameters to properly tune weights and metrics to local cus-toms or requirements of certification authorities.

Users may use Eqs. (14)–(17) as an initial library to con-struct relevant evaluation functions based on pose angles.The input angle φ may be configured to use the contactangle α or relative bearing β. A steering angle φ0 allows

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Autonomous Robots

tailorable directionality for alternative use of the same func-tions. An alternative use case might represent a passingarrangement agreed via bridge-to-bridge radio, such as a rareand non-conforming starboard-to-starboard passage. Linearand quadratic functions of range and speed are also availablewithin the initial evaluation library release. Incorporation ofother functions and input parameters is reserved for futurework. These functions are introduced to promote continueddialogue of alternative evaluation functions and approaches,including those rules whose evaluation algorithms have yetto be fully developed.

sin2(φ + φ0) (14)

step(φ) − step(φ0) (15)(

sin(φ + φ0) − 1

2

)2

(16)

(sin(φ + φ0) − 1

2

)4

. (17)

6.2 Configurability of programs

The evaluation programs are configurable for several param-eters of interest to a designer or evaluator including:

– preferred range at CPA– minimum acceptable range at CPA– range at which a near-miss occurs– range at which a collision is assumed– thresholdCOLREGS rule compliance score belowwhichinstantaneous reports should be made

– threshold safety score belowwhich instantaneous reportsshould be made

– vessel types to consider (allows knowledge of aerial,ground, and undersea vehicles without interference ofcollision avoidance evaluation)

– range at which contact detection likely occurs– maximum time threshold allowed for comparison of acontact’s position report and ownship’s position report

– display of visual indicators when configuration ranges orminimum rule compliance scores are violated

– sounding of audible alerts when configuration ranges orminimum rule compliance scores are violated.

6.3 Real-time analysis

Using the protocol library for COLREGS presented in thispaper, a real-time collision avoidance evaluation programgives instantaneous feedback to vessel designers and ameansof real-time evaluation to any certification entity. This can beused to assign penalties or warnings to vessels violating theCOLREGS, especially but not limited to training and designverification scenarios. Notifications can be sent to vessels

Fig. 16 Scoring of COLREGS collision avoidance rules allow for real-time evaluation of vehicle performance at the shoreside observationcenter. Configurable range parameters include nominal detection range,preferred range at CPA, minimum acceptable range at CPA, thresholdrange at which a near-miss occurs, and the range at which a collisionis assumed. An aggregate tally of COLREGS violations (scores belowa configurable threshold value) and of each configuration range aredisplayed. Vehicle types as specified by each vessel are used as a filter toallow consideration of only certain entities within the “visibility” of theshoreside observation center. This allows underwater and aerial vehiclesto share the shoreside observation display without unnecessarily beingconsidered as COLREGS compliance candidates

in the vicinity of non-compliant actors to allow increasedcaution while operating. Reports of egregious actions canbe passed to designers, insurance agencies, or enforcemententities as appropriate or required by statute.

Within the scope of the current work, the real-time proto-col evaluation tool was used to display important informationat the shoreside observation center including:

– COLREGS compliance scores for power-driven rules– safety scores after an encounter– rules required as determined by the observer– range at CPA– time of CPA– vessel names and types.

A real-time text report is posted to the mission con-sole including summaries of overall performance (e.g.,safety, protocol compliance, type of interaction) as shownin Fig. 16. To assist a shoreside observer with several vehi-cles underway, a series of visual and audible indicators wereincorporated to provide real-time warning of dangerous orinappropriate action. Colored range rings (Fig. 17) appearedwhenever violations occurred including:

– green—rcpa less than minimum acceptable CPA range– yellow—rcpa less than near-miss range– red—rcpa less than collision range– blue—COLREGS score less than the threshold value.

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Fig. 17 Violations of range below configurable threshold valuesresulted in displaying range rings including: a green for violating mini-mumdesired range, b yellow for violating near-miss range, and c red forviolating the collision range. Violations of COLREGS collision avoid-ance rules below a configurable threshold value result in display ofa blue ring (d) around the vehicle. Sounding of an optional audibleindicator was also possible for each violation. This COLREGS evalua-tion system allows real-time warning to an evaluator that a dangerouscollision situation or egregious violation of the rules is occurring. aMin-desired range violation. b Near-miss range violation. c Collisionrange violation. d COLREGS violation (Color figure online)

6.4 Post-mission analysis

A post-mission analysis tool was constructed to providedetailed insight into collision avoidance performance of ves-sels. The post-mission analysis requires only vehicle positionlogs; the real-time assessment program was not required tobe running to conduct post-mission analysis.

A report is generated for each run of the post-missionanalysis tool with a configurable scale of verbosity. In moreverbose modes, detailed explanations of cause for scorededuction allows designers and operators to understand therationale for evaluation scores. This can be used to providefeedback and tune future actions. In addition to the verbosityoption, all configuration parameters of Sect. 6.1 are avail-able in the post-mission analysis tool. Evaluation data areexported to a comma-separated value report for ease of metaanalysis in a user’s favorite data analysis program. This datacan then be used for performance analysis by vehicle, byrule combination, or by other parameters of interest to theevaluator.

6.5 Informing the COLREGS certification road test

In order to certify autonomous collision avoidance algo-rithms for on-water use outside of a testing environment,a road test comprised of a comprehensive scope of examina-

tion and quantifiable metrics of performance was describedin Woerner et al. (2016). To be compliant with the appro-priate protocol rule set of COLREGS, a satisfactory level ofperformance must be met across each category of evalua-tion. The categories of Sect. 2 comprise the evaluation areasfor this test and are the principal means for the road test ofWoerner et al. (2016) to be performed. Differing degrees ofroad tests may be possible for various levels of certificationfor operation.

7 Conclusion

This paper defined metrics and algorithms to quantifyprotocol compliance and safety for autonomous collisionavoidance. A library of functions was proposed to allow con-figuration of the protocol evaluation tools in both real-timeand post-mission analysis. Specific instantiation of protocolquantification and evaluation was demonstrated for the rulesof the road for sea-going vessels, i.e., COLREGS.

Real-time on-vehicle instantiations of the COLREGSevaluation program in this paper are possible to detect non-compliance of other vessels and adjust collision avoidanceparameters accordingly. Future work will allow a vessel todetect vessels with compliance scores less than a thresholdvalue and choose to maneuver sooner than normal or seek amore conservative range or pose at CPA.

Future work will enable third-party evaluation of thefull rule sets rather than limitation to power-driven vessels.Further work is required to more fully model contact-freeintentions when maintaining course and speed of a stand-onvessel in complex scenarios such as slowing to pick up a pilot.Further discussion and research is needed to fully incorpo-rate local customs and laws within COLREGS (includingU.S. Inland Rules), alternative protocols such as Rules of theAir, and special arrangements such as those made by bridge-to-bridge radio. Alternative approaches to evaluating posemay show cases where safety functions are more limited attimes other than the closest point of approach.

Before integrating human controlled and autonomoussystems outside of laboratory environments, the commonpractices, customs, and interpretations of the COLREGS bymanned operators must be fully understood. Autonomousdesigns that incorporate expectations and norms of humanoperators will achieve solutions that more naturally integrateautonomous and human-operated vessels. The categoriza-tion of scope and the incorporation of the nuance, applicablecase law, and customs related to COLREGS allows appro-priate and quantifiable assessment of autonomous collisionavoidance performance. The International Maritime Organi-zation, and other governing bodies, may choose to includethese metrics as a means to inform both regulation and policyin maritime collision avoidance protocols.

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Kyle Woerner is a post-doctoralresearcher at MIT’s Computer Sci-ence and Artificial Intelligence Lab-oratory. He received his BS in Sys-tems Engineering from Washing-ton University in St. Louis. Heholds an SM in Mechanical Engi-neering, Degree of Naval Engineer,and Ph.D. (Autonomy and MarineRobotics) from MIT. He currentlyserves as a Lieutenant Comman-der in the United States Navy withsignificant on-water experience inmaritime collision avoidance. Hisresearch focuses on autonomous

collision avoidance and human-robot collaboration.

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Autonomous Robots

Michael R. Benjamin is a researchscientist in the Center for OceanEngineering, a part of the Depart-ment of Mechanical Engineering atMIT. He is also a member of theLaboratory for AutonomousMarine Sensing Systems and theMarine Robotics Group in the Com-puter Science and Artificial Intelli-gence Laboratory. Until December2010, he worked with the NavalUndersea Warfare Center in New-port Rhode Island. In October 2014,he and his students competed andwon the 2014 International Mar-

itime RobotX Challenge. His work focuses on algorithms and softwarefor autonomous marine vehicles. In 2007 he founded moos-ivp.org atMIT, hosting the MOOS-IvP open source project in marine autonomysoftware.

Michael Novitzky is a postdoc asso-ciate in the Laboratory for MarineSensing Systems at MIT. He is alsoan Engineer at Duckietown Engi-neering Co, which is a fictionalstart-up used to teach the classMIT 2.166 Autonomous Vehicles.He completed his Ph.D. at theGeorgia Institute of Technologyunder the supervision of Profes-sor Tucker R. Balch in the Multi-Agent Robotics Systems (MARS)group.

John J. Leonard is Samuel C.Collins Professor of Mechanicaland Ocean Engineering and Asso-ciate Department Head forResearch in the MIT Departmentof Mechanical Engineering. He isalso a member of the MIT Com-puter Science and Artificial Intel-ligence Laboratory (CSAIL). Hisresearch addresses the problems ofnavigation and mapping forautonomous mobile robots. Heholds the degrees of B.S.E.E. inElectrical Engineering and Sciencefrom the University of Pennsylva-

nia (1987) and D.Phil. in Engineering Science from the University ofOxford (1994). Prof. Leonard joined the MIT faculty in 1996, afterfive years as a Post-Doctoral Fellow and Research Scientist in the MITSea Grant Autonomous Underwater Vehicle (AUV) Laboratory. Hewas team leader for MIT’s DARPA Urban Challenge team, which wasone of eleven teams to qualify for the Urban Challenge final event andone of six teams to complete the race. He served as Co-Director of theFord-MIT Alliance from 2009 to 2013. He is the recipient of an NSFCareer Award (1998) and the King-Sun Fu Memorial Best Transac-tions on Robotics Paper Award (2006). He is an IEEE Fellow (2014).

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