hazard avoidance for high-speed mobile robots in rough...

Hazard Avoidance forHigh-Speed Mobile Robots in

Rough Terrain

Matthew Spenko, Yoji Kuroda,Steven Dubowsky, and Karl IagnemmaDepartment of Mechanical EngineeringMassachusetts Institute of TechnologyCambridge, Massachusetts 02139e-mail: [email protected]

Received 13 October 2005; accepted 21 February 2006

Unmanned ground vehicles have important applications in high speed rough terrain sce-narios. In these scenarios, unexpected and dangerous situations can occur that requirerapid hazard avoidance maneuvers. At high speeds, there is limited time to perform navi-gation and hazard avoidance calculations based on detailed vehicle and terrain models.This paper presents a method for high speed hazard avoidance based on the “trajectoryspace,” which is a compact model-based representation of a robot’s dynamic performancelimits in rough, natural terrain. Simulation and experimental results on a small gasoline-powered unmanned ground vehicle demonstrate the method’s effectiveness on slopedand rough terrain. © 2006 Wiley Periodicals, Inc.

1. INTRODUCTION AND BACKGROUNDLITERATURE

Many important military, disaster relief, search andrescue, and surveillance applications would benefitfrom an unmanned ground vehicle �UGV� capable ofmoving safely at high speeds through rough, naturalterrain of varying compositions and physical param-eters �Gerhart, 1999; Walker, 2001�. High-speed UGVscan reach their target location in less time than theirlow-speed counterparts, increase reconnaissance ef-

fectiveness by traversing more terrain in a fixedamount of time, and spend less time in unsafesituations.

Often a UGV is directed to follow a preplannedroute �or navigate among predefined waypoints� gen-erated by an off-line planning algorithm using coarsetopographical map data. In natural terrain at highspeeds, dangerous situations unforeseen by the high-level planner are likely to occur that require a UGV toquickly execute an emergency maneuver. These maybe the result of outdated topographical map data,unidentified hazards due to sensor limitations or er-rors, or unanticipated physical terrain conditions. De-spite ever increasing computing power, at highspeeds there is little time to accurately model com-

Contract grant sponsors: U.S. Army Tank-automotive and Arma-ments Command and the Defense Advanced Research ProjectsAgency.

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Journal of Field Robotics 23(5), 311–331 (2006) © 2006 Wiley Periodicals, Inc.Published online in Wiley InterScience (www.interscience.wiley.com). • DOI: 10.1002/rob.20118

plex and detailed vehicle/terrain interactions in realtime and perform navigation based on these models.

This paper presents a local replanning algorithmfor emergency hazard avoidance situations appli-cable to UGVs traveling at high speed on rough natu-ral terrain. Note that “high speed” is a function of ve-hicle geometry and terrain and is loosely defined hereas speeds that excite vehicle dynamic effects, such asrollover, ballistic motion, sideslip, and wheel slip. Theproposed algorithm considers the effects of terrain in-clination, roughness, and traction. In addition, it gen-erates dynamically feasible paths by construction andis computationally efficient. The paper does not focuson path following or sensing, although they are rec-ognized as important and necessary components fora comprehensive unmanned ground vehicle.

1.1. Problem Formulation and Key Assumptions

In this paper, a UGV is assumed to be following anominal �preplanned� path, xnominal�s�= �x�s� ,y�s��, s� �s0 ,sf�. Associated with xnominal is a nominal trajec-tory comprised of a vehicle’s desired velocity andpath curvature, �nominal�s�= ��s� ,��s��. There exists aunique mapping from a vehicle’s trajectory to itspath given the vehicle’s initial curvature, heading,and position.

Hazards are defined as discrete objects or terrainfeatures that significantly impede or halt UGV mo-tion, such as trees, boulders, ditches, knolls, and ar-eas of poorly traversable terrain �e.g., water or verysoft soil�. Hazards are assumed to be detected byon-board range sensors. It is recognized that hazarddetection and sensing are important aspects of UGVmobility and an active research topic �Fish, 2003;Shoemaker & Borenstein, 2000�; however, it is not afocus of this work.

A terrain patch is described by its average roll��, pitch ��, roughness ��, and traction coefficient��. It is assumed that coarse estimates of the tire/ground traction coefficient and ground roughnessare known or can be determined online using cur-rently available techniques �Arakawa & Krotkov,1993; Iagnemma, Kang, Brooks & Dubowsky, 2003;Manduchi, Castano, Talukder & Matthies, 2005�.

The vehicle is assumed to be equipped with aforward-looking range sensor that can measure ter-rain elevation and locate hazards up to several ve-hicle lengths ahead; an inertial navigation sensorthat can measure the vehicle’s roll, pitch, yaw, rollrates, pitch rates, yaw rates, and translational accel-

erations with reasonable uncertainty; and a globalpositioning system that can measure the vehicle’sposition and velocity in space with reasonableuncertainty.

1.2. Background Literature Review

Hazard avoidance for UGVs has been traditionallyperformed by selecting from a set of candidate paths�i.e., search techniques over small spaces� or throughthe use of reactive �reflexive� behaviors. Other pro-posed methods of interest include potential fields,mixed-integer-linear programming, the curvature-velocity method �Simmons, 1996�, and the dynamicwindow approach �Fox, Burgard & Thrun, 1997�.Many of the techniques have been designed for useon flat or slightly rolling terrain at speeds that donot excite the vehicle dynamics. This paper ad-dresses hazard avoidance on flat, rough, and uneventerrain at speeds that excite vehicle dynamics.

Previous researchers have addressed this prob-lem with a search-based technique to navigate aHMMWV-class vehicle at speeds up to 10 m/s whileavoiding large hazards �Coombs, Lacaze, Legowik &Murphy, 2000�. The method relies on a precomputeddatabase of approximately 1.5�107 clothoidal paths.Since the vehicle is assumed to travel on relativelyflat terrain at fairly low speeds, the model used inthe calculations does not consider vehicle dynamics.An online algorithm eliminates candidate clothoidsthat intersect with hazards or are not feasible giventhe initial steering conditions. From the remainingpath, the algorithm chooses one that follows themost benign terrain. Several contenders of the 2005DARPA Grand Challenge utilize similar approacheswhich have proven to be successful for speeds inexcess of 8 m/s. However, the techniques do notconsider the important aspects of terrain roughness,inclination, and vehicle/terrain traction characteris-tics, all of which will become increasingly more im-portant as autonomous vehicles move from travers-ing roads and relatively benign terrain to moredangerous and extreme topography.

In another successful technique, a UGV uses avoting scheme to evaluate several forward simu-lated candidate paths through a terrain region �Kelly& Stentz, 1998�. An arbitrator chooses the path clos-est to the goal location that does not impact a haz-ard. This method has been experimentally demon-strated on a HMMWV-class vehicle at speeds up to4.5 m/s on natural terrain. This work employs kine-

312 • Journal of Field Robotics—2006

Journal of Field Robotics DOI 10.1002/rob

matic UGV models to evaluate potential paths, anddoes not account for dynamic vehicle effects, such asrollover and sideslip. An extension of this work pro-poses to limit the set of initial candidate paths byplacing constraints on the space of a vehicle’s veloc-ity and curvature �Sanjiv & Kelly, 1996�. This is simi-lar in some ways to the method presented in thispaper; however, this methodology again does notconsider dynamic effects that can be important athigh speeds.

Another class of techniques applied to mobilerobot navigation in natural terrain relies on reactivebehaviors that generate a specific action in responseto online sensor signals �Brooks, 1986�. A successfulreactive behavior technique for outdoor hazardavoidance arbitrates between hazard avoidance andgoal seeking and allows for UGV navigation atspeeds of up to 1 m/s �Daily et al. 1998; Olin &Tseng, 1991�. Another approach defined five candi-date behaviors that “voted” for or against a set ofsteering angles: “avoid obstacles,” “follow the road,”“seek the goal,” “maintain heading,” and “track thepath” �Langer, Rosenblatt & Hebert, 1994�. The steer-ing angle with the most votes was then executed.Although both of these techniques have been suc-cessful at low to moderate speeds, none explicitlyconsider vehicle dynamics and terrain characteristicswhich can result in trajectories that are impossiblefor a UGV to safely execute at high speeds on roughterrain.

Potential field methods have also been appliedto mobile ground robots in natural terrain �Chanclou& Luciani, 1996; Haddad, Khatib, Lacroix & Chatila,1998�. These methods define a potential field in Car-tesian space with goal locations corresponding to“sink” functions and hazard locations correspondingto “source” functions. A vehicle then navigates to-ward points of increasingly low potential. Thesetechniques have proven successful for slow movingUGVs on flat terrain; however, they do not considerthe effects of robot dynamics, terrain inclination,roughness, or traction. A potential field method hasrecently been developed for high speed vehicles onrough terrain that does consider these effects �Shi-moda, Kuroda & Iagnemma, 2005�. This work uti-lizes the trajectory space framework presented inthis paper.

Two similar approaches of interest are thecurvature-velocity method �Simmons, 1996� and thedynamic window technique �Fox, Burgard & Thrun,1997; Brock & Khatib, 1999; Philippsen & Siegwart,

2003�. Both consider the effects of velocity and accel-eration constraints on synchro-drive robots operat-ing in indoor environments. A two-dimensionalspace consisting of a vehicle’s translational and rota-tional velocities is created. Velocity combinationsthat cannot be reached due to acceleration con-straints and obstacle locations are removed from thisspace. A translational and rotational velocity is thenchosen from the space by maximizing an objectivefunction. Both the curvature-velocity method anddynamic window approach have similar elements tothe trajectory space method described in this paper.However, they do not consider critical vehicle/terrain interactions, vehicle dynamic effects, or ter-rain inclination.

In summary, numerous techniques have beendeveloped for navigation and hazard avoidance ofUGVs. In general, these techniques do not explicitlyconsider dynamic vehicle and terrain effects that areimportant for UGVs traversing rough terrain at highspeeds. A method that considers these effects and iscomputationally tractable is the objective of thiswork.

2. TRAJECTORY SPACE DESCRIPTION

The hazard avoidance algorithm presented here isbased on the trajectory space, defined as the two-dimensional space of a vehicle’s instantaneous longi-tudinal velocity, �, and path curvature, � �Spenko,Iagnemma & Dubowsky, 2004�. A UGV’s “position”in the trajectory space is a velocity-curvature pair�� ,��. The relationship of a point in the trajectoryspace and a vehicle maneuver is illustrated in Figure1. Velocities are limited to positive values in thiswork. A transition between two points in the spacecan be thought of as a simple maneuver.

The trajectory space is a useful space for UGVnavigation for two reasons. First, points in the trajec-tory space easily map to the points in UGV actuationspace �generally consisting of one throttle/brake con-trol input and one steering angle control input�. Thus,navigation algorithms developed for use in the tra-jectory space will map to command inputs that obeyvehicle nonholonomic constraints. Second, con-straints related to terrain parameters including incli-nation, roughness, and traction and to dynamic ef-fects, such as UGV rollover and sideslip are easilyexpressible in the trajectory space, since these effectsare strong functions of velocity and path curvature.

Spenko et al.: Hazard Avoidance for High-Speed Mobile Robots in Rough Terrain • 313


Sections 2.1 and 2.2 describe computation ofthese constraints using simple UGV and terrain mod-els. These computationally efficient, low-order mod-els have been shown to sufficiently capture the im-portant vehicle dynamics and vehicle/terraininteractions.

2.1. The Dynamic Trajectory Space

The dynamic trajectory space is a subspace of thetrajectory space that consists of velocity-curvaturepairs that correspond to dynamically feasible ma-neuvers on a given terrain patch. Dynamically fea-sible maneuvers are here defined as maneuvers thatdo not self-induce vehicle failure due to excessivesideslip �i.e., skidding� or rollover and are physicallyattainable considering vehicle steering properties.

2.1.1. Sideslip Constraint Computation

Although some sideslip is expected and likely un-avoidable, substantial slip that causes large headingor path following errors is detrimental. A constraintfunction relating UGV velocity and path curvatureto lateral traction limits can be derived from the freebody diagram shown in Figure 2, assuming �=0 and�=0. Here �xyz� represents a body-fixed coordinateframe and �XYZ� represents an inertial frame.

For simplicity vehicle roll and pitch are assumedto be equal to the roll and pitch of the terrain be-

neath the vehicle. Hence, suspension travel is ne-glected. The vehicle roll ��, pitch ��, and yaw ��associated transformation matrices are

G� = �cos � 0 − sin �

0 1 0

sin � 0 cos �� ,

G� = �1 0 0

0 cos � sin �

0 − sin � cos �� ,

G = � cos sin 0

− sin cos 0

0 0 1� . �1�

The acceleration due to gravity in �xyz� following aroll, pitch, yaw transformation is thus: gxyz=G�G�GgXYZ, where gxyz= �gx gy gz�T. A vehicle be-gins to skid when the traction force is equal to thesum of the centripetal and gravitational force compo-nents. In this simplified analysis, accelerations otherthan gravity in the z direction are ignored. The pre-dicted maximum curvature before skidding occurscan be computed as

�slipmin,max =

− gx ± �gz

�2 . �2�

The two solutions correspond to downslope/upslope travel. Treating Eq. �2� as a constraint func-tion, the sideslip space is defined as:

Definition 1 „Sideslip Space…: The sideslip space,A, is the set of velocity and curvature pairs that do notinduce vehicle sideslip on a given terrain patch:

Figure 1. Representation of vehicle action as described bycoordinates in the trajectory space.

Figure 2. Sideslip vehicle model.



A��,�,�,�� ∀��slipmin � �slip

max� . �3�

Figure 3�a� illustrates the variation of the side-slip constraint as a function of traction coefficient. Asexpected, as the traction coefficient increases �at afixed speed� a UGV can safely execute maneuvers ofincreasing curvature. Figure 3�b� illustrates thevariation of the sideslip constraint as a function ofterrain inclination. The sloped terrain constraint cor-responds to a UGV traversing a side slope of 30°with the fall line perpendicular to the vehicle’s head-ing �negative curvatures represent a downslopeturn�. As expected the UGV can safely execute adownslope turn at higher velocity than it can ex-ecute an upslope turn, as a result of the interactionof centripetal acceleration and gravity.

Clearly the sideslip model presented here doesnot include potentially significant effects such asload transfer; however it is employed due to its sim-plicity and has shown to be reasonably accurate inpractice �Spenko, 2005�.

2.1.2. Rollover Constraint Computation

Rollover is generally undesirable despite the factthat some UGVs are designed to be invertible�Walker, 2001�. A trajectory space constraint for ve-hicle rollover can be computed from analytical mod-els of varying complexity. Here a rigid body modelis presented, although models that consider the ef-fects of tire stiffness and suspension compliance arealso available �Spenko, 2005; Chen & Peng, 1999�.

Rollover is initiated when the body force vectorexpressed at the vehicle center of mass is directedoutside the convex polygon formed by the tire/terrain contact points. For a UGV with a wheelbasegreater than its track width, this most commonly oc-curs when the moment about either of the points Ain Figure 2 is equal to zero. The resulting constraintfunction for the rollover space is

�rollovermax,min =

dgz ± hgx

h�2 , �4�

where d is one-half of the axle length, h is the centerof mass height, and � is the vehicle’s longitudinalvelocity. The two solutions correspond to upslope/downslope travel. This model has been found ex-perimentally to accurately predict rollover on flat,smooth terrain �Spenko, 2005�. The effect of terrainroughness of the accuracy of this model is investi-gated in Section 2.3.

Definition 2 „Rollover Space…: The rollover space,B, is the set of velocity and curvature pairs on a giventerrain patch that do not induce vehicle rollover:

B��,�,�� ∀��rollovermin � �rollover

max � . �5�

Similar to Figure 3�b�, the rollover constraintwill vary as a function of terrain inclination.

2.1.3. Steering Constraint Computation

Steering constraints describe the limitations imposedby a UGV’s kinematic steering and handling proper-ties on its attainable maneuvers. Here, front-steered

Figure 3. Sideslip constraint comparison for varying �a�traction coefficient and �b� inclination.



vehicles that can exhibit neutral-, over-, or under-steer are considered. Many factors contribute to de-termining if a vehicle will exhibit oversteer or under-steer �Gillespie, 1992�. Tire cornering properties andthe location of the center of mass are major influ-ences, and their effects are investigated here.

The slip angle, �, is the angle between the head-ing direction of the tire and the direction of travel�see Figure 4�. At low slip angles �typically �5°�,the relationship between the cornering force and slipangles is approximately linear �Gillespie, 1992�:

Ff,r = Ck�f,r, �6�

where Ck is the cornering stiffness of the tire. Sum-ming the lateral forces acting on the vehicle resultsin

Ff cos � + Fr = m�2� ± mgx. �7�

Summing the moments about the center of massyields

Fflf cos � = Frlr. �8�

Combining Eqs. �6�–�8� and linearizing about �=0yields

�f,r =m��2� ± gx�

Ck�1 +lf,r

lr,f� . �9�

By examining Figure 4, it is evident that

� = L� + �f − �r. �10�

Combining Eqs. �9� and �10� and yields a constraintfunction for the steering space:

�steeringmin,max =

CkL�max ± mgx�lf − lr�CkL

2 + m�2�lr − lf�. �11�

Definition 3 „Steering Space…: The steering space,C, is the set of velocity and curvature pairs that are at-tainable given a vehicle’s kinematic configuration and tireparameters:

C��,�,�,�,m,Ck,lf,r� �∀��steeringmin � �steering

max � .

�12�

Figure 5 illustrates the difference in steering con-straints for generic understeered and oversteeredvehicles.

Figure 4. Single-track vehicle model for steering mecha-nism limit computation �adapted from Gillespie, 1992�.

Figure 5. Illustration of comparison of steering limits forover/understeered vehicles.



2.1.4. Drive Train Constraint Computation

Generally a UGV’s maximum forward velocity is afunction of the drive train characteristics, rolling re-sistance, aerodynamic drag effects, and terrain incli-nation. Here a trajectory space constraint related tomaximum forward velocity is computed from themodel in Figure 6.

For this system, summing the forces in the y di-rection yields

my = Fpowertrain − Fdrag − Frolling − mg sin . �13�

A model of the force generated by a general UGVpower train can be written as

Fpowertrain =T��G

r, �14�

where T�� is the torque, G is the transmission ratio,and r is the wheel radius. The aerodynamic dragforce on a vehicle can be modeled by the relation�White, 1994�

Fdrag =12

�ArCd��2, �15�

where � is the density of air, Ar is the reference areaof the vehicle, and Cd is the drag coefficient. Therolling resistance acting on a wheeled vehicle can bemodeled by the relation �Beer & Johnston, 1988�

Frolling = Crrmg cos , �16�

where Crr is the coefficient of rolling resistance.Combining Eqs. �15� and �16� and setting y=0 yieldsthe maximum vehicle forward velocity, which can betreated as a constraint function on the drive trainspace:

�max = 2�T��G − rCrrmg cos − rmg sin �r�Cd

.

�17�

Definition 4 „Drive Train Space…: The drive trainspace, D, is the set of velocity and curvature pairs that areattainable on a given terrain patch given a vehicle’s drivetrain and aerodynamic properties:

D��,�,�,�,�� ∀�0 � � � �max� , �18�

where �max is the maximum vehicle velocity.The sideslip space, rollover space, steering

space, and drive train space are subspaces of the tra-jectory space constrained by various functions re-lated to UGV mobility. Together they comprise thedynamic trajectory space.

Definition 5 „Dynamic Trajectory Space…: Thedynamic trajectory space, �, is the set of velocity andcurvature pairs that are attainable on a given terrainpatch given a vehicle’s dynamic, steering, and drive trainproperties:

� A � B � C � D . �19�

Figure 7 shows an illustration of the dynamictrajectory space. The dynamic trajectory space repre-sents all kinematically and dynamically feasiblevelocity-curvature pairs for a particular vehicle on aparticular terrain patch.

2.2. The Hazard Trajectory Space

In Section 2.1, models were presented for computingtrajectory space constraints that limit the space ofmaneuvers that are safely attainable on a given ter-rain patch at a given instant. Physical hazards �suchas large rocks, trees, deep water, etc.� also limit thespace of safely attainable maneuvers.

Hazards can be generally classified as belongingto one of two types: Trajectory independent hazards

Figure 6. Simple drive train vehicle model.



and trajectory dependent hazards. A trajectory inde-pendent hazard, such as a large tree, boulder, or wa-ter trap, is one that a vehicle cannot safely travelacross, over, or through independent of approachvelocity and direction. A trajectory dependent haz-ard is one where safe traversal depends on the ve-hicle approach velocity and/or direction, such as ashallow ditch where at high velocities a UGV maybe able to achieve ballistic motion and successfully“jump” the ditch.

The hazard trajectory space is defined as thespace of velocity-curvature pairs that, at the currentUGV position, would result in a collision betweenthe vehicle and hazard. For a trajectory independenthazard, curvatures between �hazard

max and �hazardmin in Fig-

ure 8 would thus belong to the hazard trajectoryspace. The minimum and maximum curvatures as-sociated with a hazard, �hazard

max and �hazardmin , are gener-

ally functions of a vehicle’s velocity due to the factthat vehicles follow clothoidal paths, which corre-spond to the steering angle changing with constantvelocity, when transitioning between curvatures�Spenko, 2005�. An illustration of the hazard trajec-tory space for a trajectory independent hazard isshown in Figure 9�a�. An illustration of the hazardtrajectory space for a trajectory dependent hazard isshown in Figure 9�b�.

Definition 6 „Hazard Trajectory Space…: The haz-ard trajectory space, �, consists of curvatures and veloci-

ties that, if maintained from the current vehicle position,would lead to intersection with a hazard.

�� ∀��,��hazardmin � � � �hazard

max ,�hazardmin � �

� �hazardmax �. �20�

Note that there are no limitations as to the numberof hazards that can appear in the trajectory space.The hazard trajectory space is generated by evaluat-ing a precomputed library of clothoidal paths thatconnect the current location in the trajectory space toother locations.

2.3. Effect of Roughness on Trajectory SpaceConstraints

The above models of UGV mobility have assumedthat the terrain is smooth. Terrain roughness influ-

Figure 7. Dynamic trajectory space �shaded region� illus-tration for an oversteered vehicle on flat terrain.

Figure 8. Illustration of maximum and minimum curva-tures necessary to avoid impact with a hazard.

Figure 9. Illustration of hazard trajectory space for: �a�Trajectory independent hazard and �b� trajectory depen-dent hazard.



ences UGV mobility by inducing variation in thewheel normal forces, which affects cornering andstability properties. The effect of terrain roughnesson UGV sideslip and rollover has been studied insimulation �Spenko, 2005�. Representative results foran analysis of UGV rollover are shown in Figure 10.

It can be observed that as terrain roughness in-creases �represented by an increasing fractal num-ber�, the variation in velocity and curvature at whichrollover is initiated increases. In general, terrainroughness tends to induce variation in the locationof trajectory space constraints. Based on this obser-vation, researchers have suggested that a probabilis-tic representation of vehicle mobility is a more use-ful analysis tool than a deterministic �i.e., “go/no-go”� analysis �Golda, 2003�. A more thoroughdiscussion of the effect of terrain roughness on tra-jectory space constraints can be found in Spenko�2005�.

2.4. The Admissible Trajectory Space

Not all points in the trajectory space can be reached,or transitioned to, from another point in a given timet, due to limits on UGV acceleration, deceleration,and steering rate. Thus, not all maneuvers are physi-cally realizable. Knowledge of the set of reachablemaneuvers is important during navigation, sinceUGVs often have a limited amount of time to reactto impending hazards.

A maneuver is defined as a transition betweentwo arbitrary velocity-curvature pairs. A maneuveris characterized by an initial trajectory, �0= ��0 ,�0�, afinal trajectory, �f= ��f ,�f�, and a distance s overwhich the maneuver occurs and can be described bythe quintuple �= ��0 ,�f ,�0 ,�f ,s�. A maneuver canthus be defined as:

Definition 7 „Maneuver…: A maneuver, �, is atransition of any general shape from one location in thetrajectory space �0= ��0 ,�0� to another, �f= ��f ,�f� over adistance s.

For a UGV with a location inside the trajectoryspace of ��0 ,�0�, the maximum attainable velocity intime t is

�reachablemax,min = �0 ± at , �21�

where a is the �assumed to be constant�acceleration/deceleration parameter. The maximumand minimum attainable curvatures for a front-steered vehicle in time t are

�reachablemax,min �� = �0 ± �maxt , �22�

where �max is the maximum rate of change of curva-ture, given as �see Figure 4�

�max =tan �max

L, �23�

where �max is the maximum steering rate of changeand is assumed to be constant.

The reachable trajectory space, �, which de-scribes a space of physically attainable maneuvers,can then be defined:

Definition 8 „Reachable Trajectory Space…: Thereachable trajectory space, �, is the set of admissible ve-locity and curvature pairs a vehicle can transition to in agiven time t from an initial location ��0 ,�0�.

The admissible trajectory can now be defined.An example is shown in Figure 11.

Definition 9 „Admissible Trajectory Space…: Theadmissible trajectory space, �, is the space of all dynami-cally admissible velocity and curvature pairs on a giventerrain patch that can be transitioned to in a given time tfrom an initial location ��0 ,�0� given a vehicle’s dynamic,steering, and drive train properties:

� = � � � . �24�

Figure 10. Comparison of rollover constraints on smoothand rough terrain.



3. HAZARD AVOIDANCE AND PATHRESUMPTION ALGORITHM DESCRIPTIONS

The trajectory space framework presented in Section2 yields an instantaneous description of a UGV’s mo-bility properties on a given terrain patch. During highspeed navigation, however, a hazard avoidance algo-rithm must predicatively analyze mobility over ter-rain in front of the UGV. In this section, a hazardavoidance algorithm is presented that employs pre-dictive analysis of UGV mobility over local terrain us-ing the trajectory space framework presented in Sec-tion 2.

Consider a scenario similar to that illustrated inFigure 12. Here, a UGV attempts to follow a pre-planned nominal desired path, xnominal, given by ahigh-level path planner. As discussed in Section 1.1,the nominal desired path has a corresponding nomi-nal desired trajectory, �nominal. An on-board forward-looking range sensor measures elevation and detectshazards in the local terrain region, which is dividedinto discrete patches. Calculation of the appropriatesize and number of these patches is an important is-sue, but is not discussed here �Spenko, 2005�. Notethat by separating the terrain into patches, it is pos-sible to account for the differences in terrain profilethat will exist in the current sensor scan. In general,the size and number of terrain patches is related tothe desired accuracy of the terrain inclination estima-tion used to compute the total admissible trajectory

space. As the number of terrain patches increases, theestimated terrain roll and pitch for each patch be-comes more accurate.

A hazard avoidance maneuver is enacted if either�or both� of two situations occurs: �1� A hazard lies onthe vehicle’s current desired path, xnominal; 2� An el-ement of �nominal whose corresponding path, xnominal,lies in the ith terrain patch violates a trajectory spaceconstraint corresponding to that patch. In otherwords, a UGV is commanded to follow a dynamicallyinadmissible trajectory.

At each sampling instant the hazard avoidancealgorithm can be outlined as follows:

1. Acquire range sensor scan of surroundingterrain and discretize terrain into m patches;

2. compute trajectory space constraints �Eqs.�3�, �5�, �12�, and �18�� of every terrain patch;

3. if a hazard lies on the vehicle’s current de-sired path, xnominal or an element of �nominalwhose corresponding path, xnominal lies in theith terrain patch violates a trajectory spaceconstraint corresponding to that patch, selecta hazard avoidance maneuver;

4. compute a path resumption maneuver thatwill connect the end of the path generated bya hazard avoidance maneuver to the nominaldesired path.

Figure 11. Admissible trajectory space for a HMMWV-class vehicle.

Figure 12. Nominal desired path with terrain patches.



Step 1 is an important issue but is not a focus ofthis work. Step 2 has been described in Section 2.Steps 3 and 4 are described in the following sections.

3.1. Hazard Avoidance Maneuver Selection

Hazard avoidance maneuvers are dynamically ad-missible modifications of a UGV’s nominal trajectoryinitiated by the presence of a hazard or dynamicallyunsafe trajectory. A hazard avoidance maneuver is asubset of the generalized maneuver described inDefinition 7. It is composed of two segments that aretruncated ramps of the highest possible slope. Thefirst consists of a transition between the initial trajec-tory, �0= ��0 ,�0�, and final trajectory, �f= ��f ,�f�. Thesecond consists of a constant velocity and curvatureover a fixed distance �see Figure 13�. The total lengthof the maneuver is s=sf−s0. Thus, the velocity profileof a hazard avoidance maneuver, �h��, can be de-scribed by

�h�� = ��0 +d�

ds�s − s0� for s0 s � s�,

�f for s� s � sf.� �25�

The curvature profile of a hazard avoidance ma-neuver, �h��, can be described by

�h�� = ��0 +d�

ds�s − s0� for s0 s � sk,

�f for sk s � sf,� �26�

where s0 is the initial starting point of the maneuver,sf is the final point of the maneuver, and s� and s� aregiven as

s� = s0 ±�f

2 − �02

2a, s� = s0 ± ��f − �0

�max� , �27�

where � is the average velocity over the time re-quired to reach the final curvature.

When a hazardous situation is detected, an ap-propriate hazard avoidance maneuver must be se-lected. In this work, the selected maneuver must bedynamically admissible over all local terrain patches�and not just patches intersecting xnominal� to conser-vatively ensure maneuver safety.

For a terrain region that has been discretizedinto m patches, let �j denote the admissible trajec-tory space for each terrain patch, j� �1,m�. Let p bethe number of hazards in the current sensor scan,and let Hk denote the hazard trajectory space foreach hazard, k� �1,p�. Then the total admissible tra-jectory space, Z, is defined as:

Definition 10 „Total Admissible TrajectorySpace…: The total admissible trajectory space, Z, is theintersection of admissible trajectory spaces for every ter-rain patch minus the hazard trajectory space, H, for eachhazard in the current sensor scan:

Z ��1 � . . . � �m� − H1 − �2 − . . . − �p. �28�

The total admissible trajectory space is a repre-sentation of all safe dynamically admissible andreachable trajectories through a local terrain fromthe UGV’s current position. The goal of the hazardavoidance algorithm is thus to find a maneuver, �h,such that �f= ��f ,�f��Z. This maneuver transitions aUGV from a point in the total admissible trajectoryspace that violates a constraint to one that does not.

There are numerous techniques for finding �fthat results in a “good” maneuver. Here, a simpleand effective search-based method is proposed. Inthis approach, the trajectory space is discretized intoclosely spaced points. This discretized trajectoryspace is then treated as a graph, and �f is chosen asthe point that minimizes the distance function �from the current point in the trajectory space, �0= ��0 ,�0�, to a candidate point, �i= ��i ,�i�:

Figure 13. Hazard avoidance maneuver curvature �left�and velocity �right� profiles.



� = K1

�max − �min��0 − �i�2 +

K2

�max��0 − �i�2, �29�

where K1 and K2 are static positive gain factors.These factors affect the relative weighting of changesin velocity and curvature. A variety of search meth-ods can be employed to find �f. In this work an ex-haustive search was utilized due to the small size ofthe search space.

3.2. Path Resumption Maneuvers

After a hazard avoidance maneuver has been com-puted, a UGV must plan a kinematically and dy-namically feasible path to return to the nominal de-sired path xnominal. Here, an efficient path replanningalgorithm is proposed to accomplish this. There aremany approaches to this problem, and a more de-tailed analysis of the performance and convergenceproperties of the method along with a comparisonwith other techniques is described elsewhere�Spenko, 2005; Kelly & Nagy, 2003; Reuter, 1998�.

Equations describing the motion of a front-steered vehicle can be written as

��t� = tan��t��/L �t� = ��t��t� ,

x�t� = ��t�cos �t� y�t� = ��t�sin �t� , �30�

where ��t� is the steering input, �t� is the vehicleheading angle, ��t� is the velocity input, and L is thevehicle wheelbase. If the curvature input is describedas a function of time, u�t�, integration of Eq. �30� �witha change of variable from time to distance, and as-suming constant velocity� yields

��s� = u�s�, �s� = ��0

D

��s�ds ,

x�s� = ��0

D

cos �s�ds, y�s� = ��0

D

sin �s�ds .

�31�

Consider the scenario illustrated by the plotshown in Figure 14. Here, the solid line represents anominal trajectory’s curvature as a function of dis-tance. A hazard avoidance maneuver is executed atsa, and the maneuver ends at sb. The curvature pro-files of the nominal desired path, hazard avoidancemaneuver, and path resumption maneuver are de-fined as �1�s�, �2�s�, and �3�s�. These curvature pro-files have associated heading and position profiles,�s�, x�s�, and y�s�. The goal of the path resumptionproblem is to find �3�s� in a computationally efficientmanner �i.e., completed before the UGV has finishedtraversing the path generated by the hazard avoid-ance maneuver� such that the curvature, heading,and position at sc is the same as at sd:

��sc�,�sc�,x�sc�,y�sc��1 = ��sd�,�sd�,x�sd�,y�sd��3,

�32�

where sc is a desired “meeting point” of the replan-ning maneuver and the nominal trajectory, and sd isthe terminal point of the replanning maneuver.Clearly sc and sd need not be coincident.

A path resumption maneuver has the followingproperties:

• An initial curvature and velocity that is equalto the terminal curvature and velocity of ahazard avoidance maneuver, ��sb� ,��sb��2= ��sb� ,��sb��3.

• A length sr such that sr=sd−sb.• A trajectory profile such that ��sc� ,�sc� ,

x�sc� ,y�sc��1= ��sd� ,�sd� ,x�sd� ,y�sd��3.

Figure 14. Curvature diagram for path resumptionmaneuver.



The proposed path resumption method, heretermed the “curvature matching method,” is out-lined as follows:

1. An initial choice of the location of the “meet-ing point,” sc, on the nominal trajectory ismade. Here, sc is initially chosen such that thepath length of the path resumption maneu-ver is equal to the path length of the hazardavoidance maneuver:

sc = 2sb − sa. �33�

2. An initial value of sd is chosen to be the small-est value such that a vehicle can transitionfrom �2�sb� to �3�sd� without violating the ve-hicle’s steering rate constraints:

sd =�2�sb� − �1�sc�

��max. �34�

Steps 3–6 are designed to find a path resump-tion maneuver curvature profile, �3�s�, suchthat the following condition is satisfied:

�sa

sc

�1�s�ds = �sa

sb

�2�s�ds + �sb

sd

�3�s�ds ,

�35��min � �3�s� � �max,

where �min and �max are the minimum andmaximum allowable curvatures given bythe dynamic constraints of the total admis-sible trajectory space. Since �min and �maxare included in this formulation, the curva-ture matching method is applicable forrough and rolling terrain because the cur-

vature of the resulting path will not exceedthe constraints generated by the trajectoryspace. Equation �35� states that the area un-der the hazard avoidance maneuver curva-ture profile plus the area under the path re-sumption maneuver curvature profile isequal to the area under the nominal desiredtrajectory curvature. This ensures that theheading angle at the end of the path re-sumption maneuver is identical to theheading angle of the nominal desired tra-jectory at the meeting point, 1�sc�=3�sd�.

3. Two curvature constraints, �high and �low, forthe path resumption maneuver are computed�see Figure 15�. These constraints are definedas the maximum and minimum curvaturesthat transition the final curvature of the haz-ard avoidance maneuver, �2�sb�, to the finalcurvature of the path resumption maneuver,�3�sd�, given �= �max, �high��max, and �low��min. The area between the two constraintsrepresents all possible curvatures that cantransition �2�sb� to �3�sd�. �high and �low aregiven as

�high =��sb� +

d�

dss for sb s �

dsd�

��max − ��sb�� ,

�max fordsd�

��max − ��sb�� s �dsd�

��max − ��sd�� ,

�max −d�

dss for

dsd�

��max − ��sd�� s � sd,� �36�

Figure 15. Illustration of curvature matching methodconstraints.



�low =��sb� −

d�

dss for sb s �

dsd�

��min − ��sb�� ,

�min fordsd�

��min − ��sb�� s �dsd�

��min − ��sd�� ,

�min +d�

dss for

dsd�

��min − ��sd�� s � sd.� �37�

In general, steps 4–6 generate a curvature profile that either follows the curvature constraints or tran-sitions between them. These steps are described in detail; however, it is important to realize that theend result is simply a curvature profile that satisfies Eq. �35�.

4. If the hazard avoidance maneuver has caused a UGV to deviate to the left of the desired nominal path,the path resumption maneuver generates a curvature profile that starts by following the lower cur-vature constraint, �low. This results in a path resumption maneuver that tends toward the right and isthus likely to minimize overall path deviation:

�3�s� = ��low�s� for sb s � sb + �s ,

�3�s − �s� +ds�

�max for sb + �s s � sd, � �38�

where �s is the interval defined as

�s =sd − sb

n, �39�

where n is a fixed integer that represents the number of subdivisions of the curvature profile. If theUGV is on the right side of the nominal desired path, then the curvature profile begins by followingthe upper curvature constraint, �high. This results in a path resumption maneuver that tends towardthe left:

�3�s� = ��high�s� for sb s � sb + �s ,

�3�s − �s� −ds�

�max for sb + �s s � sd. � �40�

5. If at any point the curvature profile of thepath resumption maneuver is less than thelower curvature constraint, �3�s��low�s�,then the path resumption maneuver curva-ture is set equal to the lower curvature con-straint, �3�s�=�low�s�. Similarly, if �3�s��high�s� then the path resumption maneu-ver curvature is set equal to the upper cur-

vature constraint, �3�s�=�high�s�. This ensuresthe curvature profile does not violate the con-straints imposed by the dynamic trajectoryspace and that the final curvature of the pathresumption maneuver, �3�sd� is equal to thefinal curvature of the nominal path, �1�sc�.

6. If the area under the nominal desired trajec-tory’s curvature profile is within a reasonable



tolerance, ��, of the area under the hazardavoidance maneuver plus the path resump-tion maneuver curvature profiles:

�sa

sc

�1�s�ds − ��sa

sb

�2�s�ds + �sb

sd

�3�s�ds� ��,

�41�

then the algorithm continues to step 7. Oth-erwise, �s is increased and steps 4 and 5 arerepeated. This iterative process searches thepossible curvature profiles that constitute apath resumption maneuver while maintain-ing �= �max.If the entire path resumption maneuverequals either �high or �low before Eq. �41� issatisfied, the distance for path resumptionmaneuver, sd, is not large enough. In thiscase, �s is reset to its original value, sd is in-creased by a set length, and the algorithmreturns to step 3.From the path resumption maneuver cur-vature profile, heading and position pro-files can be generated using Eq. �30�. At thispoint, there is no guarantee that the posi-tion of the path resumption maneuvermatches the nominal desired path �see Fig-ure 16�. If they do not match, sc and sd are

modified based on the Euclidian distancefrom �x�sc� ,y�sc��1 to �x�sd� ,y�sd��3.

7. An acceptable threshold for the final positionerror, �, is defined. If the total position error,etotal= �x1�sc�−x3�sd��2+ �y1�sc�−y3�sd��2, lieswithin a circle of radius �, then the algorithmis complete. If not, sc and sd are adjusted as

sci+1= sci

− kc�elon� ,

sdi+1= sdi

− kd�elat� , �42�

where kc and kd are static positive gains andelon and elat are the longitudinal and lateralerror respectively and are given as

elat = �x3�sd� − x1�sc��sin 1�sc�

+ �y1�sc� − y3�sd��cos 1�sc� , �43�

elon = �x1�sc� − x3�sd��cos 1�sc�

+ �y1�sc� − y3�sd��sin 1�sc� . �44�

Due to the fact that the equations of motion arecoupled and nonlinear �see Eq. �31�� algorithm con-vergence cannot be guaranteed. However, the con-vergence properties have been studied numericallyand have yielded excellent results �Spenko, 2005�. Aten thousand trial simulation using a PIII 1.5 GHzcomputer showed the curvature matching methodgenerating a path with a median time of 10 ms and amean time of 44 ms, which indicate the algorithm issufficiently fast for use in high-speed situations.

Figure 17 shows an example path resumptionmaneuver generated using the curvature matchingmethod. Note that the nominal path’s curvature andheading and the path resumption curvature andheading profiles are identical at points sc and sd �up-per left and upper right subplots�, and points sc andsd are coincident along the path �lower subplot�.

4. SIMULATION AND EXPERIMENTALRESULTS

4.1. Experimental System Description

Experimental trials were conducted on the Autono-mous Rough Terrain Experimental System

Figure 16. Illustration of curvature matching methodpath.



�ARTEmiS�; see Figure 18. ARTEmiS is a front-steerrear-wheel drive UGV that measures 0.88 m long,0.61 m wide, and 0.38 m high. It has a 0.56 m wheel-base and 0.25 m diameter pneumatic tires. It isequipped with a 2.5 Hp Zenoah G2D70 gasoline en-gine, Crossbow AHRS-400 inertial navigation sys-tem, Novatel differential global positioning systemcapable of 0.2 m resolution �circular error probable�,Futaba S5050 servos for steering, brakes, andthrottle, and a PIII 700 MHz PC104 computer. ARTE-miS is not equipped with forward-looking rangesensors. Instead, using knowledge of ARTEmiS’ po-sition, hazard locations are only revealed once theyare within the range of a “virtual sensor.”Simulations were conducted using a model of ARTE-miS and the commercial software package

MSC.ADAMS/Car. The steering angle and throttlewere controlled using a proportional-derivative con-trol. For the steering angle, the gain was inverselyproportional to the vehicle longitudinal velocity. Suf-ficient path following results were obtained usingpreviously developed algorithms �Canudas de Wit,Siciliano & Bastin, 1996�.

Because ARTEmiS exhibits only slight oversteer,for the purpose of the simulations and experimentspresented in this chapter the steering constraintswere considered to be derived from a neutral-steered vehicle. Also, note that the center of mass ofARTEmiS does not bisect the track width of the ve-hicle. Thus, the rollover constraints are not symmet-ric about zero curvature.

4.2. Validation of Hazard Avoidance ManeuverAlgorithm

The hazard avoidance maneuver algorithm was vali-dated through both simulation and experimentalanalysis. Over 80 h of experimental data were col-lected on a variety of terrain surfaces, profiles, andconditions, at speeds ranging from 3.0–9.0 m/s.This section provides results from five experiments.

For each experiment, ARTEmiS was placed in aninitial starting location, �x0 ,y0�, and commanded tofollow a nominal desired trajectory, �nominal, with acorresponding path, xnominal. Hazards consisted oftraffic cones placed in various configurations. Therange of the sensor varied among experiments from12 m to 20 m �21 to 35 times the vehicle wheelbase�.Other experiments were conducted to investigatethe effects of a reduced sensor range on resultinghazard avoidance maneuvers. �Due to length con-straints the results are not included here.� As ex-pected, it was found that as the sensor range is re-duced, the resulting hazard avoidance maneuversare usually more severe and performed at lower-speeds than similar experiments conducted withlonger-range sensors. Once a hazard was in range, itwas assumed that the hazard geometry was known.All experiments used the curvature matchingmethod to generate a path resumption maneuver.All experiments also used the maneuver selectioncost function given in Eq. �29� with K1K2 unlessotherwise noted.

Figure 17. Example of curvature matching method.

Figure 18. Diagram of ARTEmiS.



4.3. Multiple Hazard Simulation and ExperimentalResults

Results from two experimental trials are presentedthat illustrate the ability of the algorithm to avoidmultiple hazards. This section also contains simula-tion results for comparison to one of the experimen-tal trials.

Figure 19 shows three “snapshot” subplots ofthe global positioning system �GPS� trace from anexperiment for high-speed avoidance of two haz-ards. The experiment was performed on a field ofmixed grass and dirt, at a desired velocity of6.0 m/s. The nominal desired path was a 100 m longstraight path. ARTEmiS detected the first hazard atx=16.4 m. This is shown in the top subplot of Figure19. At this point a hazard avoidance maneuver wasexecuted. ARTEmiS followed the modified path un-til a second hazard was detected at x=43.2 m. This isshown in the middle subplot of Figure 19. A secondmaneuver was then executed and ARTEmiS success-fully resumed the nominal path, as shown in thelower section of Figure 19.

Figure 20 shows the trajectory spaces at the in-stant that the first hazard was detected. An x marksARTEmiS’ location in the trajectory space. Here,ARTEmiS modified its trajectory from �0= �6.0,0.00�to �f= �6.0,−0.03�, i.e., it executed a sharp turn toavoid the hazard.

Figure 21 compares experimental and simulated

GPS traces for these experiments. The top subplotdisplays the simulation results and the lower sub-plot shows the experimental results. The two resultsare quite similar, though the simulation generated aslightly different maneuver than the experimentalsystem for the second hazard. This is due to differ-

Figure 19. Hazard avoidance maneuvers executed formultiple hazards.

Figure 20. Trajectory space when the first hazard wasdetected.

Figure 21. Comparison of simulation �top� and experi-mental �bottom� results.



ences in ARTEmiS’ position when the second hazardwas identified. This can be attributed to position es-timation and path tracking errors that are present inthe experimental system.

Path tracking errors in the experimental systemwere due to position estimation errors and mechani-cal limitations of ARTEmiS’s steering mechanism,which are backdrivable and slightly underpowered.Thus terrain roughness caused substantial distur-bances to the steering system.

4.4. Sloped Terrain Experimental and SimulationResults

An important property of the hazard avoidance al-gorithm is its ability to account for the effects of ter-rain inclination. Here, the results of two experimen-tal trials are compared. The experiments wereidentical except that the first was performed on flatterrain and the second was on terrain with a 15–18°slope with the fall line perpendicular to the initialdirection of vehicle travel �see Figure 22�.

The experiments were performed at a desiredspeed of 8.0 m/s. The nominal desired path for eachtrial was a 100 m long curved path. For both experi-ments ARTEmiS traversed the nominal desired pathuntil it detected a hazard at s=16.4 m. At the timethe hazard was identified, ARTEmiS selected a haz-ard avoidance maneuver of �f= �8.0,0.12� on flat ter-rain. On sloped terrain ARTEmiS selected �f= �7.0,−0.06�. This is due to the fact that on sloped terrain,�f= �8.0,0.12� was not deemed to be a dynamicallyadmissible maneuver due to the effects of terrain in-clination. This can be seen in Figure 23.

GPS traces of the resulting paths are comparedin Figure 24. There is significant path tracking over-

shoot in the flat terrain case due to steering servorate limitations. However, this experiment illustratesthe effect of terrain inclination on maneuver selec-tion, and shows that the algorithm results in a dy-namically admissible maneuver even on steeplysloped terrain.

4.5. Rough Terrain Experimental Results

Experiments on rough terrain were performed atMinute Man National Historic Park. The terrain con-sisted of a bumpy, uncut grass field. Physical terrainfeatures tended to be on the order of one-half thewheel radius. Figure 25 illustrates the roughness of

Figure 22. Image of ARTEmiS sloped terrain experiment. Figure 23. Trajectory space comparison for flat andsloped terrain.

Figure 24. Hazard avoidance maneuver enacted on flatand sloped terrain.



the terrain by comparing experimentally-measuredUGV vertical acceleration measured on both smoothand rough terrain at the experiment site. Data weregathered while ARTEmiS traveled at 7 m/s.

Figure 26 shows the experimental site. Thenominal desired path is a 100 m long straight path.ARTEmiS is pictured at the start of the path. Thegoal location is obstructed from view by the hazard.The hazard consists of a cluster of tall brushes, andsmall trees.

Figure 27 shows three “snapshot” subplots ofthe experiment. The experiment was performed at aspeed of 7.0 m/s. ARTEmiS detected the first hazardat x=10.4 m. This is shown in the top subplot ofFigure 27. At this point, hazard avoidance and pathresumption maneuvers were executed, as shown inthe middle subplot of Figure 27. The lower section ofFigure 27 shows the completed path.

Figure 28 shows the trajectory space at the timethe hazard was detected. The dynamic rollover lim-its included an empirically determined “safety mar-

Figure 25. Vertical acceleration comparison on rough andflat terrain.

Figure 26. Rough terrain experimental setup.

Figure 27. Rough terrain experimental results.

Figure 28. Rough terrain trajectory space.



gin” to compensate for the effects of terrain rough-ness. When the hazard was detected, ARTEmiSmodified its trajectory from �0= �7.0,0.00� to �f= �7.0,0.03�.

This experiment demonstrates that the proposedhazard avoidance algorithm can be applied in toUGVs operating at high speeds on rough terrain.These conditions are expected to be similar to actualoperating conditions for many practical applications.

5. CONCLUSIONS

This paper has presented an algorithm for hazardavoidance for high-speed unmanned ground vehiclesoperating on rough, natural terrain. The algorithm ac-counts for dynamic effects, such as vehicle sideslip,rollover, and over/understeer, as well as vehiclesteering dynamics, drive train properties, terrain ge-ometry, and vehicle/terrain interaction. The methodis computationally efficient �operating on the order ofmilliseconds�, and thus suitable for on-board imple-mentation. Extensive simulation and experimentalresults have been presented that demonstrate the al-gorithm’s effectiveness. The hazard avoidance algo-rithm based on the trajectory space is only one ofmany that could be implemented, and future workfocuses on expanding this area.

REFERENCES

Arakawa, K., & Krotkov, E. �1993�. Fractal surface recon-struction for modeling natural terrain. Paper pre-sented at the IEEE Conference on Computer Visionand Pattern Recognition, New York, NY.

Beer, F., & Johnston, E. �1988�. Vector mechanics for engi-neers: Statics and dynamics. New York: McGraw–Hill.

Brock, O., & Khatib, O. �1999�. High-speed navigation us-ing the global dynamic window approach. Paper pre-sented at the IEEE International Conference on Robot-ics and Automation, Detroit, MI.

Brooks, R.A. �1986�. A robust layered control system for amobile robot. IEEE J. Rob. Autom., 2�1�, 14–23.

Canudas de Wit, C., Siciliano, B., & Bastin, G., eds. �1996�.Theory of robot control. London: Springer-Verlag.

Chanclou, B., & Luciani, A. �1996�. Global and local pathplanning in natural environment by physical model-ing. Paper presented at the Intelligent Robots and Sys-tems Conference, Osaka, Japan.

Chen, B.C., & Peng, H. �1999�. Rollover warning of articu-lated vehicles based on a time-to-rollover metric. Pa-per presented at the ASME International Congressand Exposition, Knoxville, TN.

Coombs, D., Lacaze, A., Legowik, S., & Murphy, K. �2000�.Driving autonomously off-road up to 35 km/h. Paperpresented at the IEEE Intelligent Vehicle Symposium,Dearborn, MI.

Daily, M., Harris, J., Keirsey, D., Olin, K., Payton, D., Re-iser, K., Rosenblatt, J., Tseng, D., and Wong, V. �1998�.Autonomous cross-country navigation with the ALV.Paper presented at the IEEE International Conferenceon Robotics and Automation, Philadelphia, PA.

Fish, S. �2003, September�. Overview of UGCV and Per-ceptOR status. Paper presented at the SPIE Un-manned Ground Vehicle Technology Conference, Or-lando, FL.

Fox, D., Burgard, W., & Thrun, S. �1997�. The dynamic win-dow approach to collision avoidance. IEEE Rob. Au-tom. Mag., 4�1�, 23–33.

Gerhart, G., Goetz, R., & Gorsich, D. �1999�. Intelligent mo-bility for robotic vehicles in the army after next. Paperpresented at the SPIE Unmanned Ground VehicleTechnology Conference, Orlando, FL.

Gillespie, T. �1992�. Fundamentals of vehicle dynamics.Warrendale, PA: Society of Automotive Engineers.

Golda, D. �2003�. Modeling and analysis of high-speedmobile robots operating on rough terrain. Unpub-lished M.S. thesis, Massachusetts Institute of Technol-ogy, Cambridge, MA.

Haddad, H., Khatib, M. Lacroix, S., & Chatila, R. �1998�.Reactive navigation in outdoor environments usingpotential fields. Paper presented at the IEEE Interna-tional Conference on Robotics and Automation, Leu-ven, Belgium.

Iagnemma, K., Kang, S., Brooks, C., & Dubowsky, S.�2003�. Multisensor terrain estimation for planetaryrovers. Paper presented at the Seventh InternationalSymposium on Artificial Intelligence, Robotics, andAutomation in Space, i-SAIRAS, Nara, Japan.

Kelly, A., & Nagy, B. �2003�. Reactive nonholonomic tra-jectory generation via parametric optimal control. Int.J. Robot. Res., 22�7�, 583–602.

Kelly, A., & Stentz, A. �1998�. Rough terrain autonomousmobility—Part 2: An active vision, predictive controlapproach. Auton. Rob., 5, 163–198.

Langer, D., Rosenblatt, J.K., & Hebert, M. �1994�. Abehavior-based system for off-road navigation. IEEETrans. Rob. Autom., 10�6�, 776–783.

Manduchi, R., Castano, A., Talukder, A., & Matthies, L.�2005�. Obstacle detection and terrain classification forautonomous off-road navigation. Auton. Rob., 18, 81–102.

Olin, K., & Tseng, D. �1991�. Autonomous cross-countrynavigation: An integrated perception and planningsystem. IEEE Expert, 6�4�, 16–30.

Philippsen, R., & Siegwart, R. �2003�. Smooth and efficientobstacle avoidance for a tour guide robot. Paper pre-sented at the IEEE International Conference on Robot-ics and Automation, Taipei, Taiwan.

Reuter, J. �1998�. Mobile robot trajectories with continu-ously differentiable curvature: an optimal control ap-proach. Paper presented at the IEEE/RSJ Conferenceon Intelligent Robots and Systems, Victoria, B.C.,Canada.



Sanjiv, S., & Kelly, A. �1996�. Robot planning in the spaceof feasible actions: Two examples. Paper presented atthe IEEE International Conference on Robotics andAutomation, Minneapolis, MN.

Shimoda, S., Kuroda, Y., & Iagnemma, K. �2005�. Potentialfield navigation of high speed unmanned ground ve-hicles on uneven terrain. Paper presented at the IEEEInternational Conference on Robotics and Automa-tion, Barcelona, Spain.

Shoemaker, C., & Borenstein, J. �2000�. Overview and up-date of the Demo III experimental unmanned vehicleprogram. Paper presented at the SPIE UnmannedGround Vehicle Technology, Orlando, Fl.

Simmons, R. �1996�. The curvature-velocity method for lo-cal obstacle avoidance. Paper presented at the IEEE

International Conference on Robotics and Automa-tion, Minneapolis, MN.

Spenko, M. �2005�. Hazard avoidance for high-speedrough-terrain unmanned ground vehicles. Unpub-lished Ph.D. thesis, Massachusetts Institute of Tech-nology, Cambridge, MA.

Spenko, M., Iagnemma, K., & Dubowsky, S. �2004�. Highspeed hazard avoidance for mobile robots in roughterrain. Paper presented in the SPIE Conference onUnmanned Ground Vehicles, Orlando, FL.

Walker, J. �2001�. Unmanned ground combat vehicle con-tractors selected. DARPA News Release February 7,2001.

White, F. �1994�. Fluid mechanics. New York: McGraw–Hill.



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