A Multirobot Path-Planning Strategy for Autonomous Wilderness Search and Rescue

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A Multirobot Path-Planning Strategy forAutonomous Wilderness Search and Rescue

Ashish Macwan, Julio Vilela, Student Member, IEEE, Goldie Nejat, Member, IEEE, and Beno Benhabib

Abstract—This paper presents a novel strategy for the on-line planning of optimal motion-paths for a team of autonomousground robots engaged in wilderness search and rescue (WiSAR).The proposed strategy, which forms part of an overall multirobotcoordination (MRC) methodology, addresses the dynamic natureof WiSAR by: 1) planning initial, time-optimal, and piecewisepolynomial paths for all robots; 2) implementing and regularlyevaluating the optimality of the paths through a set of checksthat gauge feasibility of path-completion within the availabletime; and 3) replanning paths, on-line, whenever deemed nec-essary. The fundamental principle of maintaining the optimaldeployment of the robots throughout the search guides the MRCmethodology. The proposed path-planning strategy is illustratedthrough a simulated realistic WiSAR example, and compared toan alternative, nonprobabilistic approach.

Index Terms—Multirobot coordination (MRC), path-planning,wilderness search and rescue (WiSAR).

I. INTRODUCTION

SEARCH and rescue (SAR) is an application domain formobile robotics that has received significant attention in

recent years. SAR missions have been classified as: 1) urbansearch and rescue (USAR) and 2) wilderness search andrescue (WiSAR). Thus far, much research attention has beendevoted to USAR operations, where the objective is to searchfor survivors trapped underneath collapsed structures.

In particular, research in USAR has focused on the designof robotic platforms [1], [2], human-robot interaction [3],and/or multirobot cooperation [4]–[6]. For example, in [1], aserpent-shaped robot was proposed to access holes and crossirregular obstacles including staircases, which are typicallyfound in USAR environments. In [2], the individual perfor-mances of terrestrial robot agents with tracker treads on areal-life mudslide accident response were evaluated.

In [3], the World Trade Centre disaster, showed that tele-operation of robot agents leads to human operators losingsituation awareness, suggesting that some level of autonomyin SAR missions is highly desirable. Consequently, multi-robot coordination (MRC) approaches have been proposedin the literature. For instance, several strategies in USAR,

Manuscript received April 18, 2014; revised July 11, 2014; acceptedSeptember 19, 2014. This work was supported by the Natural Sciences andEngineering Research Council of Canada. This paper was recommended byAssociate Editor S. X. Yang.

The authors are with the Department of Mechanical and IndustrialEngineering, University of Toronto, Toronto, ON M5S 3G8, Canada (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCYB.2014.2360368

including the C-net approach where robots bid for tasks, theStigmergy strategy that uses pheromone dynamics, and thesignaling approach, were compared in [4]. The study showedthat depending on the strategy selected, more robots are pre-ferred at a lower individual cost without compromising teamperformance. However, these strategies are not directly trans-latable to WiSAR due to communication constraints and therequirement for robots to remain in the vicinity of each other.

The WiSAR problem commonly involves the search for amoving lost-person (i.e., the target) in the wilderness. Theuse of rescue robots in WiSAR has not been explored aswidely as in USAR. Recent research efforts have been ondeveloping target-location prediction models and resource-deployment methods [7], [8], without special attention topath planning. Other works have proposed the incorporationof cameras into unmanned aerial vehicles (UAVs) to searchand/or track targets [9], [10], in addition to human-UAV coop-erative strategies [11], [12]. For example, in [9], human-robotinteraction issues are considered when using UAVs to pro-vide aerial imagery in order to assist WiSAR personnel, whileSymington et al. [10] used camera equipped UAVs to track atarget using probabilistic estimators for target behavior.

WiSAR is a complex problem, since the moving target isnontrackable, and the search area expands as a function oftime. Therefore, the state of the target at any given time mustbe predicted using available, time-varying, and probabilisticinformation. This prediction must consider factors unique toWiSAR, including varying terrain, target physiology and psy-chology, as well as clues that may be found during the search.Adding to the complexity is that a probability distribution fortarget-specific motion may not be available.

To date, research on autonomous WiSAR has mainlyfocused on robot implementation issues rather than on thedevelopment of overall MRC methodologies. Moreover, sinceWiSAR often requires the rapid coverage of rugged terrains,research focus has been on the use of tele-operated UAVs toassist ground searchers. The UAVs in [9] apply a coverage-search pattern, with no form of autonomous coordinationamong multiple UAVs or utilization of probabilistic target-location information. This paper is extended further in [11] tostudy the roles of the UAV aviation and navigation operator,as well as the UAV sensor operator. The goal was to increaseUAV autonomy and thereby minimize the number of operatorsrequired.

The design of a robust, real-time, and trajectory-planningsystem for UAVs intended to serve in uncertain environments,such as in the wilderness, is proposed in [12]. Given a set of

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waypoints, the proposed algorithm plans a trajectory on-linethat satisfies UAV kinematic constraints and that accounts fordynamic obstacles. A tracking algorithm is also employed toensure that the trajectory is followed satisfactorily. Custom-designed UAVs are used to implement and test this approach.

State-of-the-art methods that use the Bayesian approach topredict the location of lost people are limited by computa-tional cost (e.g., [13]–[15]). As the search space increaseswith time, so does the grid resolution associated with theworld model, which elevates computational costs to pro-hibitive levels. Similarly, others showed that partially observ-able Markov decision processes (POMDP) can evaluate theexpected reward of search agents over a time horizon, but thismethod becomes infeasible once the state space of the POMDPincreases [16]. Lastly, some recent works (see [17]) comparemethods that define searchable areas without proposing a wayof autonomously guiding search agents. Thus, so far, an effec-tive on-line MRC method has not been formally proposed forunbounded WiSAR environments.

A series of experiments on collaborative searches conductedby various human SAR teams have been reported in [18]–[20].For example, Foothills Search and Rescue [18] and SARGlobal 1-Ottawa Gatineau Volunteer Search and Rescue [19]are two typical Canadian nonprofit organizations that con-duct mock searches to train volunteers. Another example isthe Utah County Search and Rescue group (UCSR), whouse tele-operated camera-equipped mini-UAVs in simulatedexperiments to assist human operators [20].

The above groups share the common principle that themain search is supervised by experienced human searchers,who use their knowledge to deploy search agents. Clearly,then, an automated decision-making process would facili-tate a move toward greater autonomy in search coordination.This would also facilitate the incorporation of robotic agentsinto WiSAR. Such a process would need to generate specificinstructions for the search about optimal deployment positionsand subsequent paths to be followed by human or robot agents.

Several general search methodologies have been reported inthe search theory [21]–[26]. However, most rely on analyticalsolutions that assume a priori knowledge of a 2-D probabilitydistribution for the position of the target. Furthermore, they donot easily lend themselves to multirobot WiSAR implementa-tion. Similarly, current MRC strategies [27]–[33], centralizedor decentralized, make numerous simplifying assumptions.These include stationary targets, a priori known probabilityinformation, and/or bounded environments, which limit theirusefulness for WiSAR.

As an example of centralized MRC, the approach in [29]represents the problem as a discrete-time system and combinespredictive control and mixed integer-linear programming tosolve for feasible robot control inputs on-line. However, theproblem is modeled as one where robots must reach fixedtarget positions while adhering to formation constraints andavoiding obstacles. Consequently, this provides an ineffectivesolution for the challenges of multirobot WiSAR.

As an example of decentralized MRC method in [33], eachrobot navigates by selecting regions in which to take mea-surements in decreasing order of the probability of containing

“good” information. An underlying function for the probabil-ity of detecting the target over the search area is, nevertheless,assumed to be known. As well, the target is assumed to bestationary and the search area bounded, so that the densityfunction does not propagate with time.

Prior to this paper, in our extensive paper on develop-ing an autonomous MRC methodology for WiSAR, we haveaddressed the initial sub-problems of target-motion predic-tion [7] and robot-team deployment [8]. Herein, therefore, ourfocus is on the third and last sub-problem, namely, the devel-opment of a novel, effective, and efficient strategy for on-linerobot path-planning using iso-probability curves.

Our proposed robot path-planning methodology presentsseveral contributions to WiSAR research. First, it does notassume the existence of an a priori known target locationprobability density function (PDF). Instead, it makes use ofreadily available lost-person empirical data and terrain infor-mation to generate 1-D PDFs that remain computationallyfriendly, even over expanding search areas. In addition, ourpath-planning approach takes into account WiSAR-specificissues, such as target psychology and the impact of terraintopology on possible target motion, when optimally allocat-ing search resources. Lastly, although, our method is targetedtoward robots, it can be used by human agents. It is uniquein that it makes use of the novel iso-probability curves forrobot path-planning in WiSAR, which is scalable to bothlarger robot team sizes and unbounded search spaces withoutcompromising on-line feasibility.

II. OVERVIEW OF PROPOSED METHODOLOGY

Robot path-planning as it relates to autonomous multirobotWiSAR refers to the problem of using available probabilis-tic target-location information to plan optimal paths for allrobots throughout the search. Moreover, due to the dynamicnature of WiSAR, this probabilistic information varies withtime. Consequently, path-planning must be dynamic in tworespects: 1) the search paths must be reconstructed every timethe probabilistic target-location information is updated and2) the optimality of the search-paths must be regularly reeval-uated in-between these updates (i.e., while the paths are beingexecuted by the robots) and replanned, when necessary, tomaintain optimality. This paper, therefore, presents a novelmethodology to address the need for a dynamic, probabilis-tic path-planning strategy for autonomous robotic WiSAR ina computationally-efficient manner.

A robotic WiSAR scenario is assumed to proceed as fol-lows. At a certain point in time, a notification arrives of amissing person (i.e., target). The last known position (LKP)of the target at time t = 0 is given. Next, probabilistic infor-mation about the location of the target within the search areais derived. This information is used to determine an optimalinitial deployment of robots within the search area, starting att = Ths (i.e., the target’s “head-start”). Optimal search-pathsare, then, planned for each robot, and the robots commencethe search by executing these paths.

In order to effectively plan, these paths in a multi-robot WiSAR problem, the following requirements need to


MACWAN et al.: MULTIROBOT PATH-PLANNING STRATEGY FOR AUTONOMOUS WiSAR 3

be considered: 1) the time-varying probabilistic informationregarding the target-state; 2) terrain influence; 3) target physi-ology and psychology; 4) clues found; and 5) maintaining anoptimal deployment of robots.

In our quest for an effective approach to MRC for WiSAR,a novel means of representing probabilistic target-locationinformation was proposed in [7], which is an important con-struct that ties all the different elements of our overall searchmethodology together. In addition, a novel method for optimalresource deployment was proposed in [8], which prescribes themost effective way to dynamically distribute the search effortover the search area. Since, both these components play a criti-cal role in planning robot search-paths, they will first be brieflyreviewed below in Sections II-A and II-B, respectively, beforepresenting our proposed multirobot path-planning strategywhich is the focus herein.

A. Prediction of Target Location via Iso-Probability Curves

In order to represent the probabilistic information abouta target’s location within the search area at any given time,a novel representation mechanism was proposed in [7]. Theadopted strategy makes conservative estimates of the target’smotion in order to establish boundaries delimiting regionswithin which he/she may be located, with a certain proba-bility, at any given time. These boundaries are termed as the“iso-probability curves.”

Iso-probability curves are constructed by first considering aPDF for average target-propagation rate along a single, straightline of travel (from the LKP outward), herein referred toas a “ray.” This mean target-propagation rate PDF can beobtained from data pertaining to past successful lost-personsearch incidents available from SAR organizations [34]. Thedata is typically organized according to different categories oftargets (e.g., experienced hikers, young children, despondentpersons, etc.), since targets falling within any particular cate-gory tend to behave in a similar manner. This allows for thederivation of a unique mean target-propagation rate PDF foreach target category.

As described in [7], using the target-propagation rate PDF,a distribution for the position of the target along a ray can beobtained for any given point in time. This target-location PDFis, then, overlaid onto the ray, and used to delimit “control-points” along the ray, one for each cumulative probabilityvalue [Fig. 1(a)]. Let us consider the ray extending horizontallyto the left from the LKP (overlaid with a normal target-locationPDF). Five control points have been noted on this ray, cor-responding to cumulative probabilities of 40%, 50%, 60%,80%, and 100%, respectively. Control point A on this ray, forinstance, is the position corresponding to a cumulative prob-ability value of 50%. Namely, at time t, there exists a 50%chance that the target is somewhere on this ray, from the LKPup to the control point A, if the target were to be travellingalong this ray.

Since one may not know the exact direction of the target’stravel from the LKP, multiple rays in different directions mustbe considered, with the same target-location PDF and controlpoints placed along each ray. Control points corresponding to

Fig. 1. Illustration of iso-probability curve propagation. (a) Iso-probabilitycurves at time t. (b) Iso-probability curves propagated up to time (t + 600 s).

the same cumulative probability value along the rays are, then,connected via piecewise curves to obtain an iso-probabilitycurve.

The influence of terrain on target motion is incorporatedinto the iso-probability curves by scaling the mean target-propagation rate PDF along each ray. This is done basedon knowledge of the terrain topology along each ray and itspotential impact on target propagation rate. This produces, ingeneral, irregularly-shaped iso-probability curves [Fig. 1(a)].

The set of iso-probability curves need to be propagatedoutward from the LKP in order to keep the probabilistic target-location information up-to-date, as time progresses. In orderto be computationally efficient, these propagations can beinvoked at user-specified discrete time intervals, �tprop. Thepropagations in time and space are achieved by recomput-ing the control points on each ray for the new point in time,(t + �tprop), using the mean target-propagation rate PDF, andreconstructing the curves accordingly. For example, propagat-ing the iso-probability curves in Fig. 1(a) forward in time by�tprop = 600 s yields the curves shown in Fig. 1(b).

The iso-probability curves, therefore, bound the differentsearch regions of probable target presence. Since, one maynot know a priori how the target may move (speed or direc-tion), a reasonable strategy would be to utilize the conservativeestimate that he/she is traveling outward from the LKP with aprobable (outward) propagation rate (not necessarily followingan outward straight line—as will be shown in our simulatedexample below). This worst-case scenario estimate providesfor reliable boundaries. As a result, we do not need to be con-cerned with guessing the exact path that the target is movingon at any given time, yet perform an effective search.

As noted above, iso-probability curves are suitable for anytarget motion, straight-line or otherwise, and with nonconstantspeed. Targets that move slower in a straight line are equiva-lent to those moving faster and circulate/backtrack, since theaverage outward propagation distance from the LKP wouldbe similar. Our search methodology does allow for naturalvariations in target direction and speed.

B. Optimal Deployment of Search Robots

Deployment refers to the distribution of resources withina given search area in a way that optimizes the locations



and amount of search effort. Herein, the probabilistic target-location information represented by the iso-probability curvesis used to accomplish this task. An efficient formulationis used to optimize: 1) the number and positions of theiso-probability curves; 2) the number of robots to assignto each curve; and 3) the positions of the robots on theirrespective assigned curves [8]. Each time the iso-probabilitycurves are propagated, the optimal deployment solution isreevaluated.

Our deployment optimization procedure uses a weightedsum of metrics that quantify the impact of any particulardeployment solution on two key attributes of the search. Thefirst is search-time (i.e., the expected total time that wouldbe required to find the target under that deployment), andthe second is success-rate (i.e., the probability of findingthe target under that deployment). The optimal deploymentsolution implemented links the iso-probability curves, andthe corresponding assignments of robots to those curves,to the overall optimality of the search, thereby making itimperative that the robots maintain their deployment as theysearch.

C. Robot Path-Planning

The proposed path-planning algorithm ensures that allrobots maintain their optimal deployment as the search pro-gresses. Namely, search optimality is achieved by makingthe utmost effort to keep the search robots on their opti-mal iso-probability curves in an on-line manner. Due to thispremise, all robot paths are planned concurrently and immedi-ately after every iso-probability curve propagation. Therefore,the planned paths are optimal in the sense that they pre-serve the optimal deployment of the robots to their respectiveiso-probability curves at all times.

In order to achieve this, first, it is necessary to determineeach robot’s future iso-probability curve position. Namely, if arobot is situated on its assigned iso-probability curve at sometime t, this curve must first be propagated forward to the futurepoint in time (t + �tprop). Second, a specific position on thisfuture curve must be determined to serve as the destinationpoint for the robot. A path can, then, be planned from therobot’s current position to this destination point. However, thisdestination point must be selected such that the planned pathallows the robot to reach the propagated iso-probability curveat precisely (t + �tprop). This would ensure that the robotremains on its iso-probability curve during and at the end ofthe completion of its path. Thus, the selection of the desti-nation point and the construction of the corresponding pathrequire an optimization approach.

Once this initial robot path is planned and its executionstarts, it is also necessary to regularly recheck the time-optimality of this path on-line, and replan it, if necessary, toensure that the propagated iso-probability curve can indeedbe reached at the desired time, (t + �tprop). A replan wouldentail conducting another optimization step to determine a newdestination point on the propagated iso-probability curve and anew path to reach that point. Once the robot completes its pathand reaches its propagated iso-probability curve, the abovepath-planning procedure is repeated.

Since each iso-probability curve is associated with a nom-inal target propagation rate, and it is propagated outwardaccordingly, the spacing between any two successive curvesafter any given propagation time-step does not increase as afunction of search time—this spacing would only change asa function of terrain, according to the ability of the target tonavigate it. Therefore, as long as robots move faster than thefastest nominal target propagation rate (i.e., nominal propaga-tion rate associated with the 100% iso-probability curve), norobot could fall behind its assigned curve.

D. Centralized Nature of Proposed Methodology

Our proposed method makes use of a centralized system,where robots must communicate with a central controller todetermine the path they must follow between iso-probabilitycurve propagations. In addition, robots would redeploy accord-ing to the new optimal positions that the central controllerwould determine. To accomplish such communication require-ments, robot positions could be tracked and planned pathscould be forwarded via GPS or cellular networks. Furthermore,robots must have sensing capabilities to detect a clue and/orthe target (via computer vision and/or thermal sensors), andcapabilities to avoid known/unknown obstacles (via computervision, range finders, and/or proximity sensors). It is impor-tant to note that robots are preferred over human agents,since it is easier for robots to follow a given path andchange in real-time their direction of motion and speed.They are also durable and have lower performance deterio-ration over time with better resistance to harsh environmentalconditions.

III. PROPOSED ROBOT PATH-PLANNING METHODOLOGY

The proposed on-line strategy for WiSAR would benefitfrom the search robots remaining on their respective iso-probability curves throughout the search in a continuousmanner. However, the iso-probability curves need to be propa-gated with time, for example, every �tprop, to keep up with theestimated motion of the target. Given an iso-probability curveat time t, and its propagated pair at (t + �tprop), a robot pathwould, then, need to be constructed between these two curves.Namely, the two endpoints for this path would correspond,respectively, to the point on the starting iso-probability curveon which the robot is currently located at time t, and a pointon the propagated destination of this iso-probability curve, onwhich the robot is required to be at time (t + �tprop). Asthe value of �tprop approaches zero, these paths would the-oretically allow the robot to remain on its assigned optimaliso-probability curve in a continuous manner as that curvepropagates forward with time.

The above ideal approach would require the calculation ofan infinite number of curves for every search robot, and deter-mination of the corresponding paths that must be continuously“stitched” together to maintain at least first derivative robot-motion continuity. During implementation, however, therewould not be sufficient time to compute all such intermedi-ate curves. Practical limitations only allow the computationof a limited number of iso-probability curves, every �tprop,



Fig. 2. Outline of path-planning strategy.

where the value of �tprop is dictated by the available com-puting resources. This paper, thus, proposes an approximationto calculating multisegment motion paths between individualpropagations of an iso-probability curve.

The proposed robot path-planning strategy is a recursiveapplication of: 1) initial optimal path-planning and implemen-tation; 2) regular optimality evaluations; and 3) replanning,when necessary (Fig. 2). The checking of path-optimality, andsubsequent replanning if required, occurs in-between the iso-probability curve propagations while the robot is executing itscurrent path. Once a robot completes its path and reaches itsdestination iso-probability curve, that curve is propagated for-ward another �tprop time into the future, and this procedurerepeats.

A. Initial Path Planning

1) Overview of Path-Construction: To illustrate the processof path-construction, the black-colored solid and dashed linesin Fig. 3 represent the starting and the (propagated) destina-tion positions of an example iso-probability curve. Also, twoexample intermediate curve propagations corresponding to twounique intermediate points in time (t1 and t2) are shown asgreen-colored, dashed lines, where t < t1 < t2 < (t + �tprop).For a chosen path, the robot would ideally need to be at pointsL1 and L2, respectively, as it crosses these two intermedi-ate iso-probability curves. Given the two intermediate pointsand the initial and destination points for the robot, one cancalculate a three-segment smooth robot-motion path.

Since it would be computationally prohibitive to deter-mine intermediate iso-probability curves, we suggest a way toapproximate the locations L1 and L2 using the alternative ofinterpolation points placed on the individual rays that are usedto construct the iso-probability curves. Thus, the first step inour proposed path-construction process would be to determinethe locations of these approximate path-interpolation points—one example of which is interpolation point P, located betweencontrol points A and B, on one of the rays used for curveconstruction, shown in Fig. 3.

Herein, we require that the ratio of AP to AB be the sameas the ratio of the length of path traversed so far by the robotwhen it crosses that ray relative to the total length of the pathit is planning to follow to reach its destination on the nextpropagated curve (Fig. 3).

This path-segmentation ratio, rk, must be estimated, sincethe path itself cannot be constructed without first specifying

Fig. 3. Example of an initial planned path.

the exact positions of the interpolation points. An angularestimate of rk, for any given interpolation point, k, is defined as

rk ∼= αk

αTOT(1)

where the angles αk and αTOT are as defined in Fig. 3. Theangle αTOT is determined between two rays originating fromthe LKP: 1) one ray passing through the robot’s current posi-tion and 2) another ray passing through the destination pointon the propagated iso-probability curve. The destination pointis selected by the optimization algorithm presented herein.

Once all the interpolation points have been determined,we propose the use of piecewise cubic-polynomials [35] toconstruct the path segments between these path-interpolationpoints. This would require polynomial position continuity andfirst-derivative continuity to obtain the system of equations,which can be solved to obtain the path. At start, the currentposition and orientation of the robot provide the necessaryconstraints for the starting point of the first cubic polynomialsegment of the path. Likewise, the desired destination-pointcoordinates and robot orientation on the propagated curve pro-vide the corresponding constraints for the endpoint of the lastcubic polynomial segment of the path. In our approach, werequire that the orientation of the robot at the destination pointbe tangent to the propagated destination curve.

The above described robot path represents an estimate as towhere the robot should be throughout the propagation time-interval, �tprop, so that its position roughly corresponds to apoint on its assigned iso-probability curve as it propagatesin time and space. Therefore, by following this path, therobot should remain close to, or directly on, its assigned iso-probability curve at all times. In this way, we adhere to thefundamental principle of WiSAR search optimality by makingthe utmost effort to keep the search robots on their optimaliso-probability curves in an on-line manner.

2) Optimization of Path-Construction: For any robot, Ri,its respective path needs to be optimized independently, but,concurrently with the paths of the other robots. In each case,the objective is to construct a smooth path from the robot’scurrent position at time t to a point on its propagated futuredestination iso-probability curve, so that the path-traversal-time is as close as possible to the desired curve-propagationtime-interval, �tprop. Thus, the optimization is one of search-ing for the best position of the endpoint on the propagated



Fig. 4. Multiple robot paths showing path subdivisions for estimating pathtraversal-time.

iso-probability curve that will yield an overall path by whichthe robot arrives at its destination iso-probability curve at atime as close as possible to (t + �tprop). If this endpoint opti-mization objective is achieved, while also using the proposedsegmentation of the robot paths in correct ratios, one canassume that all robots would remain on their assigned iso-probability curves throughout the search and, thus, preservethe optimality of the proposed WiSAR method.

Let us suppose that at time Tcurrent, the robot Ri is locatedat {xcur, ycur}i on its assigned iso-probability curve. The cor-responding propagated destination curve is defined by thefunction fdest,i and the available time until the next curvepropagation (i.e., the time available for the robot to reach itsdestination curve) is �tavail. For the initial path to be plannedjust before implementing a curve propagation, �tavail must beequal to �tprop.

The search for the optimal destination point {xdest, ydest}i,for Ri is, then, formulated as

min |�τ trav − �tavail|, subject to (2)

�τ trav ≤ �tavail, and (3)

{xdest, ydest}i ∈ fdest,i. (4)

Above, �τtrav is the estimated time to traverse the entirepath, given knowledge of the terrain over which the path passesand the speed capability of the robot when travelling on dif-ferent slopes. �τtrav is a function of the decision variables,{xdest, ydest}i, that are to be optimized. Thus, for any givenpotential destination point that is considered during this opti-mization, a path first has to be constructed from {xcur, ycur}i to{xdest, ydest}i, before the objective function can be evaluated.

An estimate of the traversal-time for any chosen path,�τtrav, can be determined by dividing the path into a num-ber of pieces, or “subdivisions,” of equal length, computingthe average terrain slope along each subdivision, estimatingthe time the robot would take to travel along each of thoseslopes corresponding to each subdivision, and, then, summingthese subdivision-traversal-times. Namely, if a given path isdivided into N subdivisions, each subdivision, j ∈ [1, N], isbounded by node j at its start and node j+1 at its end (Fig. 4).

TABLE IPATH-PLANNING DECISIONS FOR EACH CHECK PASS/FAIL CONDITION

The terrain height at each node is obtained from the avail-able topology map, and the average slope for each pathsubdivision is computed. Subsequently, using an estimate ofthe robot’s maximum speed over each subdivision, the aver-age subdivision-traversal-times, �τtrav,j, j ∈ [1, N], can beobtained, and utilized to compute �τtrav as

�τ trav =N∑

j=1

�τ trav,j. (5)

Since path traversal-time is dependent on complex factors,such as the difficulty of the terrain and potential obstacles, theobjective function in (2) would, in general, not be a closed-form differentiable function. Thus, to determine {xdest, ydest}i,the user may select any derivative-free direct-search techniquefor constrained optimization, such as the Nelder-Mead methodor others, as reviewed in [36].

B. Path Implementation and Evaluation

As a robot travels along its initially planned path, the(N+1) nodes that were defined for the path subdivisionsbecome the check-points at which the path must be eval-uated to ensure that it remains optimal. However, ratherthan rerunning the entire path-optimization algorithm at eachcheck-point, three time-efficient investigative checks are pro-posed herein to estimate and examine arrival-time uncertainty.These uncertainty checks are conducted to ensure that afeasible path, which guides the robot to its propagated des-tination curve in the available time, always exists. A checkpasses/fails if a certain computed value of interest is found tobe below/above a corresponding threshold.

There are three types of checks that are performed duringpath optimality evaluation at every subdivision of the path.Checks #1 and #2 are conducted at every checkpoint alongthe path. If either Check #1 or #2 fails, the optimal path isreplanned through the optimization method proposed herein.If both Checks #1 and #2 fail, the shortest path to the prop-agated destination curve is selected as the optimal path. Ifboth Checks #1 and #2 pass, a third check, Check #3, is con-ducted. If Check #3 passes, the robot proceeds on its plannedpath. Otherwise, the path is replanned optimally. The decision-making process based on these check pass/fail conditions issummarized above in Table I.



Fig. 5. Shortest-path estimates for Checks #1 and #2.

1) Check #1: Next Shortest-Path Feasibility: While a robotis executing its planned path, there may exist an undesirablepossibility that not only would the current path be unable toguide the robot to its destination within �tavail, but that evenan alternative (shortest) path to the propagated destination iso-probability curve, taken upon arriving at the next check-point,may not be feasible (i.e., achievable within �tavail). In orderto check for this extreme possibility expeditiously, we esti-mate the shortest possible path from the next check-point tothe propagated destination iso-probability curve by assuminga simple straight-line path (Fig. 5). Details on the computationof the traversal-time associated with this shortest-path (fromthe next check-point), and verification of its feasibility, aredescribed in the Appendix.

2) Check #2: Current Shortest-Path Feasibility: Herein,we determine whether a feasible shortest-path to the propa-gated destination iso-probability curve exists from the robot’scurrent position. This shortest-path is estimated via a straight-line path from the robot’s current position to its destina-tion curve (Fig. 5). The Appendix provides the details ofhow this path’s traversal-time is computed and checked forfeasibility.

As seen in Fig. 5, Check #1 is performed first to evaluate theshortest path from the next check point, while Check #2 occursafterwards to evaluate the shortest path from the robot’s currentposition. The uncertainty check for the upcoming check pointis more critical than the check for the current position, hencethe labeling as Checks #1 and #2, respectively.

If both the abovementioned Checks #1 and #2 fail, this maybe an indication that the robot is in a time-critical situationwhere it has possibly deviated significantly from its assignediso-probability curve so that, soon, even the shortest-path maynot allow the robot to reach its propagated destination curveon time. In this case, the robot’s path is replanned, where theshortest-path is accepted as the optimal path (i.e., the one thathas minimum estimated traversal-time) rather than the paththat comes closest to �tavail.

If either Check #1 or #2 fails (but, not both), this isan indication of a lower level of time-criticality in pathreplanning and, thus, we simply conduct a regular reoptimiza-tion and replanning for the remainder of the path, as willbe explained in Section III-C. In the above two scenarios,

Check #3 described below is not performed. However, if bothChecks #1 and #2 pass, then, Check #3 is conducted.

3) Check #3: Destination Arrival-Time Feasibility: The lastcheck that needs to be performed is to determine how earlyor late a robot can be expected to arrive at its propagated des-tination curve if it were to continue to follow its current path.A ±3σ confidence interval can be constructed for the esti-mated arrival-time error, relative to the desired arrival-timeof (t + �tavail), that can be expected by travelling along theremainder of the path. The details on computing this confi-dence interval, and verifying its acceptability, are given in theAppendix.

If Check #3 passes, namely, the robot is expected to arrive atits destination within a arrival-time-error confidence interval,the robot will continue on its current path. Otherwise, the pathis replanned as described in Section III-C below.

C. Path Replanning

Optimal path replanning resembles initial (optimal) path-planning, except that the starting point of the path is taken tobe the current position of the robot, and the first derivativeconstraint to be used for the first cubic-polynomial segmentof the path is taken to be the current orientation of the robot.With these modifications, the optimization defined by (2)–(4)is reapplied, where �tavail is the remaining available time untilthe next curve propagation.

It is, however, important to note that even though we opti-mize the initial path, as well as reoptimize the remainingpath for the robot when required, there is still no guaran-tee that the robot will remain precisely on its iso-probabilitycurve at all times and arrive at its destination point in exactly�tavail. Thus, herein, it is proposed that if the robot arrivesearly, it would simply continue to travel along its propagateddestination iso-probability curve. If the robot is not able toarrive within the available time, then, the next path planned tothe subsequent propagated destination iso-probability curve isconstructed from the robot’s current position.

D. Path-Planning for Centre Robot

Since iso-probability curves propagate outward from theLKP with time, and robots search by remaining on theirassigned curves, an unexplored region is formed by the searcharea bounded by the innermost curve. Since it is possible thatthe target could be present in this region during the search,our proposed MRC methodology designates one robot to thiscentral area, referred to as the “centre robot.”

When the search commences, the centre robot is initiallydeployed at the LKP. Just as for the other robots, its searchpath is planned one curve-propagation time-interval at a time.However, this path is composed of two segments. The firstsegment is a path leading from the LKP to a destination pointon the current, innermost, iso-probability curve (Fig. 6), wherethe destination point is found via optimization, as describedabove. The second segment is a path leading from this desti-nation point back to the LKP (Fig. 6). Since the destination forthe second segment is the LKP, no optimization is required.Instead, a smooth, single-polynomial path is planned back to



Fig. 6. Path-planning for centre robot.

the LKP, dependent upon the position and the heading-angleat the end of the first segment of the path.

Finding the optimal path for the centre robot, thus, entailsdetermining the optimal destination point on the innermost iso-probability curve such that the total estimated time requiredto traverse both segments of the path is as close as possible tothe curve-propagation time-interval, �tprop. Upon returningto the LKP, the centre robot repeats this two-segment path-planning process using the heading-angle at which it arrivedat the LKP to determine the starting trajectory of its next path.The intent here is not to conduct exhaustive coverage of thecentral region, however, but rather to implement a type ofnear-random search of this region so that it does not remainunexplored.

E. Coping With Obstacles

If an a priori known obstacle obstructs a planned path,the search-strategy requires that the robot move around theboundary of the obstacle on the side that minimizes theamount of travel (Fig. 7). This allows the robot to returnto its planned path expeditiously. In the case of an a prioriunknown obstacle, however, as an arbitrary, real-time choice,the robot commences travelling along the boundary of theobstacle in the clockwise direction until it is able to rejoinits originally-planned search-path.

F. Discovery of Clues

In our approach, a clue found is abstracted as representinga source of information that indicates a position within thesearch area where the target might have been at some pastpoint in time since the start of the search. As a conservativeestimate, the time at which the target might have left the clue isestimated based on the shortest possible time the target wouldtake to arrive at that position from the original LKP.

Using the latest found clue’s position as the new LKP,the iso-probability curves are reconstructed and a new opti-mal robot-deployment solution is computed and implemented.However, the optimality of the search depends on the robotssuccessfully attaining their new deployment positions andremaining on their assigned iso-probability curves. As such,all robots take the quickest path to their assigned positions on

Fig. 7. Example of robot circumventing a priori known circular obstacles.

their respective curves after a clue has been found. Hence, theformulation for path-optimization given by (2)–(4) is modifiedto one that simply finds the shortest possible path, where eachrobot’s path is constructed as a single cubic polynomial

min(�τ trav

), subject to (6)

{xdest, ydest}i ∈ fdest,i. (7)

The proposed search methodology resets the LKP whenpositively-identified clues are found during the search. In areal WiSAR mission, searchers may encounter clues whoseauthenticity needs to be verified. Therefore, it is important toincorporate domain expert judgment in validating whether aclue found is truly a positive one before resetting the LKP andredeploying the robots.

G. Multirobot Path Intersection

There is a chance that the robot paths could intersect.Occasional path intersection is desirable to account for recon-tamination. Robots are separated due to the planned distancesbetween the iso-probability curves, and the likelihood of tworobots simultaneously occupying the same point in space, dueto expected events (e.g., redeployment due to clue finding) orunexpected events (e.g., a priori unknown obstacles) is mini-mal. In the event that two robots do come close to each other,one robot would first yield the way to the other robot and, then,perform path optimality checks where appropiate. This woulddetermine whether the robot can remain on its assigned pathor an optimal path to its respective destination iso-probabilitycurve must be replanned.

IV. SIMULATED EXPERIMENTS

In order to demonstrate the overall tangible effectivenessof the proposed MRC methodology for WiSAR, numer-ous realistic search simulations were performed. One suchexample is detailed in Section IV-A. The methodology wasfurther validated through its comparison with a traditionalWiSAR method. The results of are presented in Section IV-B.Simulations were also conducted to gauge the robustness ofthe methodology to an incorrectly-estimated target-locationPDF. Section IV-C discusses the effect of such discrepancies.

A. Example Search Simulation

In this simulated realistic WiSAR example, the target wasassumed to be a hiker lost in a terrain permitting only ground-based search. The terrain, generated using the Terragen Classicscenery generator program [37], was represented in the formof a height-map matrix overlaid onto the search area.



Fig. 8. Example of target path.

1) Target Parameters: A normal distribution was assumedfor the mean target-propagation rate PDF, from which the sim-ulator randomly selected a nominal mean speed of 0.158 msfor the target in this example. The target moved outward fromthe LKP with normally-distributed random propagation ratevariations of ±3σ = ±0.0158 ms about the nominal meanpropagation rate, as well as normally-distributed random direc-tion changes, thereby mimicking drift in target motion. Thesimulation was programmed such that the target left behindclues every 1200 s. The resulting target path for this example,if not intercepted for a period of 9000 s, would have been asshown in Fig. 8.

2) Search-Robot Parameters: All 11 search robots used hada maximum attainable speed of 1.39 ms. However, the actualspeed varied based on the terrain experienced. The robots hada target-detection radius of 10 m and a clue-detection radiusof 3 m.

3) Optimal Deployment/Redeployment Parameters: Thetarget was assumed to have an 1800 s head-start, representingthe time taken for the robots to arrive and be initially deployed.Optimal initial deployment was carried out to determine theinitial number and positions of the iso-probability curves, aswell as the deployment positions of the robots. In addition tothe centre robot, the optimal solution dictated a deploymentof (2,2,2,2,2) robots on the five optimal iso-probability curves,respectively, positioned as shown in Fig. 9. The robots wereassumed to be dropped directly onto these initial positions.Twelve uniformly-distributed rays were used in order to com-pute the iso-probability curves, which were propagated every600 s throughout the simulation.

Optimal deployment was redetermined at 600 s time-intervals and compared to the existing one. A new optimalredeployment solution was implemented only if the percent-age improvement in the deployment optimization objectivefunction exceeded a threshold—herein, set arbitrarily to 4.5%.

4) Path-Planning Parameters: As noted above, since theiso-probability curves were propagated every 600 s, newrobot search-paths were planned and executed from eachrobot’s current position to a destination point on its respectiveassigned propagated destination iso-probability curve 600 sinto the future. All paths were planned with ten check-pointsper path.

Fig. 9. Optimal initial deployment of the search-robots at t = 1800 s.

Fig. 10. Search-path traced by rescuer R8 (blue) and another robot, R9 (gray),throughout the search simulation.

5) Search-Simulation Results: During the search, five iso-probability curve propagations were required. Redeploymentwas executed for each of the two found clues. The target waslocated by Robot #8 (R8) at 4868 s. For illustrative purposes,Fig. 10 shows the path (in blue) taken by R8, the path (in red)taken by the target, and the path (in gray) taken by anotherrobot, R9, throughout the search simulation. Table D1, in theAppendix, provides a walk-through of R8’s search-path, sum-marizing information corresponding to key points along thepath, which are indicated by “×,” and labeled as “P#,” inFig. 10.



Fig. 11. Illustration of the deterministic method with five robots.

B. Comparison to Nonprobabilistic Approach

A novelty of our WiSAR methodology is the representationof probabilistic information on target location through the useof iso-probability curves, and their subsequent use in on-linerobot path-planning. Due to the lack of existence of a com-parable probabilistic method for autonomous robotic WiSARin the literature, an alternative, nonprobabilistic method, simi-lar to grid-search, had to be developed and implemented, withwhich to compare our method.

1) Alternative Search Method: To our knowledge, no path-planning method in the literature makes use of the concept ofiso-probability curves, thereby precluding a “state-of-the-art”comparison. Thus, an alternative method for path planning thatwould make for a fair comparison is proposed. This nonproba-bilistic method resembles a grid-search technique, traditionallyused in WiSAR with human search agents [38]. It is deter-ministic in the sense that paths are planned according to afixed, a priori known pattern. The method starts the search byplacing all the robots at the LKP at time t = Ths, where theboundary of the search space is dictated by the 100% iso-probability curve at time t = Ths. The robots, then, moveradially outward with uniformly distributed heading-angles.If the robots reach the search-area boundary before the endof the available search time, they travel along this boundaryfor a while and, then, return to the LKP along new radialpaths (Fig. 11).

2) Simulation Set-Up and Procedure: A total of 1000 ran-dom simulations were performed for each of the two methods.For fairness, both the proposed and the alternative methodswere implemented using the same number of robots, maxi-mum search area, and search-time limit. Furthermore, no clueswere used in the probabilistic method, and a flat, planar terrainwas used for both methods. Both methods also used the same21 search robots moving with a maximum attainable speedof 1.39 ms. All robots were assumed to have a target-detectionradius of 20 m.

The target was given a head-start of 7200 s and moved witha mean speed of 0.139 ms, with random variations following anormal distribution with ±3σ = ±0.0139 ms. The initial targetheading angle outward from the LKP was selected randomlyat the start of each simulation based on a uniform distributionranging from 0◦ to 360◦. Throughout each search the target’sheading angle was also subject to random normal variationswith a mean of 0◦ and ±3σ = ±15◦. The maximum avail-able search time for each simulation run was set to 4000 s,beginning after the 7200 s head-start of the target, for a totalpossible target motion of 11 200 s. A search was considered

TABLE IISUMMARY OF COMPARATIVE SEARCH-SIMULATION RESULTS

to be unsuccessful if the target was not found withinthis time.

The maximum search-area boundary was defined as theperimeter of the circular region with a radius equal to thetotal distance that the target could travel, if it were to moveat its maximum outward propagation rate from the LKP on astraight-line path until the search-time-limit.

3) Simulation Results: The comparison of the two methodsis based on their resulting average search-time and success-rate over the 1000 simulations. The average search-time isthe arithmetic mean of the search-times of all the successfulruns, and the success-rate is the percentage of runs that weresuccessful (Table II).

The results show that the probabilistic method was able toattain a success-rate in locating the target of over 3 timesthat of the deterministic one. As well, a nearly 30% relativeimprovement in average search-time for successful searcheswas observed. A two-sample t-test was conducted to determinethat a statistically significant difference in search-times doesexist, t(200) = 5.39, p < 0.001. These significant benefits insearch-time and success-rate can be attributed to the utilizationof probabilistic information on target location.

Since the two methods achieve different percentages ofsuccessful searches, a more unbiased method of comparingsearch-times could be to average over the same number ofsuccessful runs. Since the deterministic method had the fewertotal number of successful runs of 201 out of 1000, wecould compare the average of the top 201 search-times of thetwo methods, respectively. Such a comparison yields averagesearch-times of 276 and 1811 s for the probabilistic and deter-ministic methods, respectively, resulting in about a 6.5 timessearch-time advantage for our proposed method.

In order to test a different deployment strategy for the deter-ministic method, this time, the search robots were initiallyrandomly placed on their respective rays, as opposed to allbeing placed at the LKP. The subsequent simulations validatedour above conjecture that significant benefits in search-timeand success-rate can indeed be achieved through the utiliza-tion of probabilistic information on target location. The newdeployment strategy yielded an average search-time of 2400 swith a success-rate of 71/425, approximately 17%. A two-sample t-test verified that a statistically significant differencein search-times does exist, t(153) = 3.84, p < 0.001.

4) Discussion: Although, the simulations verified that thereis indeed significant advantage provided by conducting thesearch according to the overall proposed MRC methodology,it is important to realize that, given the probabilistic nature ofthe WiSAR problem scenario, there cannot be any guaranteesfor always finding the target. In the WiSAR problem, the targetis not observed during the search, and, at best, one only has a



probability distribution of average propagation rate of typicaltargets falling under different categories. Moreover, the abso-lute mean values for both success-rate and search-time are notthe focus of this discussion, but rather the relative importanceof the results reported by the different search methodologies.The probabilistic method is favorable over the determinis-tic method. However, one can achieve an even lower meansearch-time, for example, by doubling the robot team size, asdiscussed in Section IV-D. Therefore, one would expect to findmore targets within a given search time with a greater robotteam size, resulting in a higher success-rate.

Even though, the alternative method makes use of the samesearchable area, robots are distributed in a nonoptimal man-ner. In addition, the target may always be moving, so anysearched area may be reoccupied by the target at a later time.It is, thus, preferable to allocate resources in an efficient andlogical manner, for example, by using probabilistic informa-tion about the probable location of the target with time, ratherthan blindly trying to cover as much unsearched area as pos-sible. Furthermore, our method attempts to keep the robots ontheir iso-probability curves, maintaining the optimal allocationof the search effort. Therefore, performance is not dictated interms of the size of the searched area, but by the appropriateallocation of resources within the searchable area.

C. Robustness Tests

Given how iso-probability curves are constructed in ourmethod, one concern that can be raised is that circum-stances may arise whereby the actual, or “true,” mean target-propagation rate PDF that pertains to the target being soughtis significantly different from the assumed one that is usedto compute the iso-probability curves. However, since thetype of target being sought would always be known (e.g., anadolescent child, an experienced, healthy hiker in his/her mid-20s, etc.), and since all raw data used to construct the meantarget-propagation rate PDF comes from historical data that iscategorized by target-type, such differences can be expected tobe minimal. Nevertheless, it is instructive to consider how theproposed methodology would behave if the assumed and truemean target-propagation rate PDFs were to, indeed, differ.

In order to inject more reality into our simulations, sev-eral robustness tests were performed, where the true (normal)mean target-propagation rate PDF governing target-motionwas intentionally scaled relative to the assumed (normal)mean target-propagation rate PDF used to construct the iso-probability curves. Three scale factors were considered: 0.75,1.00, and 1.50 (the 1.00 scale-factor serving as the benchmarkcase where the assumed and true PDFs are the same).

For each scale-factor scenario, 1000 simulation runs wereconducted. The same parameter settings as those for the com-parative simulations (Section IV-B) were used, except that thetarget was given an 1800 s head-start, and the available searchtime thereafter was set to 5400 s. Table III summarizes thetest results.

When the mean target-propagation rate PDF is significantlyover-estimated (i.e., 1.00 versus the scale-factor of 0.75), thetrue PDF has a smaller mean and variance relative to theassumed one and is, therefore, contained within the assumed

TABLE IIISUMMARY OF ROBUSTNESS TEST RESULTS

PDF. Hence, for these circumstances, we can still expect agood success-rate value, as for the ideal case, since the targetwould remain within the boundaries of the area being searched.This is corroborated by the results in Table III. It is observedthat the corresponding average search-time is about the sameas that for the benchmark case.

With the actual mean target-propagation rate PDF scaleddown, the resulting lower actual target propagation rate wouldimply that the target would tend to reside, on average, inthe regions closer to the LKP, where lesser search-effort isplaced relative to the region near the mean of the assumedPDF. This accounts for the somewhat increased search-timefor the over-estimation scenario relative to the benchmarkcase. However, a two-sample t-test confirms that a statis-tically significant difference in average search-times exists,t(924) = 1.60, p < 0.1.

When the PDF, however, is significantly under-estimated(i.e., 1.00 versus the scale-factor of 1.50—a 50% error), thereis the possibility that the target could have a mean propa-gation rate much greater than the maximum assumed, andmay travel so fast as to move out of the area being searched.In our 1000 simulated cases, this would imply an increasednumber of failed searches, as noted in Table III. With respectto search-time, since the actual mean target-propagation ratePDF is scaled up, the resulting higher actual target propaga-tion rates mean that, among the successful runs, the targetwould tend to reside, on average, in the regions further fromthe LKP. Again, lesser search-effort is placed in these regionsrelative to the region near the mean of the assumed PDF. Asa result, the tests showed greater average search-time for theunder-estimation scenario relative to that for the benchmarkcase. As expected, the two-sample t-test confirms that a sta-tistically significant difference in average search-times exists,t(602) = 3.53, p < 0.001.

Hence, the results show that even when the true meantarget-speed PDF differs from the assumed one by as muchas 25% (for the over-estimation cases), the proposed methodis robust, producing negligible changes in success-rates andsearch-times. For greater discrepancies between the true andassumed mean target-propagation rate PDFs (especially for theunder-estimation cases), the performance of the method can beexpected to drop.

D. Robot Team Size

Robot team size directly affects the total search time. Lowernumbers imply that robots take a longer time to cover the sameworking space while still maintaining their optimal deploy-ment. In contrast, a team of robots with a larger size indicates



that there are more robots to deploy using more iso-probabilitycurves, which increases the search effort over the search space.Furthermore, the underlying assumption that any robot is fasterthan the fastest target nominal propagation rate, associatedwith the 100% iso-probability curve, promotes the fact thatrobots would likely find the target in a reasonable amount oftime.

In order to illustrate the impact of robot team size onsearch time, simulations were run for the example scenariodescribed in Section IV-A, but with double the number ofrobots (i.e., 21 robots). The simulations, as expected, showedthat an increase in robot team size reduced the search timefrom 4868 to 3517 s.

V. CONCLUSION

In this paper, a novel robot path-planning strategy was pre-sented to facilitate autonomous, MRC in WiSAR scenarios.The proposed methodology provides a means for construct-ing on-line, optimal search-paths for the robots, based on theprinciple of keeping each robot on its assigned iso-probabilitycurve at all times to maintain the optimal deployment. Themethod works by: 1) constructing an initial search-path withestimated traversal-time as close as possible to the time avail-able until the next iso-probability curve propagation; 2) reg-ularly monitoring path-optimality during path-implementationusing a set of three logical and quick checks; and 3) reopti-mizing and replanning the path appropriately, if necessary.

A simulated WiSAR search example was presented inthis paper to illustrate the ability of the method to workin tandem with the propagating iso-probability curves dur-ing a search scenario to successfully plan effective robotpaths. Numerous comparative simulations with a determin-istic, pattern-based search method validated the proposedMRC methodology by demonstrating its ability to achieve asignificantly higher success-rate and shorter average search-time. Finally, numerous additional simulations demonstratedthe proposed method’s robustness to discrepancies in theassumed mean target-propagation rate PDF relative to the truedistribution, and the effect of robot team size on search time.

Our proposed methodology is not exclusive to roboticagents. It can also be used in a simpler form by human agents.As long as there is a centralized system that is able to coordi-nate with such human agents during the iso-probability curvepropagations, human-based WiSAR missions could make useof our proposed algorithms. In addition, the methodology canbe further expanded to consider both cooperative and evad-ing targets, where the use of iso-probability curves may assistrobots in tracking the target.

APPENDIX

A. Check #1

When examining the optimality of a robot’s search-path dur-ing implementation in order to determine if the path needs tobe replanned, the first check that is conducted is to determinewhether a feasible shortest-path exists from the next check-point to the propagated destination iso-probability curve. Thetraversal-time associated with this shortest-path is estimated in

the same manner as for any general path as described earlier inSection III-A. However, due to varying terrain, the robot mayend up travelling slower or faster over the next subdivision,compared to what was estimated during initial path-planning.This results in uncertainty as to the actual arrival-time atthe propagated destination iso-probability curve, if the robotwere to take this shortest-path. This uncertainty might requirereplanning the robot’s path. Therefore, rather than obtaininga single estimate of the arrival-time via the shortest-path andcomparing it to �tavail, one can construct a confidence intervalfor this shortest-path arrival-time, given probabilistic informa-tion about the inherent uncertainty in traversal-time per pathsubdivision.

As the robot travels along its path, a record is kept of theactual time, �ttrav,j, spent to traverse each of the past pathsubdivisions. Based on the initial path-plan, the correspondingestimated traversal-times, �τtrav,j, for each of those subdivi-sions are also known. This allows for the computation of thetraversal-time estimation error, εtrav,j, for each path subdivisionj, that has been traversed up to the robot’s current position,where

εtrav,j = �τ trav,j − �ttrav,j. (A1)

It is assumed that these errors have a normal distribution.Thus, once a robot has completed two path subdivisions, therewould be enough error data to compute an estimate, εtrav, ofthe average error in the estimated traversal-time per path sub-division due to terrain variations, as well as a correspondingconfidence interval. This error information, in turn, is used toconstruct a ±3σ confidence interval for the arrival-time at thepropagated destination iso-probability curve if the robot wereto take the shortest-path from the next check-point. As a result,an upper and lower limit, TC1,HI and TC1,LO, respectively, forthis arrival-time confidence interval is computed every time arobot arrives at a check-point and performs Check #1.

It is critical to verify in Check #1 that the robot does not runout of time to reach its propagated destination iso-probabilitycurve even via its shortest-path from the next check-point.Thus, the upper-bound, TC1,HI, of the confidence interval forthe estimated shortest-path arrival-time is compared with athreshold on maximum arrival-time, TC1,Max, given by

TC1,Max = Tcurrent + (�tavail + M�tavail) (A2)

where Tcurrent is the current time and M is a user-specified per-centage margin of error, so that M. �tavail represents a safetymargin added over and above the time available to reach thepropagated destination curve. The condition to be satisfied inCheck #1, then, is

TC1,HI ≤ TC1,Max. (A3)

B. Check #2

The second path-optimality check that is performed to deter-mine whether a path being implemented by a robot needsto be replanned is to determine whether a feasible shortest-path exists from the robot’s current position to the propagateddestination iso-probability curve. The traversal-time, �τC2,



associated with this shortest-path is estimated in the same man-ner as described earlier in Section III-A. However, since it isonly an estimate, the user must allow for a certain marginof error, similar to that used in Check #1. Thus, rather thancomparing this traversal-time estimate directly with �tavail, wepropose that the comparison be made instead with �tC2,Max

�tC2,Max = �tavail + M�tavail (B1)

where M is the same user-specified percentage margin of erroras that used in (A2). Thus, the condition to be satisfied is

�τC2 ≤ �tC2,Max. (B2)

C. Check #3

The third path-optimality check is to determine the expectederror in the estimated arrival-time at the propagated destinationiso-probability curve, if the robot were to continue to followits current path. This check uses the subdivision traversal-timeerror data that is gathered as the robot passes through eachcheck-point. Although, this error-data yields an approximationof the error in traversal-time estimate per path subdivision, itwould be unrealistic to assume this error will continue to existover all the remaining subdivisions on the robot’s current path.Thus, the uncertainty in the arrival-time estimation error overthe remaining path (represented in terms of a corresponding±3σ confidence interval) is computed based on the uncertaintyin the arrival-time estimation error over the next immediatepath subdivision only.

Upon computing this confidence interval, upper and lowerlimits, EC3,HI and EC3,LO, respectively, for the arrival-timeestimation error for the remaining path will have beenobtained. These limits are compared to corresponding upperand lower arrival-time error thresholds. As more subdivisionsare traversed and more error data is collected, the arrival-timeerror confidence intervals narrow. Since errors are assumed tobe normally distributed, this narrowing should conform to anexponential function. Thus, it would be reasonable to constructupper and lower confidence-interval thresholds that narrowcorrespondingly (i.e., exponentially). Moreover, we allow fora 100% margin of error for the confidence interval derivedbased on error-data from just two path-subdivisions, and a10% margin of error for the last confidence interval that willbe computed (i.e., the confidence interval computed at the endof the second-last subdivision, N-1, along the path).

The user may change these error-margins if he/she wishesto be more conservative, or liberal, for Check #3. However,the error thresholds must be larger at the beginning of the path(i.e., at the second check-point) than at the end of the path (i.e.,at the second-last check-point) since there is greater uncer-tainty in arrival-time error estimates near the beginning (whenonly two data-points are available) than at the end (when moretraversal-time data will have been gathered).

From these specified error-margin conditions at the twopath-end-points, we can derive corresponding upper andlower arrival-time error threshold functions, EC3,Max( j) andEC3,Min( j), respectively. These exponential functions out-put the upper and lower arrival-time error thresholds usedfor Check #3, when the robot is at the end of any path

TABLE D1SUMMARY INFORMATION AT KEY POINTS ALONG R8’S PATH

P# Time[s] Notes

P1 1800 � Optimal initial deployment = 5 curves � R8 is assigned to curve #4 � Path planned to destination point on curve #4 600s into the future

P2 2400 � Curve propagation #1 occurs � Current deployment solution is still optimal � New path to next destination curve is planned

P3 2564

� Clue found at (-86.9 m, -25.2 m) � Re-deployment occurs; new optimal deployment with 9 curves � R8 remains assigned to curve #4 � Shortest-path to future curve #4 is planned



P6 3964

� Clue found at (23.7 m, -74.8 m) � Re-deployment occurs; new optimal deployment with 9 curves � R8 remains assigned to curve #4 � Shortest-path to future curve #4 is planned

P7 4200

� Curve propagation #4 occurs � Current deployment solution is still optimal � R8 is assigned to #5 � New path to next destination curve is planned


P9 4868 � Target is found by R8 � Search is complete

subdivision j. Thus, the conditions given below must besatisfied for Check #3 to pass

EC3,HI ≤ EC3,Max ( j) (C1)

EC3,LO ≥ EC3,Min ( j). (C2)

D. Key Points Along R8’s Path

Table D1 summarizes nine key points of interest along thepath taken by R8 (see Fig. 10) during the example WiSARsearch simulation that was presented in Section IV-A.

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Ashish Macwan received the B.A.Sc., M.A.Sc., and Ph.D. degrees in mechan-ical engineering from the University of Toronto, Toronto, ON, Canada, in2000, 2002, and 2013, respectively.

His current research interests include multirobot coordination and its appli-cations to autonomous search and rescue, as well as design, planning, andcontrol for mobile robots operating in challenging environments.

Julio Vilela (S’13) received the B.A.Sc. degree inengineering science from the University of Toronto,Toronto, ON, Canada, in 2013, where he is currentlypursuing the M.A.Sc. degree in mechanical engi-neering under the supervision of Dr. Benhabib andDr. Nejat, with a focus on multirobot coordinationfor wilderness search and rescue.

Goldie Nejat (S’03–M’06) received the B.A.Sc. andPh.D. degrees in mechanical engineering from theUniversity of Toronto, Toronto (UofT), ON, Canada,in 2001 and 2005, respectively.

She is currently an Associate Professor anda Director of the Autonomous Systems andBiomechatronics Laboratory with the Department ofMechanical and Industrial Engineering, UofT. Sheis also the Director of the Institute for Roboticsand Mechatronics at UofT and an Adjunct Scientistat the Toronto Rehabilitation Institute, Toronto,

ON, Canada. Her current research interests include sensing, human–robotinteraction, semi-autonomous and autonomous control, and intelligence ofassistive/service robots for search and rescue, exploration, healthcare, andsurveillance applications.

Dr. Nejat is a member of the American Society of Mechanical Engineers.

Beno Benhabib received the B.Sc., M.Sc., and Ph.D. degrees all in mechan-ical engineering in 1980, 1982, and 1985, respectively.

He has been a Professor with the Department of Mechanical and IndustrialEngineering, and the Institute for Biomaterials and Biomedical Engineeringat the University of Toronto, Toronto, ON, Canada, since 1986.

His current research interests include the design and control of intelligentautonomous systems.

http://www.foothills-sar.ca

http://www.sarglobal1.ca

http://planetside.co.uk/terragen-classic-windows-download

http://planetside.co.uk/terragen-classic-windows-download

Documents

A Multirobot Path-Planning Strategy for Autonomous Wilderness Search and Rescue