a graph-based exploration strategy of indoor exploration

7/29/2019 A Graph-Based Exploration Strategy of Indoor Exploration

1/7

Proceedings of the 1998 IEEEInternational Conference on Robotics&Automation

Leuven, Belgium * May 1998

A Graph-Based Exploration Strategy of Indoor Environmentsby an Autonomous Mobile RobotJane Yung- jen HSU* Liang-Sheng HwangDepar tment of Computer Science and Informat ion Engineer ingNat ional Taiwa n Univers i ty , Taipei , Taiwan 106, R.O.C.

AbstractT h i s p a p e r p r e s e n t s a provably complete s t r at e g y f o r i n d o ore n v i r o n m e n t e x p l o ra t i o n b y a n a u t o n o m o u s m o b i l e r o bo t.W i t h o u t p r i o r k n o w l e d ge a b o ut t h e e n v i r o n m e n t , t h e s t r at -egy guarantees the construction of a grid-based map of theentire reachable area within a bounded region. Multip lema p re present ations are uti l ized inc6uding a topological gridma p fo r gu id ing the exp lora t ion p rocess , a mod i f ied occu-p a n c y g r id f o r u s i n g d a t a f r o m m u l t i p l e r an g e s e n so r s , a n da h ie rarchy of g r id s fo r rea l - t ime nav iga t ion . Exper imen tsu s i n g a N o m a d 200TMrobo t have shown accura te map con -struction while navigating at a s teady speed of 0 . .2m/sec.

1 IntroductionThere are many potential applications of mobile

robots in our everyday life. Imagine a floor-cleaningrobot t hat plans a priori the optimal path to clean anarea using a map. To ensure successful completion ofthe task, access by other agents to the area has to berestricted. Moreover, the task may fail if the layout offurniture has changed. For applications like householdvacuuming, demanding an accurate map is simply im-practical.

A mobile robot operating in the real world needs todeal with such incomplete and uncertain informationabout i ts environment. Although sensor-based navi-gation techniques enable a robot to negotiate its waythrough unknown obstacles without a map, for moreeffective navigation and task execution, it is useful forit to construct and update its world model dynami-cally [ a ] . An autonomous mobile robot should 1) havean exploration strategy to guide its search, 2 ) constructa world model by fusing dat a collected through mul-tiple sensors, and 3) utilize the dynamically updatedmap for real-time navigation and task achievements.

*This research was suppor ted in part by the Natio nal ScienceCouncil of ROC under grant NSC 86-2212-E-002-024.

0-7803-4300-~-5/9810.000 998 EE E 1262

This paper presents a graph-based explorationstrategy that is provably complete with respect to anybounded region, e.g. indoor environments. The explo-ration results in a grid-based map constructed on-lineby fusing range data from multiple sensors while therobot navigates in an initially unknown indoor envi-ronment. The resulting map consists only of stat icfeatures as desired. In Section 2 , we begin by brieflyoutlining the proposed graph-based search algorithm,followed by detailed descriptions and the completenessproof in Section 3 . Section 4 presents a simplified cer-tainty grid method for fusing dat a from multiple rangesensors according to the sensor characteristics. Theproposed method achieves real-time updating whilepreserving enough accuracy for global planning andnavigation within the environment. Experiments on aNomad 200TM mobile robot with sonar, infrared, andlaser range sensors are presented in Section 5. The re-sults showed that the system is efficient, effective androbust in a dynamic environment.

2 Graph-Based Exploration StrategyTerrain exploration has been an importan t research

problem for autonomous mobile robots [ l o , 9 , 4 , 51.In this work, a graph traversal algorithm is proposedto guide a robot in exploring its environment so thatevery reachable area will be visited. Th e algorithmalso minimizes the overhead in moving from one ex-ploration point to another.

An unknown bounded region can be decomposedinto a two-dimensional tessellation. The size of eachcell in the tessellation is decided by the radius of therobots effective sensor range. Each cell is mapped in toa vertex in the corresponding gr aph, whose connectiv-ity is defined by the special adjacency relation amongcells. Figure 1 shows a sample mapping into the graphrepresentation. Such a topological graph records thestatus of each cell as one of u n k n o w n , visited, passed,or inaccessible.


2/7

Figure 1: The topological grid of a bounded region

3 Algorithms and CompletenessThe exploration strategy is summarized as follows.

1. Initialize every cell to unknown.2 . c c the cell where exploration starts.3. loop until every cell is visited or inaccessible;loop until obstacle detected at c ;

Move straight to next cell c;Mark c as passed;c + c.end

c- canline --

Figure 3: A sample IU consisting of cells 2, 3, and 4.Cells 1 and 5 straddle the scan line.

Figure 4(a ) illustrates the sequence of a typical tra-jectory generated by our robot. Figure 4(b) shows thecorresponding boundary chain. Note that the subse-quence of cell 22 is cell 26; the subsequence of cell31 is cell 33. The re are three IUS (IU1[30/32,29,28],IU2[2/24], and IU3[48,47]) on the indicated scan line.IU 1 will be misjudged as a breaking IU, which leadsto an incorrect fill! The misjudgment of IU1 is due tothe jumping connectivity of cells (31+33).

scan -line 4

(a) (b)f c is not visited,then Circumnavigate obstacle boundary;Update geometric world model;Mark cells travelled as visited;Fill cells inside obstacle as inaccessible.

Figure 4: (a ) The sequence of cells passed by therobot, and (b) its corresponding boundary chain.

c t est-Next-Cell(c)Navigate to c.Mark cells on the path as passed.c t .

The problem can be solved by relaxing the con-strai nt tha t only one visit is permi tted for each cell inthe polygon boundary. The algorithm for computingthe breaking IU S are summaried below.

end Requirement:Figure 2: The Graph Traversal Algorithm A vertex chain V of polygon boundary withoutjumpi ng connectivities.

A tessellation buffer tess initialized with 0s.3.1 The Filling AlgorithmThe filling algorithm marks the inner cells of an

obstacle as inaccessible. Due to poor resolution ofgrids, standard filling algori thms such as the even-oddneeds t o be modified. Cells on the boundary of a grid-type polygon are viewed as vertices. A scan line mayintersect with a polygon at a continuous segment ofboundary cells, which are called an intersection unit(IU) (e.g. Figure 3 left). Each IU is treated as a sin-gle intersection point . If the cell immediately beforeand after an IU straddle the scan line (as shown inFigure 3 right), it is a breaking IU.

Passl: for each vertex vi in V , oAY t oorY(succ(vi))- CoorY(pre(wi))tess[CoorY (vi)][CoorX(vi)]

t ess[CoorY (wi)][C:oorX(wi)]+AYPass2:

for each horizontal scan line 1 , dofor each intersection unit P on 1 do

t tCV,EPess[CoorY(v;)][CoorX(vi)]if t #0 , P is a breaking IU

The function succ (pre) takes a vertex as argumentand returns the succeeding (preceding) element in the

1263


3/7

chain V . Th e function CoorX (CoorY) takes a vertexas argument and retur ns its z ( y ) coordinate. Figure 5(b) shows the results given the boundary in Figure 5(a).

Figure 5: Results of intersection computation

3.2 Selecting the Best Next NodeEach cell in the tessellation T can be in one of the

following four states:Unknown ( U ) : the cell is unknown to the

robot; all cells are in this state initially.Boundary ( B ) : the cell has been visited by therobot while it is in the circumnavigation

mode.Pass (P): the cell has been visited by the robot

while it is no t in the circumnavigationmode.

Forbidden (F): the cell is marked as forbiddenin the filling process.

Our goal is to select the best cell in state U asthe next exploration target . Not all cells are reachablefrom the current position of the robot and there maybe unobserved obstacles. However, we can always nav-igate to a cell in state U th at is next t o some visitedcells. We first identify as target any cell in state Por B having unvisited neighbors. The robot will thenproceed to explore one of its unknown neighbors.

The simple shortest dzstance first heuristic is usedin choosing the best next node. The idea is similar tonumerical potential field [1]. Imagine the closed envi-ronment as a pond and the forbidden cells as islandsin it. Ripples propagate outward from the position ofthe robot. Assuming there are no reflected waves, thefirst candidate cell encountered by the waves is thetarget. More precisely,

10 otherwise

if the robot is currently at cell z-1 if z is a forbidden cell (2)

~;l.+~enotes the s ta tu s of a cell r with respect to theripples at ti me step k +1: 0 indicates it has not beenreached by any ripple; i indicates it was first reachedby the ith ripple; -1 indicates a forbidden cell. N4 is afunction tha t takes a cell as argument and returns theset of its four neighbors. Figure 6 shows the values ofsuch a computation.

forbidden cell

Figure 6: Th e numerical ripple.

3.3 Completeness of the StrategyThe section presents some formal results for theproposed approach.

Lemma 1 Th e procedure described in S ecti on 3.2 al-ways selects an unknown cell if one exists.Lemma 2 Th e proposed graph-based t erruz n acquisi-tion ulgorathm terminates.Theorem 1 (Completeness) When the programterminates, all reachable cells are visited b y the robot.

Proof B y Lemma 2 , when the algorithm termi-nates, all cells are known to the robot, either visitedor forbidden. Since the filling algori thm correctly fillthe inside and outside of a polygon, all reachable cellswill be correctly classified into state B or F .

k +1.+ ={ u i otherwise

( 1 )where k =1 , 2 , 3 , .. The initial values are defined as.

if U; =0 and 32 E N4(u;l.) s.t . U: >0 We can also show that the total distance traversedby the robot has an upper bound of O ( N 2 ) and alower bound of O ( N ) ,where N is the total number ofreachable cells in t h e environment.

1264


4/7

4 World Modeling 4.1 Occupancy probability profileOccupancy grids [6,7] or cer ta in tyg r id s [ll] rovide

a good way to fuse sensor da ta over time. Using theBayes rule, one can compute the improved probabilis-tic estimates by integrating a new observation withthe existing model. Several modifications have beenproposed to allow grid values based on fuzzy [12] orevidential [13] theories. However, updati ng the gridvalues is very comput ationally intensive. Given anarea of n * n cells, it takes 0 ( Y 2 )mount of compu-tation to update the probability of whether a singlecell Ci is occupied when a new sensor reading is ob-tained. If the values are calculated off-line for reuse, atable of size O(2) is needed. As a result, occupancygrids are feasible only within a local region [14] sincethe m ap may not reflect in time dynamic changes inthe environment. On the other hand, computing thevector field histograms [3] is simple, but the resultingmodel is only good for local obstacle avoidance ratherthan global path planning.

This research proposed a simplified computationrule for updating a grid-based geom etric m ap that pro-duces reasonably accurate results for navigation. Theproposed approach can be used to integrate data frommultiple sensors according t o the different sensor char-acteristics. The size of the cell is determined by thehighest sensor resolution as well as the minimal per-formance requirements. The basic idea is to associateeach cell Ci with a real number, called cer ta in ty d u e ,which indicates how likely the cell is being occupied byan obstacle. Let V(Ci)denote the measure of confi-dence that an obstacle exists within cell C; . A highercertainty value indicates a stronger evidence for be-lieving the cell to be occupied. The gr id-updating pro-cedure can be summarized below, where F is a smallnumber as the default certainty value.

1. Initialize each cell V(Ci )=E .2. loop until exploration is completed.

0 Obtain the current sensor readings r .

The occupancy probability profile specifies the areaof interest, i.e. the set of cells relevant to the currentreading,. Given a sensor reading r for an d e a l sensor,a possilble profile is defined as follows:

0 i f x < r{ i f x > rP ( x ) = l i f x = r (3 )where :E is any cell along the direction of the detectedobstacle. Th at is, the probability is 1 for some ob-ject to be within the cell boundary corresponding tothe givien sensor reading, and it is 0 for all intermedi-ate cells between the robot and the detected obstacle.The cells behind the detected obstacle are not observ-able from the vintage point of the robot a nd thereforeare equally probable to be occupied or empty, i.e. aprobability of 3.In general, the scanned obstacle may lie anywherewithin a cone-shaped neighborhood along the acousticaxis. Considering the trade-offss between computationand accuracyr a combined appiroach was employed inour implementation: the line model is adopted whensomething is detected by the sonar; otherwise, use thearea model. The intuition was that the ar ea modelis significantly harder to compute in the former case,yet its benefit is uncertain.

Unfortunately, indoor experiments on real robotshave shown that echoing and (deflection of the sonarsensors present a serious problem under the areamodel: map corruption OCCUrB too frequently, espe-cially in the regions near the robots trajecto ry. Sincesonars use the tzme-of-flzght of the reflected signal tocompu1,e the distance t o the sensed obstacle, the inten-sity of reflecting waves depend:; on the incident anglebetweein the acoustic axis of the sonar and the nor-mal of the obstacle. Inaccurate measurements are aninherent problem with the ultrasonic sensors.

To overcome such problems, the idea of a certazntym o m e n t u m f u n ct z o n is introduced. The momentumis defined as a function of the certaznty values rather

Interpret r using occupancy probabzlzty pro-file.. ~~~ multiple sensor readings by sensorwezght functaon s.Update certaznty value for each cell.

0 end

than of dzstance. Since the certainty value of any cellhas to be computed incrementally, a high certaintyvalue can be accumulated only if the cell has been es-tima ted to be occupied for a large number of times. Itmakes :sense to ignore an occasional wrong reading.A typical momentum function defines cells with highervalues 1o have a higher probability to st ay occupied byan obstacle. When nothing is detected by the sonar,cells with certainty values over a threshold will remainintact to avoid map corruption. With continuous and

Figure 7: The cell updating cycle

1265


5/7

rapid sampli ng, the approach generates reasonable re-sults in ou r experiments. More details can be foundin [8].4.2 Sensor Weight Functions

The objective of fusing data from multiple sensorsis to produce a robust, consistent, and fault-tolerantdescription of the environment. None of the rangesensors is perfect. Each typ e of sensors has its owncharacteristics, and multiple sensors can be combinedto compensate for one another. For example. thelaser range finder produces accurate readings, but itseffective range is smaller than the sonar; infrared da tavaries with lighting conditions; sonar readings are af-fected by surface materials.

In this framework, two weights are associated witheach sensor: sensor type, Ws, , and dis tance, Wdis .The former is defined in term s of the relative accuracyof a partic ular typ e of sensor. Given a sensor s , itsaccuracy A(s ) s defined as:

IT-dlA( s )= '- (4 )# dd R

where T is the range reading, d is the actual dis-tance, R s the effective range, and # d is the num-ber of measurements taken. Thre e types of rangesensors including laser, sonar, and infrared are usedin our experiments. The ir accuracies are orderedas A(Zs) > A(ir) > A(sn) . Let A be the sum ofA(ls)+A(sn)+A( ir ) . The sensor type weights aredefined as follows.

A( s )w, - ( 5 )The latter, distance weight, represents the relativeaccuracy of a given sensor over its effective distance.Let W& denote the distance weight function of sen-sor s. Figure 8 shows the different Wdis functions oflaser, sonar, and infrared. To model the decayed den-sity of reflected signal with the increase in distance tothe robot, sigmoid functions were used for sonar andinfrared. On the other hand, the laser is modeled bythe normal distribution function to capture its utilitywithin a limited range.

The to tal weight for a specific sensor s with readingT is calculated by combining the two weights.

Such sensor charact eristics are often available fromits specifications as well as through empirical tests.

Figure 8: Weight functions of different sensors.

The weight functions can be computed off-line andstored in look-up tables to speed up subsequent ma pupdating.4.3 Certainty Value Updates

We are now ready t o present the fo rmula for up-dating certainty values during each sensing cycle. Tocompose the sensory information incrementally, oneneeds to combine the cumulative value with the newobservation. The sequentia l update momentum func-t ion m( z ) s used to define the relative weight of thetwo. Some typical momentum functions are shown inFigure 9. For example, Figure 9(a) shows that the rel-ative weight decreases smoothly with the decrease ofdistance to the robot. This comes from the intuitivelyappealing result that the areas around the robot hasa higher tendency of being updated than those fartheraway.

Figure 9: Sequential up date mome ntum functionsFor each cell z, a gain (loss) of credibility is added

to its certainty value C ( x ) f it is judged to be occu-pied (emp ty) in the current cycle. Assume that therange sensor s returns a reading of T at stage /c. Th ecertainty value ck(2) of cell z at stage k is:

(7 )where gain is a constant value, Q =m( z ) s the mo-mentum function, and the update ratio p is:

( 8 )= (1- y ) * P ( z )* W"1266


6/7

Due to frequent ma p updatin g, the world model candynamically reflect changes, such as moving obstacles,in the environment. As a result, the path plannercan replan a better path whenever substantial changeshave occurred in the map.

5 ExperimentsTo verify the feasibility of the proposed method,

experiments have been performed both in a simu-lated environment and on a mobile robot. The No-mad 200TM is an integrated mobile robot system withfour sensory modules including tac tile, infrared, ultra-sonic, and structu red light vision system. It has an on-board computer for sensor and motor control as wellas for host co mputer communication. The mobile basekeeps track of its position and orientation over time.The tactile system consists of 20 independent pressuresensitive switches arranged in two rings, which detectcontacts with an object. The 16-channel, reflective in-tensity based infrared ranging system provides infor-mation up to 30 inches, under proper conditions. The16-channel, tim e of flight based ultrasonic ranging sys-tem provides information from 17 inches to 256 inches.The two-dimensional, triangula tion based laser rang-ing system has an operat ing range of 12 to 120 inches.The initial certainty values were V(Ci )= 5 in ourexperiments.

Figure 11 shows the results from experiments ina simulated environment with static obstacles (Fig-ure 10. The resulting map has IOP=2.5744 in. andIOA=99 .OS%.

I1 .Figure 10 : A simulated world with static obstacles

Figure 11: Learned map for the simulated world

To demon strate the effects (of dynamically movingobjects within the environment, a series of experi-ments were performed in a real-world environmentTwo irregularly shaped thin cazdboards were laid outin the middle of the room with a person moving abou twithin the space throughout the experiments. Fig-ures 12 and 1 3 shows the results. In particular, thecardboards were positively identified, while the mov-ing person didn't show up on the map. Using the map,the robot was able to navigate freely within the spacewithout bumping into any obstacles.

Figure 12: Sensor traces in a real environment

6 ConclusionsThis paper presented a graph-based exploration

strategy for a mobile robot in indoor environments.

1267


7/7

Certainty Value150

Figure 13 : Results in an environment with dynamicobstacles (IOP=9.0056 in., IOA=95.8679%)

Our approach utilizes different levels of maps for ex-ploration control, world modeling, and real-time nav-igation. In particular, the proposed strategy guar-antees complete exploration of any bounded enclosedarea. The overall performance has been shown to beboth robust and efficient. The current system usesstandard sensor-based postion estimation techniques[2] to correct it s cumulative odometry errors. Whilethe resulting map is adequate for navigation of ser-vice robots for house cleaning, bette r localization tech-niques in unknown environments will be necessary forhigher precision tasks.

Reference s

obstacles of polygonal shape. Robotica, 12:33-44,1994.

[5] T. Edlinger and E. von Puttkamer. Explorationof an indoor-environment by an autonomous mo-bile robot. In Proceedings o f the IEEE/RSJ In-ternational Conference on Intelligent Robots andS ys tems , pages 1278-1284, September 1994.

[6] A. Elfes. Sensor-based real-world mapping andnavigation. IEEE Journal of Robotics and Au-to ma t io n , 3:249-265, June 1987.

171 A . Elfes. Occupancy grids: A stochastic spa-tial representation for active robot perception. InProceedings of the Sixth Conference on Certaintyi n A I , July 1990.

[8] L.S. Hwang. Automatic map building for a mo-bile robot. Ms thesis, National Taiwan University,June 1995.

[9] J. J . Leonard, H. F. Durrant-Whyte, and I. J.Cox. Dynamic map building for an automous mo-bile robot. The In ternational Journal of RoboticsResearch, 11(4):286-298, August 1992.

[ l o ] V . Lumelsky, S. Mukhopadhyay, and K . Sun.Sensor-based terrain acquisition: The sightseerstrategy. In Proceedings of the 28th Confer-ence on Decision and Control, pages 1157-1161,Tampa , Florida, December 1989.

[ l l ] H. P. Moravec. Sensor-fusion in certa inty grids formobile robots. AI Magazine, pages 61-74, Sum-mer 1988.

[ l a ] G. Oriolo, M. Vendittelli, and G . Ulivi. On-linemap building and navigation for autonomous mo-bile robots. In Proceedings of th e IEE E In tern a -.

J. Barraquand, B. Langlois, and J.-C. Latombe.Numerical potential field techniques for robotMa n, and Cybernetics, 22(2):224-241, April 1992.J. Borenstein, H . R . Everett, and L . Feng. Nav-igating Mobile Robots: Systems a n d Technzques.A .K . Peters, 1996.

tional Conference on Robotics and Automation,pages 2900-2906, 1995.

path planning. IEEE Transactions On [13] D, Pagac, E, M. Nebot, and H , Durrant-Whyte.An evidential approach to probabilistic map-building. In Proceedings of the IEEE Interna-tionul Conference on Robotics and Au to mu t io n ,pages 745-750, April 1996.

[14] F. Wallner, R. Graf, and R. Dillman. Real-timemap refinement by fusing sonar and active stereo-vision. In Proceedings of the IEEE In ternationalConference on Robotics a n d A u t o m a t i o n , pages

J . Borenstein and Y . Koren. The vector fieldhistogram-fast obstacle avoidance for mobilerobots. IEEE Transactions on Robotics and Au-tomataon, 7(3):278-288, June 1991. 2968-2973, 1995.Z. Chen and C.-M. Huang. Terrain explorationof a sensor-based robot moving among unknown

1268

a graph-based exploration strategy of indoor exploration

Documents