Global Navigation in Dynamic Environments Using Case-Based Reasoning

Autonomous Robots 14, 71–91, 2003c© 2003 Kluwer Academic Publishers. Manufactured in The Netherlands.

Global Navigation in Dynamic Environments Using Case-Based Reasoning

MAARJA KRUUSMAA∗

Intelligent Systems Laboratory, School of Information Science, Computer and Electrical Engineering,Halmstad University, Sweden

[email protected]

Abstract. This paper presents a global navigation strategy for autonomous mobile robots in large-scale uncertainenvironments. The aim of this approach is to minimize collision risk and time delays by adapting to the changes ina dynamic environment. The issue of obstacle avoidance is addressed on the global level. It focuses on a navigationstrategy that prevents the robot from facing the situations where it has to avoid obstacles. To model the partiallyknown environment, a grid-based map is used. A modified wave-transform algorithm is described that finds severalalternative paths from the start to the goal. Case-based reasoning is used to learn from past experiences and to adaptto the changes in the environment. Learning and adaptation by means of case-based reasoning permits the robot tochoose routes that are less risky to follow and lead faster to the goal. The experimental results demonstrate that usingcase-based reasoning considerably increases the performance of the robot in a difficult uncertain environment. Therobot learns to take actions that are more predictable, minimize collision risk and traversal time as well as traveleddistances.

Keywords: robot navigation, case-based reasoning, obstacle avoidance, dynamic environments

1. Introduction

This paper presents a global navigation strategy for au-tonomous mobile robots in dynamic environments. Itis further assumed that the robot is operating in a large-scale real-world environment. It has a general modelof the environment in a form of a grid-based map sothat it can localize itself and determine where and howto go. However, the presence and location of the ob-stacles is unknown or partially unknown and changesover time. It is also assumed that the robot is put intothis environment with a purpose. It has a task to com-plete or a mission to carry out and the robot is expectedto fulfil its assignment as fast and as safely as possi-ble. The possible application areas would be field andservice robots in large real-world domains, which aremore dynamic than traditional industrial environments(e.g. transportation robots in stores or outdoor servicerobots).

∗Present address: Department of Mechatronics, Tallinn TechnicalUniversity, Ehitajate tee 5 19086, Tallinn, Estonia.

For a mobile robot operating in an uncertain envi-ronment, a natural requirement is obstacle avoidance.Intensive work throughout the last decade has providedus with fast and effective obstacle avoidance methods(e.g. several implementations of potential fields (Zelek,1999)). Learning and reflexive behavior has also beenused for collision avoidance (Fagg et al., 1994; Ramet al., 1994).

However, obstacle avoidance, no matter how goodit is, always implies a collision risk due to the uncer-tainty in sensor readings, motion planning, obstacleposition or computational imprecision. An especiallydifficult case is avoiding moving obstacles becausemost of methods are too complicated to be perma-nently recomputed in real-time. Another difficult caseis a blocked path where the robot has to replan the wholeroute.

Minimizing collision risk locally means choosingthe most effective collision avoidance algorithm. Min-imizing collision risk globally means choosing routeswhere as few obstacles as possible are encountered.In order to operate reliably and safely in a dynamic

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environment, a mobile robot needs both local andglobal obstacle avoidance.

So far, most of the research has tackled the prob-lem of obstacle avoidance on a local level. Global levelobstacle avoidance is addressed rather seldom. Hu andBrady (1997) have described global path planning withuncertainty in manufacturing environments. To modelthe changing environment, they use a topological graphweighted by cost functions. When the robot is operat-ing, it uses Bayesian updating to assign new valuesto the cost functions. Knowing those cost functionshelps the robot to find an optimal path. This approachis feasible in an industrial environment where there ismuch a priori information about the static obstacles(e.g. manufacturing cells), and narrow passages be-tween the production lines make it easy to constructa topological map. Attributed graphs are also used inBourbakis (1995) and Wallner et al. (1994) to assign acost to a route.

The robotic agent ROGUE uses a previously ac-quired topological map of an office environment to planbetter and faster routes (Haigh and Veloso, 1998). Thenavigation unit is based on partially observable Markovdecision processes. The path planner uses the topolog-ical map and a modified A∗ algorithm. The arc costsare calculated considering their length, robot’s veloc-ity and travel time. Using its A∗ algorithm, the plannerselects the path with the best expected travel time. Thearc costs are time dependent so that the robot learns toselect best paths depending on the time of the day.

PRODIGY/ANALOGY is a case-based reasoningsystem used for route planning in dynamic environ-ments. It is used for dynamic path planning in thecity of Pittsburgh (Haigh and Veloso, 1995). The agentROGUE is also based on PRODIGY but does not usecase-based reasoning for route planning.

While the above cited approaches use a topologicalmap, we use a grid-based map. On the one hand, a grid-based map is more general. Even if there is nothingknown about the environment, except its size, a gridcan be laid over it. On the other hand, a grid-basedmap permits much more detailed path planning due tothe high resolution of the grid. We use a probabilisticmodification of a wavefront planner to generate a newalternative solution to a path planning problem. Theplanned and traversed paths are stored in the casebasetogether with the measure of their traversability. Byremembering the past cases, the robot learns about theenvironment and uses this information to solve newproblems.

The basic difference of our approach from Hu andBrady (1997) and Haigh and Veloso (1995, 1998) isthat it does not presume a priori known rigid structureof the environment. Our experiments demonstrate thatthe robot adapts to use easily followable paths even ifnothing is a priori known about the environment exceptits size and the coordinates of the start and goal pointsand even if the environment is completely restructuredduring the mission.

The a priori known maps of Hu and Brady (1997) andHaigh and Veloso (1995, 1998) are either constructedmanually by the designer or based on robot’s sensordata. Even in the latter case the designer has to possessknowledge about the characteristics of the environmentin order to not map dynamic obstacles (e.g. people inthe corridor or replaced furniture). In many cases (e.g.construction sites or rescue sites), discrimination be-tween static and dynamic obstacles is not obvious. Thecharacteristics of the environment may change unex-pectedly and frequent remapping of the whole envi-ronment may be too dangerous or too time consuming.In our approach we do not update the robot’s map butstore the information about dynamic changes in thecasebase. The content of the casebase can be updatedfaster and easier than the map.

On a topological map, the number of paths froma specific start to a goal is limited by the number ofedge combinations. Grid-based path planning can of-fer many more alternative solutions to a single path-planning problem. We introduce a probabilistic mech-anism that generates new alternative solutions throughan unknown environment.

The casebase does not have to be reorganized whenthe environment changes or the robot discovers moreopportunities. At the same time, if the structure of an apriori known environment of Hu and Brady (1997) andHaigh and Veloso (1995, 1998) unexpectedly changes,new opportunities will never be discovered unless thetopological map is reorganized regularly.

The problem of world representation is tightly cou-pled with the problem of localization. A graph repre-sentation implies that there are distinct landmarks inthe environment and the robot is able to localize it-self with respect to the graph nodes. Reversely, if theenvironment does not contain static distinct features,the robot cannot use sensor-based localization. To beable to travel through such an environment, a globalreference is inevitable.

The comparison of Hu and Brady (1997) and Haighand Veloso (1998) with the current approach suggests

Global Navigation in Dynamic Environments 73

that the two former ones should be favored whenthe robot’s working environment has a steady struc-ture, the map is known or can be extracted fromsensor data and the environment is suitable fromlandmark-based localization. The current approachhas advantages over the former ones if the environ-ment is unstructured, unknown and/or too dangerousto be fully explored and when global localization ispossible.

The experiments described in this paper reveal thatunder these circumstances our approach to global nav-igation reduces collision risk, traversal time and traveldistance as well as deviation from the original pre-planned path during path following.

1.1. Dynamic Environments

For path planning in dynamic environments, the keyissue is how to model that environment. The choice ofthe model strongly depends on the nature of the robot’soperation. If the aim is just to avoid obstacles, the en-vironment does not need to be modeled at all. Simplesensor-motor pairs can be used instead to implement re-flexive collision avoidance behavior (Arkin, 1995). Ifthe robot exhibits some kind of deliberative behavior,like planning and plan execution, a world model cannotbe avoided. Even a noisy and inexact world model canbe beneficial (Thrun, 1997).

1.1.1. Grid-Based Maps. In dynamic environments,a robot uses its sensors to detect unexpected changes.The sensor information, in turn, can be used to keepthe world model updated. In the case of grid repre-sentation, the probabilistic values of the grid cells arechanged. The value of a grid cell would have to reflectthe imprecision caused by sensor noise and localizationerrors (Thrun, 1988; Elfes, 1987) as well as statisticalproperties of the grid.

Keeping this kind of model updated can pose a dif-ficult problem. It was assumed in this paper that therobot is operating in a large real-world environment.Constantly updating a map of a large environment canbe an intractable task. We have also assumed that therobot operating in this environment has a mission tocomplete. Therefore it cannot spend all recourses justfor model updating.

In the real world, especially in one not prepared for arobot, wandering or exploration can be risky, harmingthe robot or the environment. Paradoxically, the envi-ronment should be explored to find possible hazards,

but at the same time exploration significantly increasesthat risk of hazard we aim to reduce.

Kruse and Whal (1998) use video cameras mountedon the ceiling to collect the statistical data about obsta-cle motion. This data is then used to update cell valuesand is taken into account when planning safer paths. Ifcamera installation is possible and image processing iseasy, this approach eliminates the risks of exploration.

Grid-based maps commonly use potential fields orwavefront based algorithms for path planning. Theoriginal algorithm of Jarvis (Jarvis and Kang, 1986)has been modified to reduce the collision risk withobstacles and to replan in changing environments(Zelinsky, 1994; Azarm and Schmidt, 1994; Murphyet al., 1999).

Wavefront path planners follow the gradient decentto the goal. Therefore they always find the shortestpath from every possible starting point. However, indynamic environments, the best path to the goal is notnecessarily the shortest. If the shortest route is occu-pied, taking a longer route can sometimes reduce thecollision risk. A probabilistic path transform algorithmdescribed below is a modification of the path trans-form algorithm. It finds several alternative solutionsfor a single path-planning problem.

1.1.2. Topological Maps. Topological maps repre-sent the world in a form of a graph as a set of dis-tinct places and connections between them. To updatethe model in dynamic environments, the attributes ofthe graph edges can be changed using sensor data. Thevalue of an edge would then reflect the traversability ofthe whole segment of the path.

This model is much easier to update. Localizationerrors and sensor noise do not affect the cost functionvery much since the robot has to localize itself only atgraph nodes. Only one cost function has to be updatedinstead of a large number of grid cells. From the pointof view of risk minimization, this approach is also morelogical. It does not matter where the obstacles exactlylie and what shape and size they have, it only mattershow fast and safely the robot follows those paths to itsgoal.

1.1.3. Hybrid Maps. Several hybrid world modelshave been proposed, e.g. Thrun (1998), to unite theadvantages of grid-based and topological maps.

In this paper, we use the combination of grid-basedmap for path planning and case-base reasoning. A grid-based map permits detailed path planning and finds

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many alternatives for a path-planning problem. Case-base stores the statistical properties of those paths in aform of a simple cost function that is easy to update. Atthe same time, casebase is more flexible than a topolog-ical map. It does not have to be reorganized when theenvironment changes and more edges are discovered.It also permits storing a more detailed description ofpaths.

If the robot knows where the obstacles are, it canreplan a route before it detects them with its sensors.On the other hand, if it always plans a route around,it will never know when the obstacles are removed.The robot can miss short and easily traversable pathsbecause it is not able to keep the map constantly up-dated. Therefore, we have decided to store all the dataabout changes in the environment in the casebase. Thegrid-based map is not updated at all, it will just de-scribe the general geometry of the environment. Staticobstacles can be stored on the map by a human if theyare known to be never removed (e.g., walls, pillars,machinery or areas where the robot is not allowed toenter). However, since the robot cannot decide whichobstacles will be removed and which will stay for alonger period, it will not add them to the map. In-stead, the properties of paths are updated in a casebase.The robot then uses the information stored in a case-base to decide which is the best way to traverse theenvironment.

The disadvantage of this approach is that it cannot beused in a completely unknown environment. At leastthe shape and size of the environment must be knownvery precisely to model it by a grid-based map. Grid-based path planning also implies that the position ofthe start and goal points must be known exactly.

1.2. Case-Based Reasoning

Case-based reasoning (CBR) is a learning and adap-tation technique that helps to solve current problemsby retrieving and adapting past problems (Aamodt andPlaza, 1994; Watson and Marir, 1994). Past experiencesare stored in the casebase in the form of cases. A caseusually consists of the description of the problem, thesolution that was used to solve that problem and theoutcome of problem solving.

The idea of CBR is based on the assumption thatsimilar problems have similar solutions. When a newproblem occurs, the most similar problem is found fromthe casebase. If the old problem and new problem arenot identical, the solution of the old problem probably

has to be somewhat modified to fit to the changed con-ditions. The modified solution is then used to solve theproblem at hand. The new problem together with thenew solution and the outcome of that solution makes anew case that in turn, is stored and can be used later.Thus in CBR, learning and adaptation are through ac-cumulation of cases.

A casebase is implemented very much like an ordi-nary database. The difference is that while in a databaseone is looking for a certain record, in a casebase one islooking for the most similar one.

The concept “similar problems have similar solu-tions” implies defining a similarity measure. Both caseretrieval and case adaptation use a similarity measureto find the best solution. Similarity measure by itself isnot an explicitly defined concept in CBR but dependsstrongly on the task and domain at hand and on thecreativity of the system designer.

The advantage of CBR compared to black-box tech-niques, such as neural networks, is that the cases in thecasebase are explicitly stored. The human operator hasa clear idea of what the robot has learned and why itcomes to one or another conclusion. Also, it is possi-ble to seed the casebase with a priori knowledge. Forexample, when the human knows a good path, he/shecan store it to the casebase by hand so that the robotdoes not have to look for it.

The few cases, where CBR is used in robotics, in-clude behavior selection (Moorman and Ram, 1992)and robotic systems maintenance (Crowder et al.,2000). Path planning by means of CBR is describedin Vasudevan and Ganesan (1994), Goel et al. (1994),Fox and Leake (1995), and Branting and Aha (1995).None of these approaches are used for planning in dy-namic environments. In Likhachev and Arkin (2001),CBR is used for behaviour selection for schema basedreactive navigation and to our knowledge it is theonly CBR based navigation approach tested on realrobots.

In the approach described in this paper, the problemis to find the best path from a given starting point to agiven goal. The solution to the problem is the path thatis found in the casebase and traversed. The outcomeof the solution is the cost of that path that reflects howeasy that path was to follow. If the robot traverses apath repeatedly, the cost of the path is updated afterevery traversal. The cost will then reflect the averagecharacteristics of that path. By choosing the path withthe lowest cost, the robot can reduce collision risk andminimize travel distance.


Figure 1. System architecture.

2. System Description

The system architecture is presented in Fig. 1. Theglobal planner of the mobile robot uses the grid-basedmap to model the environment and a casebase to storeits experiences. Given a new task to drive from its cur-rent location to a specific goal point, it can choose be-tween planning a new path on the grid-based map orusing the description of an old path from the casebase.

Case-based path planning and map-based path plan-ning are complimentary methods to achieve safe navi-gation in dynamic environments. The map-based pathplanner seeds the casebase with new innovative so-lutions. The case-based path planner remembers thecharacteristics of the paths traversed in the past. It isup to the global planner to solve the conflict betweenexploration and exploitation, i.e. to decide whether touse an old well-tried solution from a casebase or tolook for a completely new alternative solution to theproblem.

Once the solution is found, it will be executed bythe local planner. The local planner gives commands tothe motors and collects sensor data. It follows the pre-planned path until it detects a possibility of collision.The path is then replanned to avoid obstacles. The localplanner uses a wavefront algorithm on a temporary gridcreated at the runtime. Every time a path is traversed,the obstacles are removed from the temporary map.The obstacles encountered are not stored to the map ofa global planner, so the map of the global planner isnever updated.

The navigation and localization unit keeps track ofthe robot’s position. In the next sections, map-basedpath planning and case-based path planning are de-scribed in detail.

Table 1. Symbol table.

P Path

ci i th grid cell

cs Start cell

cg Goal cell

P(cs , cg) Path from cs to cg

D(P1, P2) Dissimilarity between paths P1 and P2

d(ci , c j ) Euclidean distance between cells ci and c j

Dmax Maximal possible distance between similar paths

γ1(P) Primary cost of the path P based on deviation

γ2 Secondary cost of the path P based on travel time

t Travel time

Pp Planned path

Pf Followed path

2.1. Map-Based Path Planning

All wave transform algorithms work by propagatingvalues over the grid, then following the gradient de-cent to the goal. From every grid cell, they find theshortest path to the goal if one exists. A dynamic envi-ronment may contain obstacles, the presence and den-sity of which are unknown. In such an environment,the best path in terms of the risk of path followingis not necessarily the shortest. The probabilistic pathtransform method described here uses a probabilisticmechanism to find alternative paths from the given startto the given goal. These paths are not best in terms ofthe traveled distance but can be better in terms of theirtraversability. Let P denote the set of all possible pathson the grid (the most often used mathematical sym-bols are represented in Table 1). The probabilistic pathtransform plans a path P(cs, cg) ∈ P from the start cellcs to the goal cell cg . A path P(cs, cg) is specified asan ordered set of grid cells ci

P(cs, cg) = (cs, . . . , ci , . . . , cg) (1)

The probabilistic path transform method works bypropagating cell values along the map. Each cell whichdoes not contain a fixed obstacle gets a value which is acombination of the distance from the goal, the measureof the discomfort from moving near obstacles and aparameter with a random value:

PT (c) = minP(c,cg)∈P∗(c,cg)

(length(P(c, cg)) +∑

ci ∈P(c,cg)

× α · obstacle(ci ) +∑

ci ∈P(c,cg)

grow(ci ))

(2)

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where P∗(c, cg) is a set of all possible paths from thecell c to the goal. The function length(P(c, cg)) is thelength of the path to the goal. The function obstacle(ci )represents the discomfort the nearest fixed obstacle ex-erts on the cell c. The parameter α ≥ 0 determines howstrongly the path transform will avoid obstacles.

Let N (ck) be a neighborhood of a randomly cho-sen cell ck with a random width ε. The functiongrow(ci ) = C if ci ∈ N (ck), where parameter C is a ran-dom positive constant. The third term in (2) then rep-resents a disturbance of the path transform in the formof higher cell values in N (ck) so that new paths arecreated.

Once the values of all grid cells are calculated, thepath is found by tracing the path of the steepest descentfrom the start to the goal.

Figures 2–4 illustrate how the paths are created using(2). The first term in (2) would create the path in Fig. 2,which is the shortest possible way from the start to thegoal. The two first terms in (2) would create the path inFig. 3. Because the cells near the obstacles get highervalues, the path does not go too close to the edgesof the obstacles. The third term in (2) creates an areaN (ck) with higher cell values on a random place of themap. Whereas the path is found by tracing the steepestdecent the path is repulsed away from the area withhigher cell values and the result may look like in Fig. 4.This path represents a completely new alternative pathfrom the start to the goal. Naturally, this path is longerthan the other paths created by other wave transformalgorithms, but it can be easier to traverse. However,there is no guarantee that the path created by (2) isdifferent from the ordinary wave transform algorithms(such as using only the two first terms of the formula)or that the algorithm will find all possible paths from

Figure 2. The shortest path.

Figure 3. The shortest path avoiding collisions with the edges.

Figure 4. An alternative randomly modified path.

the start to the goal. The purpose of the third term in(2) is to suggest new solutions to a pathfind problemthat make the robot explore the environment in searchof safe and easily traversable routes.

2.2. Case-Based Path Planning

The problem of path planning is to find a way fromthe start to the goal. The solution to the path-planningproblem is the planned path.

Let P denote the set of all possible paths on the grid.The probabilistic path transform method plans a pathP(cs, cg) ∈ P from the start cell cs to the goal cell cg . Apath P(cs, cg) that is stored in the casebase is definedby (1) as an ordered set of grid cells.

Cases in a casebase are indexed by the start and goalpoints. Since the probabilistic path transform algorithmcan find several alternative solutions to a path-planning


problem, several cases with the same index can exist inthe casebase.

2.2.1. Similarity Measure. In order to find the mostsimilar case in the casebase, we need to define the sim-ilarity between two problems. Before defining thesimilarity of the problems, we first start by definingthe similarity between two solutions, i.e., between twopaths.

It is more convenient to think of the reverse concept,the dissimilarity between two paths. Let two paths P1

and P2 be defined by (1). Let ci be any cell on the pathP1 and c j be any cell on the path P2. On the grid-basedmap, the dissimilarity between the two pathsP1and P2

is defined as

D(P1, P2) = maxc j ∈P1

{minc j ∈P2

{d(ci , c j )}}

(3)

where d(ci , c j ) is the Euclidean distance between cellsci and c j .

The definition (3) captures one possible intuitiveconcept of similarity: two paths are similar if they arenot too much separated from each other. Figures 5 and6 illustrate this notion. In Fig. 5, the paths P1 and P2

are similar because they lead from the start cs to thegoal cg through approximately the same region. Othercharacteristics of a path (like the number of turns, ob-stacles, length) do not matter in the case of this defini-tion. The measure of similarity is only the separation ofone path from the other. Figure 6 represents two pathsthat are different according to the definition (3) becausethey lead to the goal through geographically differentareas.

Figure 5. Similar path.

Figure 6. Different paths

How large the separation has to be in order to classifypaths as different strongly depends on the problem, do-main and designer. We treat paths P1 and P2 as similarif they differ less than by a value Dmax

D(P1, P2) < Dmax (4)

2.2.2. Cost Function. All the cases stored and tra-versed are characterized by a cost function γ (P). Thecost function is the outcome of problem solving andit reflects the properties of the path. There are severalalternatives to calculate the cost. An obvious choice isspeed. The faster the robot can drive the better the pathis. Another possible option is the number of collisionsor the number of obstacles encountered. Since everyobstacle on the path implies collision risk, the pathwith fewer obstacles is better. In our experiments, theprimary cost depends on the deviation of the plannedpath Pp from the actually followed path Pf

γ1(Pp) = f (D(Pp, Pf ))

and the secondary cost depends on the travel time t

γ2(Pp) = f (t)

Dynamic obstacles cause the robot to replan its routeand therefore it deviates from its course. The path with asmaller deviation is better because the robot followedthe pre-planned path and therefore robot’s motion ispredictable. If two paths are equally good in terms ofdeviation, then the faster path is preferred.

We update the cost simply by calculating the meanvalue over the all traversals but more sophisticated tech-niques, like bayesian updating, reinforcement learningor TD-learning can also be used.

2.2.3. Case Retrieval. Let the new problem be findinga path Pnew from the cell cnew

s to cnewg . An old problem

in a casebase is solved finding a path Pold from colds to

coldg . The two problems are similar if

d(cnew

s , colds

)< Dmax and d

(cnew

g , coldg

)< Dmax (5)

If the paths are two-way paths then Pnew and Pold aresimilar also if

d(cnew

s , coldg

)< Dmax and d

(cnew

g , colds

)< Dmax (6)

Since several paths can exist between specific startand goal points, there may be several solutions to one

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problem. The case retrieval routine uses the cost of apathγ (P) to select between all possible solutions. A so-lution becomes selected with a probability proportionalto its cost, i.e., the better the solution is, the more prob-ably it becomes selected. The way the probabilities aredistributed depends on how exploration-oriented therobot is. If the system has to be risk-averse, the caseswith a satisfactory outcome should become selectedwith a high probability. If the system is more explo-ration oriented, it uses more map-based path planningin search for better solutions.

2.2.4. Case Adaptation. Having selected a similarpath Pold(cold

c , coldg ), the next step is to see if it has to be

modified to provide a solution.If cnew

s = colds and cnew

g = coldg , the new problem is

exactly the same as the old one. The solution does notneed to be modified and is ready to use. Otherwise, thecase adaptation is straightforward. If cnew

s �= colds , a new

path P1(cnews , cold

s ) is planned. If cnewg �= cold

g , the pathPs(cnew

g , coldg ) is planned. Now the paths P1, Pold and

P2 are concatenated unless cnews ∈ Pold or cnew

g ∈ Pold.In the latter case, the redundant cells are removed.

2.2.5. Casebase Management. Learning systemslearn by remembering past experiences. However,when problems scale up, forgetting becomes as equallyimportant an issue as remembering.

To keep the size of the casebase constrained and tohave a better overview of the learning process, a newcase is stored only if there is no similar case in a sensedefined by (5) or (6). Otherwise an old case is forgottenand the new one is stored if the cost of the new one islower. The old experiences thus can be replaced withthe similar but better ones, resulting in the casebasecontaining only one characteristic example from eachcluster of similar solutions.

Storing only dissimilar cases slows down the growthof memory but does not guarantee that the casebase willstay constrained. If the casebase grows beyond a certainlimit, the cases that will be forgotten are chosen con-sidering their cost. In the experiments reported below,the robot forgets the solutions with the worst outcome.As the learning process converges, the casebase willcontain better solutions.

Other forgetting strategies are also possible. If therobot remembered only cases with a high cost, the sys-tem would implement failure-driven learning.

Cases with a high cost can play a positive role in thedecision making process. They can warn the robot from

taking actions that probably lead to a risky behavior.When the map-based planner comes up with a newsolution, it is first verified with the existing cases tosee if the robot has already had experiences with asimilar case and what the outcome has been. If thesimilar outcome is not effective, the new solution willbe rejected.

2.2.6. Previous Experiments. In our previous work,we have extensively tested the approach in simulatedenvironments, evaluated its adaptability, forgetting anddecision-making strategies (Kruusmaa, 2002). The ex-perimental results show that the main problems are themaintenance of the casebase because of the large sizeof the solution space and finding a cost measure for areal robot.

On the contrary, case adaptation is usually not diffi-cult. Basically, the approach described in Section 2.2.2is a nearest neighbour retrieval that is the most oftenused case retrieval method in CBR. Case adaptation isalso rather straightforward; it is done by adding anddeleting segments of a path.

The experiments below concentrate mainly ondemonstrating the aspects of the approach that in ourprevious work have appeared to be the most problem-atic. First, we want to demonstrate that it is possible tokeep the solution space constrained without loosing theability to adapt and generalize. Despite that there is the-oretically an enormous amount of possible solutions toevery single problem, a successfully defined similaritymeasure permits to reduce the solution space to a smallnumber of characteristic examples.

The second main objective of the tests is to definea cost function suitable for real robots in real environ-ments. In simulated environments we have evaluatedthe traversability of paths by assigning a traversabil-ity measure to every grid cell. This approach is notapplicable in reality. We define a new cost measurebased on deviation from the planned path and traveltime.

3. Experiments

This section describes the experimental environment,domain-dependent details of the system and discussesthe experimental results.

The experiments present a mission consisting of 500tasks. Each task implies path planning and traversingbetween specified start and goal points. The robot hasno a priori knowledge of the environment where it is


going to operate except its size and the coordinates ofthe goal points.

By “dynamic environment” we mean here that theplacement of obstacles changes during the mission, par-ticularly, before every task (the obstacles are not movedduring the task fulfillment because of technical reasons,it would disturb the camera based robot localization).Some obstacles are fixed during a longer period, othersare replaced after every task. For the robot it means thatit faces different environmental conditions every timeit traverses the environment.

The casebase in these experiments consists of twocases (moves from one target points to another and backagain). The objective of the experiments is to demon-strate if the robot can retrieve these cases, adapt themto the current situation and if the similarity and costmeasures are successfully defined, and if this approachhelps to reduce the risk of path following.

3.1. Setup of the Test Environment and the System

3.1.1. Robot. The experiments are made using themini-robot Khepera developed by K-Team. It is a smallcircular robot with differential drive that can be con-nected to a PC over a serial link. The on-board sensorsof Khepera consist of eight infrared distance sensorsmounted around the robot. The size of the test environ-ment is 1.5 m × 2 m. The range of the infrared sensorsis very small (5–30 mm for objects used in the test envi-ronment). The radius of the robot is 26 mm, thus the en-vironment can be considered to be rather large with re-spect to the size of the robot and the range of its sensors.

3.1.2. Localization. Since Khepera lacks the sen-sors for accurate localization we solved this problemwith a global vision system. The localization systemis represented in Fig. 7. A video camera is mounted

Figure 7. Localization system.

to the ceiling to recognize the pose of the robot. Tomake it easier to detect the robot, three LEDs thatform an isosceles triangle are mounted on it. Thecamera image is processed in the host computer torecognize the robot’s position and orientation. Thisdata is then used to correct the localization errors.The camera image consists of 640 × 480 pixels, thusone pixel corresponds to an area of 3.1 × 3.1 mm.The vision system is used only to update the robot’spose.

Since the robot does not have to localize itself bymeans of odometry, landmarks and onboard sensors(which is quite unthinkable with IR-sensors only) butuses an off-board system, the localization errors arerather small and do not accumulate. If the image pro-cessing system determines the robot’s position and ori-entation correctly, the errors are usually not larger thanthe size of the robot. An example in Fig. 8 illustratesthe error correction. In this and in all the followingfigures representing the test environment, the area hasthe size 1.5 × 2 m. The start and goal points lie in theupper left and bottom right corner of the test environ-ment. The thick line represents the shortest path fromthe start to the goal. The dotted line is extracted fromthe camera image and represents the path that the robothas actually followed.

3.1.3. The Mission. A task given to the robot is tomove from one given point on the grid to another. Startand goal points are shown in Fig. 8. The robot movesfrom the start to the goal and back again. The wholemission consists of 500 tasks, i.e. 500 traversals of thepaths between the start and goal points.

Let Pp denote a planned path and Pf an actuallyfollowed path. One task to move from the start cs to thegoal cg is executed as follows:

1 Choose Pp(cs, cg) from the casebase orplan it on a map.

2 Follow the planned path Pp. The fol-lowed path Pf is usually different fromthe planned one.

3 Calculate the cost γ (Pp) = f (D(Pp,

Pf ), t).4 Store Pp(cs, cg) and γ (Pp) if there isno path similar to Pp. Otherwise updateγ (Pp).

The more detailed description of the algorithm is rep-resented in Section 3.1.7.

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Figure 8. A planned path (thick line) and an actually followed path (dotted line).

3.1.4. Test Environments. The placement of the ob-stacles is shown on three camera images (Figs. 9–11).The first 80 tasks are executed in the environment inFig. 9. Larger objects, like books, the chessboard andthe toy centipede, are fixed during that period. Smallerobjects on that scene (marked with circles) are ran-domly placed after every task. The robot is connectedto the PC by a serial cable. Sometimes the cable be-came too loose, the robot detected it with its sensorsand interpreted as a moving obstacle. However, therobot has no means to distinguish between the tem-porarily fixed and randomly replaced obstacles and itdoes not have a priori knowledge at all about their pres-ence and location (i.e., its grid map contains no ob-stacles). Neither does it know when the obstacles arereplaced.

The temporarily fixed obstacles block the shortestpath between the start and goal points on all the scenes.There is no case where the ordinary wave-transformalgorithm would lead the robot to the goal along theshortest way.

There are two obvious possibilities to traverse be-tween the start and goal points in the environment in

Fig. 9. One is to pass through the obstacles in the up-per right corner (e.g., path A in Fig. 9) and the other isthe narrow passage between the obstacles in the lowerright corner (like the path B in Fig. 9).

Considering the small range of IR-sensors (mini-mum 0.5 length of a cell), the environment is very dif-ficult for Khepera. The extension of most of the obsta-cles largely exceeds the range of the sensors, so that therobot finds it difficult to determine which the shortestway around them is. It is also disturbed by replacedobstacles and localization errors.

After 80 tasks the scene is rearranged as shown inFig. 10. This environment is even more difficult. Thepath through the upper right corner is blocked. The onlypossibility to reach the goal is to go through the narrowpassage in the lower part of the picture (e.g., follow-ing the path C in Fig. 10) which, due to sensor noise,replaced obstacles and localization errors, may appeareven narrower to the robot.

After 300 tasks, the environment is set up as shownin Fig. 11. The shortest path is still blocked but thetemporarily fixed obstacles are sparse and there aremore alternatives for planned paths.


Figure 9. Environment 1 for tasks 1–80. The randomly replaced objects are marked with circles and replaced after every traversal.

Figure 10. Environment 2 for tasks 81–300.

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Figure 11. Environment 3 for tasks 301–500.

3.1.5. The Map. The robot has two maps. The globalmap is used by the global planner (Fig. 1) and can con-tain only a priori known obstacles. The local planneruses a temporary map for replanning.

In these experiments, we are concerned with an ex-treme case where the robot has no knowledge at allabout its working environment except the coordinatesof its start and goal points and the size of the environ-ment. The global map contains no obstacles. It is justan empty grid that permits fine path planning.

The temporary map of the local planner is used foron-line replanning. The temporary grid comprises thewhole environment since planning on the grid of thissize is not particularly time consuming and the extentof the obstacles varies largely. Obstacles that the robotencounters during the path following are marked on thetemporary map. The wave transform algorithm is thenused to plan a path to avoid them. As the robot cannotknow which obstacles will be removed and which willstay for a longer period, the temporary map is cleanedafter every traversal.

Usually, the size of a grid cell is equal to the size ofthe robot to guarantee that the robot can pass obstacles.However, we have decided to use a smaller grid size

since a coarse grid would expand obstacles too muchand the robot would miss narrow passages. The size ofa grid cell is chosen to be 29.2 mm (and the grid mapsare thus 51 cells × 67 cells).

Figure 12 illustrates the execution of one task. Thethick line represents the path Pp planned by a globalplanner on the global map. The obstacles (representedby black squares) are stored on the temporary map andthe dotted line is the path Pf planned on-line by a localplanner.

3.1.6. Casebase. The use of the casebase requires adefinition of a similarity measure and a cost function.

The similarity measure cannot be less than the lo-calization precision since we cannot require a smallervalue than we are able to measure. On the other hand,the similarity measure can always be larger because theway we interpret similarity between two paths largelydepends on the domain and the task. We have chosen thesimilarity measure to be Dmax = 4 × 29.2 = 116.8 mm.Thus, two paths are similar if they do not deviate fromeach other more than by four grid cells.

When the traversability of a path has to be evaluated,an obvious choice would be, e.g. traversal time, average


Figure 12. A planned path (thick line) and an actually followed path (dotted line). The robot traverses from the lower right corner to the upperleft corner.

speed or number of collisions. However, when the pathPp and Pf are very different from each other (like inFig. 12), the cost γ (Pp) would measure characteristicsof a completely different path Pf . Therefore it wasdecided to use the deviation itself as the measure of theprimary cost.

γ1(Pp) = f (D(Pp, Pf ))

The disadvantage this cost measure is that all thepaths where the robot does not deviate from its courseare equally good despite of their length. Therefore asecondary cost function was introduced that dependedon the traversal time t .

γ2 = t

The selection of the best possible solution was doneas follows: from all the solutions the primary cost ofwhich (based on deviation) is under a certain level thefastest path was chosen.

Thus, the lower the cost is, the more the plannedpath and the actual path resemble each other accordingto (3). It also appeared that with fewer obstacles onthe way, the robot replanned its path seldom, did not

deviate much from its original path and reached thegoal faster.

The primary cost of the path Pp after traversal iscalculated as follows:

γ1(Pp) ={

0, if dev ≤ 2 × cell

dev − 2 × cell otherwise(7)

where dev is the deviation of Pf from Pp calculatedaccording to (3) and cell is the size of the grid cell.

If the path in a casebase is traversed repeatedly, themean value of γ (Pp) is calculated over all traversals.

To calculate the traversal probability based on (7)the weight is normalized so that 0 ≤ γ1 ≤ 1. At caseretrieval, the best possible solution from the casebaseis found and accepted with the probability inverselyproportional to its cost. The robot is thus forced to usepaths which are faster and which it is more likely ableto follow. Paths with a high cost and with a low costare represented in Figs. 13 and 14 respectively.

It was decided to make the path selection rather risk-averse as the environments seemed to be difficult totraverse. According to (7), a path the deviation of whichis less than two grid cells is selected with probability 1.

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Figure 13. Path with a high cost.

Thus, the deviation less than 58.4 mm is not consideredto be significant. This kind of selection criterion wouldforce the robot to keep using a solution that has anacceptable cost.

The deviation-based cost calculation also re-veals another important measure of performance—predictability. When the planned path Pp and traversedpath Pf are similar in the sense defined in (3), the be-havior of the robot is predictable; it really did followthe path that it intended to. Predictability is an impor-tant issue when robots are working in teams or in thecase of human-robot interaction. The effectiveness of ateam is higher if the behavior of their members is morepredictable.

It also appeared that because of the nature of thewave transform algorithms, that was used to plan newroutes and replan the route around obstacles, the direc-tion of the deviation depended on which direction therobot was moving. When traveling from left to right,the deviation was usually in the opposite direction thanwhen the robot was travelling back from right to left.Therefore, the paths that the robot actually followedtended to be very different. It was therefore decided totreat all the paths as one-way paths.

The previously done computer simulations suggestthat if the similarity measure is successfully definedand the environment is not very cluttered, only veryfew solutions are needed to cover the whole solutionspace. Therefore, and since the mission actually con-sists only of two problems repeated after each other,the maximum size of the solutions space was chosento be 25 solutions.

3.1.7. The Algorithm for Global Navigation. To ful-fil the mission consisting of 500 traversals, the globalplanner of the robot was executing the algorithm rep-resented in Fig. 15.

The aim of the experiments was to investigatewhether and how much using CBR would influencethe global navigation in a difficult and risky environ-ment. If CBR is effective and the system is designedfeasibly, the robot would adapt to the changes in theenvironment and learn from its experiences. Learn-ing would lead to the measurable increase in perfor-mance, the collision risk will be reduced, the tasks willbe executed faster and robot’s behavior becomes morepredictable.


Figure 14. Path with a low cost.

3.2. Experimental Results

To complete 500 tasks, the tests were run for 25 hoursand the robot traversed 1700 m. The average speed ofthe robot was 0.02 m/s.

Table 2 illustrates the usage of CBR during the tests.As the experiments proceed, the robot starts more andmore trust its past experiences and uses less map-basedplanning to find innovative solutions.

Figure 16 plots the six best paths Pp that the robotmanaged to find during its mission. The histogram inFig. 17 together with the Fig. 16 gives a better insightinto the adaptation process.

3.2.1. Environment 1 (tasks 1–80). In the beginningthe robot intensively uses the map to find new solutions

Table 2. Usage of the casebase.

Tasks completed 30 40 80 130 300 500

Using CBR 3% 12% 53% 45% 59% 66%

until, executing the 42nd task, it plans a path throughthe passage in the upper right corner in Fig. 9 usingmap-based path planning. This path is marked as P1

pin Fig. 16. This path has a low cost and now the robotkeeps using that case. After 55 traversals it finds anotherpath (P2

p in Fig. 16) in an opposite direction. Now ithas two very good cases in the casebase and it usesthose cases most of the time. The casebase is used tocomplete 96% of tasks during that period.

3.2.2. Environment 2 (tasks 81–300). After 80 tasks,the path in the upper right corner will be blocked likeshown in Fig. 10. Now costs of P1

p and P2p slowly in-

crease and as shown in the diagram in Fig. 17, the robotbecomes more exploration oriented.

It uses the map until it finds the paths through thegap in the lower part in Fig. 10. Here it appears thatsaving one-way paths was an unfortunate mistake. Inone direction, the path through the gap (marked as P3

pin Fig. 16) was found almost immediately (after 84tasks) and it would have been well travesable in both

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Figure 15. The global navigation algorithm.

(Continued on next page.)


Figure 15. (continued).

Figure 16. The six best paths in the casebase after 500 tasks.

directions. The path in an opposite direction (P4p in

Fig. 16) was found on the 131st traversal and it wasvery similar to P3

p . Treating the paths as two-way orat least using a path in an opposite direction as a seedin the casebase would have increased the performancealmost by half.

When P3p and P4

p are found, the usage of the casebaseincreases. 70% of path-planning problems are solved

by the casebase. However, those paths are not as easyto follow as the paths in environment 1 because thegap is very narrow and the robot deviates often fromits course when it detects the edges of the gap or re-placed obstacles. Therefore their cost stays higher thanin the first scene and the robot is more exploration-oriented, hoping to find better solution to theproblem.

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Figure 17. Usage of the casebase during the tests.

3.2.3. Environment 3 (tasks 301–500). After 300tasks, the scene is rearranged as shown in Fig. 11. Thisenvironment is different by nature. There are severalmore-or-less good solutions because the temporarilyfixed obstacles are sparse and there are many alterna-tives to travel between the start and goal point.

First the usage of the casebase decreases slightly un-til the system adapts to the changes. New alternativesare found quickly (P5

p and P6p in Fig. 16). The dia-

gram in Fig. 16 reveals that the new good solutions willbe reused in 80% of cases. However, the robot neverfinds the most optimal paths between the start and goal.The optimal risk-sensitivity of the robot depends on theproperties of the environment. If the robot or the sys-tem designer has no knowledge about those properties,it does not know how risk averse it should be. Whilein the Environments 1 and 2 it was an advantage thatthe robot behaved very risk-aversely, in Environment3, the robot could have been more exploration oriented.The path P6

p in Fig. 16 is far from optimal in terms ofspeed, and there exist several better solutions.

3.2.4. Comparison of Performance. Table 3 showsthe statistics about the quality of case-based solutionsvs. map-based solutions.

The first row of data in Table 3 represents the av-erage number of replannings during a traversal. Pathsare replanned when the robot detects an obstacle orbumps onto it. Thus the number of replannings shows

the number of possibly harmful situations. It appearsthat the robot had to replan its path more when it usedmap-based solutions. Using the casebase reduced thecollision risk 3.8 times.

The primary cost of the solutions was based on de-viation of the followed path from the planned one. Asit can be seen from the next row of Table 3, the averagedeviation of the case-based solutions was 2.8 times lessthan that of the map-based solutions. Thus, when us-ing CBR, the robot followed a pre-planned path moreprecisely.

Traveling time was used as the secondary cost ofthe cases. If two cases both had a small deviation, thefaster path was used. The statistics reveal that pathsplanned using the casebase are 1.6 times faster thanpaths planned on the map.

Although the goal was not to minimize the traveleddistance, on the contrary, longer paths were preferredif they were less risky, it appears from the last row of

Table 3. Statistical data of the experiments.

CBR-based Map-based Ratio map-based/planning planning CBR-based planning

Replannings 7.95 30.1 3.8

Deviation 171.85 488.35 2.8

Time 145.4 226.4 1.6

Distance 2879.6 4124.55 1.4


Table 3 that using CBR also minimized the traveleddistances 1.4 times. Apparently obstacle avoidance in-creases the length of the route so that much longer butmore predictable paths eventually are shorter than theshort but risky ones. In practice, distance minimizationhas a great importance. The motors of a mobile robotare consuming more energy when the robot is moving.Thus, minimized traveling distances mean minimizedenergy consumption.

Tables 4 and 5 show how much the performance ofthe system depends on the properties of the environ-ment. Table 4 gives the statistics of the performance inEnvironments 1 and 2. Table 5 contains data collectedin Environment 3. In all aspects, the utility of CBR ishigher in the first two environments. This is partly be-cause of the properties of the environment and partlybecause the system is designed to be very risk averse.

Environments 1 and 2 are more complicated andthere are only very few good solutions like P1

p , P2p ,

P3p and P4

p . It is a great advantage if the robot can findthose solutions by trial and error and then store themfor later usage. It is not probable that the robot occa-sionally comes to a good solution since most of thesolutions that the map-based planner comes up withare very risky.

Obstacles in the Environments 1 and 2 are dense andof much larger size than the range of the sensors, there-fore CBR most drastically reduces collision risk. Theaverage number of replannings using CBR is 5.7 timesless compared to map-based planning. The deviation

Table 4. Statistical data of the experiments. Environments 1and 2.



Deviation 153.9 539.4 3.5

Time 167.8 303.0 1.8

Distance 3289.6 5180.4 1.60

Table 5. Statistical data of the experiments. Environment 3.



Deviation 189.8 437.3 1.21

Time 123.0 149.8 2.30

Distance 2469.7 3068.7 1.20

from the pre-planned path is also considerably reducedbecause larger obstacles cause a larger deviation.

Environment 3 is more tractable and the robot copesbetter with unexpected situations even without a prioriknowledge. Besides, the global path planner was notdesigned to look for the best possible solution and theoptimal cases remained undiscovered. However, in allenvironments all aspects of the system performanceare noticeably improved by means of CBR. This in-crease in performance is achieved despite that the sys-tem is not optimally risk averse in all cases and despitethe incorrect design of the casebase (as it was men-tioned above, treating paths as two-way would haveincreased the performance considerably).

During the testing ca 20 tasks were removed fromthe list because the robot got stuck in the corners ofobstacles. This always happened when the robot triedto follow a new map-based path. If we consider the riskcaused by driving into a deadlock and the time spent forrestarting the system or helping the robot, the advan-tages of a learning system become even more obvious.

The robot uses unsuccessful cases in the casebase toavoid taking a risky map-based path if it already hada poor experience with a similar solution. Althoughno statistics is available about how many map-basedpaths were rejected based on the information in thecasebase, it is possible that CBR also helped to reducethe risk of map-based planning by means of failure-driven learning.

The comparison of performance in Environments 1,2, and 3 suggests that CBR for global navigation is moreeffective in difficult environments where the extensionof obstacles exceeds the sensor range. In environmentswith few and sparse obstacles or for the robot with richsensing, simple obstacle avoidance algorithms can besufficient to achieve a near-optimal performance.

During the tests, it was observed that when the robotreplanned its path at runtime, the eventually followedpath was sometimes rather close to an optimal one. Therobot did not store the actually followed paths becausethey were usually crooked and too close to obstacles.It suggested that learning could be speeded up if therobot optimized the accidentally found paths and usedthem as a seed in a casebase. This idea was later testedin Kruusmaa (2001) and it confirmed that the acci-dentally found paths could be successfully used whensmoothened and approximated.

As it was estimated based on the previous simula-tion results, case adaptation and case retrieval did notcause problems for the robot. Frequently, the current

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location of the robot was not exactly in the start pointbut differed by one or two cells because of localiza-tion errors. Since the errors were always smaller thanDmax, the robot always retrieved an appropriate caseand adapted it to the current situation. It suggests thatthe robot will perform equally well when there are morecases in the casebase.

4. Discussion

The results suggest that CBR-based global navigationis more beneficial when the obstacles are large anddense and only few good solutions exist. In simple dy-namic environments, local obstacle avoidance can besufficient to find near-optimal solutions.

It can be argued that if the system designer has noknowledge at all about the environment, the robot mayfind only a sub-optimal solution or become too explo-ration oriented. Even having a vague imagination aboutthe degree of possible hazards and the overall structureof the environment would help the designer to adjustthe right degree of exploration. However, the experi-ments show that the performance is improved even ifthis information is not available.

It is an advantage if the robot could make use of thepaths created while avoiding obstacles. Finding goodapproximations of paths that the robot has accidentallyfound would speed up learning. This idea was testedand reported in Kruusmaa (2001) and confirms thatconclusion. In some cases, the robot remarkably re-duced the collision risk on the second traversal already.It suggests that the CBR-based learning is speeded upby adding accidentally found paths and the method isapplicable in highly dynamic environments.

In Haigh and Veloso (1998), the robot learnssituation-dependent rules to decide what time of a dayto avoid or favor certain areas. Implementing navi-gation in time-space could also extend the methodrepresented here. However, we anticipate that in un-structured and reorganized environments, where thisapproach is claimed to outperform other approaches,this feature is not so important. Periodic changes areusually characteristic to man-made structured environ-ments (e.g. in Hu and Brady (1997) the shifts start andend and in Haigh and Veloso (1998) the classes in theuniversity let out at the same time.). In unstructured en-vironments, changes in obstacle distributions dependrather on irregular and unpredictable events or naturalphenomena (e.g. a building on a rescue site collapsesor some tracks become impassable when it rains). The

experiments show that this approach can well cope withthis kind of unpredictable changes. The method can beextended to work in an event-space where the events arehand-picked by the designer. However, this implies thatthe designer has quite good knowledge of what eventscan possibly influence the obstacle distributions.

The test environment is rather large compared to thesize of the robot and the range of its sensors. To com-pare with other commonly used robots, if the radiusof the robot was 0.6 m (like of the popular RWI B24base), the size of the test environment scaled respec-tively would be 46 × 35 m and the total travel dis-tance would be ca 40000 m. The scale of the environ-ment mostly increases the size of the possible solutionspace—between more distinct target points there aremore alternative paths. At the same time, the increaseof cases (start and goal points) only increases the size ofthe casebase linearly. The casebase here contained only25 solutions. It suggests that if new cases are added, theapproach will easily scale up. Given a very low numberof necessary solutions, a few times larger environmentwill definitely not be a problem. For a very large envi-ronment, it might be necessary to increase the similaritymeasure Dmax to reduce the size of the solution space.In a very large environment, a fine discrimination be-tween paths is usually even not necessary.

5. Conclusions

This article has investigated global navigation strategyin uncertain environments. The aim of the approachwas to minimize collision risk and traversal time byadapting to the changes in a dynamic environment. Agrid-based map was used to model the uncertain envi-ronment and to plan several alternative paths from thestart to the goal. CBR was used to store those solutionsand their outcomes for a later use.

The experimental results show that using CBR sig-nificantly reduces the collision risk, traversal time anddistance and makes the behavior of the robot more pre-dictable. The results of this work can be used in large-scale domains where the changes of the environmentare difficult to model, the safety of the robot or/and theenvironment is an important issue and the robot, havinglimited resources, has a certain mission to complete.

The restrictions of this approach are that the size ofthe environment and the position of the goal points haveto be known precisely and the localization errors haveto be small (like it is with outdoor applications withGPS).


Acknowledgment

The author wishes to thank prof. Phillip McKerrow forhis valuable feedback.

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Maarja Kruusmaa received her Dipl. Eng. from Tallinn TechnicalUniversity, Estonia, in 1994. In 1996 she started her Ph.D. studies inChalmers University of Technology (Sweden), Dept. of ComputerEngineering. From 1998 to 2002 she worked in Intelligent SystemsLaboratory of Halmstad University where most of the experimentalwork of her Ph.D. studies was completed. She received her Ph.D. inComputer Engineering from Chalmers University of Technology in2002. She is currently employed as a senior researcher in Instituteof Mechatronics, Tallinn Technical University, Estonia. Her researchinterests include robot learning and adaptation and sensor processing.

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Global Navigation in Dynamic Environments Using Case-Based Reasoning