Navigation and Path-Planning of Mobile Robots with Real-Time Map-Building

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					          Navigation and Path-Planning of Mobile Robots with Real-Time

                     Atsushi Fujimori, Takahmi Murakoshi and Yoshinao Ogawa
                            Departmenf ofMechanica1 Engineering, Shizuoku Universig
                                     3-5-1 Johoku, Hamamatsu 432-8561, Japan
                       Phone Br Fax: +81-53-479-1064, E-mail:

    This paper presents a navigation technique for a sonar-
equipped mobile robot with real-time local map-building
in unhown environments. A navigation algorithm is con-
structed with the proposed local map-building and reac-
tive obstacle avoidance behaviors. The obtained local map
could be used to build and/or update a global map of the
environment. It is used to plan a desirable path for the
next run. In navigation experiments using a commercial
mobile robot named Pioneer-I, the built local map was ef-
fective for navigation in several environments compared
to a reactive navigation technique without map-building,
especially in complicated environments.
Keywords: Mobile robot, navigation, map-building, ul-
trasonic sonar, image processing                                                    Fig. I Photo of Pioneer-I.

1 Introduction
                                                                   2     Mobile Robot Pioneer-1
   Navigation techniques of mobile robots are generally
classified into reactive and deliberative techniques [I]. In           Figure 1 shows a photo of the Pioneer-]. The Pioneer-
the former, a mobile robot is navigated from the start to          1 measures 18 inches (45 cm) from stem to stem, 14.3
the goal and avoids obstacles by directly referring to sen-        inches (36 cm) across the wheels, and nine inches (22.5
sory information. The reactive technique is easily imple-          cm) to the top. The drive system is powered by two re-
mented on mobile robots hut the robots may sometimes               versible DC motors. Each drive motor includes an optical
fall into the deadlock in complicated environments [2]-[4].        encoder for position sensing; that is, deadreckoning.
On the other hand, in the latter, models such as environ-              The Pioneer-I has seven ultrasonic sonar transducers
mental maps are used for navigation. The more accurate             to provide object detection and range information. The
the obtained map is, the larger amount of computation is           sonars are attached to the interior front and sides; one on
required [5]-[7]. This technique seems too expensive for           each side and five facing forward at 15 degree intervals.
the navigation from the start to the goal.                         Although the ultrasonic sonar is one of familiar distance
    This paper proposes a new navigation technique for             sensors for mobile robots, the uncertainties are included
a sonar-equipped mobile robot with real-time local map-            in the sonar output [I], [7]:
building. A map is built near a forward area of the mobile             (a) The sonar output is affected by an error with a van-
robot in real-time, and a path for the time being is planned               ance.
according to the obtained local map. The obtained local
map is furthermore used to build and/or update a global                (h) The measurable region is restricted within a radia-
map of the environment. It is used to plan a desirable path                tion cone with respect to the distance and the angle.
for the next run. In this paper, a commercial mobile robot
                                                                       (c) Multiple reflections may occur for large angles of
“Pioneer-I” [8] is used in experiments to evaluate the pro-
posed navigation technique.                                                incidence to the object.

0-7803-7657-9/02/$17.000 2002 IEEE.                            7                            IEEE ICIT’OZ, Bangkok, THAILAND
                                                                      to the first subgoal for the time being.

                                                                      3.1 Sonar output and cell coordinate
                                                                          The ultrasonic sonar output includes uncertainties de-
                                                                      scribed in the previous section. When the sonar is cor-
                                                                      rectly detecting an object; that is, the object is in the radi-
                                                                      ation cone and the angle of incidence is small, the cause
                                                                      of the errors in the sonar output is only uncertainty (a) and
                                                                      the variance of the sonar output almost remains at a con-
                                                                      stant value. Otherwise, the variance is violently varying
                                                                      for each measuring interval. In this paper, the reliability
                                                                      of the sonar output is evaluated by the variance using a fi-
                                           unit : m                   nite number of the sonar outputs. Letting a(k) be the k-th
                                                                      sonar output, the mean m(k) and the variance s(k) of N
Fig. 2     Detectable region of Pioneer-l using seven ul-             sonar outputs for the recent sampling are given by
trasonic sonars.

                                                                         s(k) = s ( k - l ) + m ( k - 1 ) 2 - m ( k ) 2
  (d) It is impossible to determine the angular position of
      the object that originated the echo.                                            +a(k)* -x(k-N)’
                                                                                                                  (k > N ) .      (2)

he ultrasonic sonars of the Pioneer-I were evaluated with             Ifs(k) is less than a threshold smm, it is evaluated that a(k)
respect to the uncertainties (a) - (c). As a result, the radi-        is reliable.
ation cone of the sonar was that the measurable distance                  The reliable sonar outputs are transformed into the cell
was from 20 to 200 cm and the visible angle was f 12 de-              coordinate. If a(k) is reliable and is positioned in a cell,
gree. Figure 2 shows the detectable region of the Pioneer-            it is regarded that the cell isfiring. Taking into account
1 using the seven ultrasonic sonars. The angular position             uncertainty (a), the number of the firing sonar outputs is
of the object is roughly determined by the firing sonars              counted for each cell in the cell coordinate. If the firing
taking into account the uncertainties.                                number is greater than a threshold c f r ,the cell is classified
                                                                      into occupied cell otherwise empty cell. Figure 3 shows
                                                                      a distribution of the occupied cells in the cell coordinate,
3 Real-Time Local Map-Building
                                                                      where the black box means the occupied cell and the white
   As shown in the previous section, the measurable: re-              box means the empty cell.
gion by the seven sonars is restricted around the Pioneer- 1.
Therefore, a large amount of time and effort is required to           3 2 Image processing of cell
build a global map over the entire environment. Since the                To provide a map for path planning, the binary image
purpose of this study is to navigate a mobile robot from              processing [9] is applied to the cell coordinate. The pro-
the start to the goal without collisions, the global map is           cesses used are fusion, deleting, skeletonization, thinning,
not necessarily needed to do this.                                    labeling and merging. Figure 4 shows a local map after
   A concept of map-building proposed in this papar is                applying the above processes to Fig. 3.
given as follows: a local area around the mobile robot is
partitioned into small squares, called cells; that is, the cell       3.3 Subgnal selection
coordinate whose origin is the position of the robot is de-              To avoid the detected occupied cells; that is, obstacles,
fined. Whether the sonars detect an object inside a cell              and navigate the mobile robot to the final goal, two sub-
or not, the cell is classified into occupied or empty cell.           goals for the time being are given in the safe areas as fol-
A local map is then obtained by applying the image pro-               lows:
cessing [9] to the cell coordinate. For planning a feasible
path, a comer of the occupied cell region is detected. ‘Tak-             Step 1: Obtain the comers which the lines connecting
ing into account the size of the mobile robot, it is judged                 between the comers and the robot do not traverse
whether the empty cell region around the comer is suffi-                    the occupied cell regions.
ciently large to pass the robot; that is, safe area, or not. If
                                                                         Step 2 : From the comen obtained in Step 1, select the
a safe area is found, two suhgoals are given by taking into
                                                                            comer for subgoal selection in which the distance
account the final goal position, and the robot is navigated

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                                                               Corner for
                                                               slmgual selection

                                                           Fig. 5 Position of two subgoals.

                                                     between the comer and the final goal is the mini-

                                                 Step 3: Refemng the comer for subgoal selection, two
                                                    subgoals, SuhGoal-1 and SubGoal-2 are geometor-
                                                    ically located as shown in Fig. 5 , where d is the
                                                    distance for locating the two subgoals and is given
                                                    by taking into account the size of the mobile robot
                                                    and the environment. SuhGoal-l is the first target to
                                                    navigate the mobile robot, while SuhGoal-2 is the
                                                    second one.

                                                 Step 4: If SuhGoal-1 is not in the empty cell regions,
                                                    go hack to Step 2 and re-select the comer for suh-
                                                    goal selection in which the distance between the
                                                    comer and the final goal is the next minimum.

                                                  Step 4 is needed to keep the safety of a path planned
                                               for the time being. The path is more easily found by using
                                               two subgoals than one subgoal. Unfortunately, the path
                                               between SubGoal-1 and -2 may traverse the occupied cell
                                               regions. Since the local map is updated for a specified
                                               period, SubGoal-2 will be re-located by the updated map.
                                               Furthermore, reactive obstacle avoidance behaviors are in-
                                               cluded in the following navigation algorithm for backup
Fig. 4 Local map after image processing.       safety.

                                               3.4 Structure of Navigation Algorithm
                                                 The Pioneer-I is controlled by the forward speed com-
                                               mand v* and the angular speed command w ' . In this study,

                                           9                          IEEE ICIT'02, Bangkok, THAILAND
          Mode selection
                                                                                     art      -4              God


                                                           .             Fig. 7 Trajectories of Pioneer-l without map-building.

                                                                              Map-building mode: When the number of the re-
          Fig. 6 Structure of navigation algorithm.                           liable sonar outputs is greater than M, the local map
                                                                              in the cell coordinate is built and two subgoals are
                                                                              located in the empty cell regions. The location of
Y* is given by a constant value except near the final goal.                   the suhgoals are sent to the navigation mode.
The navigation algorithm consists of the following three
                                                                           Figure 6 shows the relation between the Pioneer-I and
                                                                        a user program which includes the above modes. The
    e   Navigation mode: w* are given so as to navigate                 sonar and the encoder outputs are used to select either the
        the Pioneer-] to a targeted goal which is assigned              navigation mode or the avoidance mode and compute the
        to the subgoal or the final goal. The position of               forward speed command v* and the angular speed com-
        the Pioneer-I is represented by the Cartesian co-               mand w’. They are returned to the Pioneer-I to drive
        ordinates (x,y). The direction angle is 0. In this              the wheels. In the user program, the navigation mode is
        study, ( x , y ) and e are obtained by deadreckoning            usually selected. Since the local map is not always pre-
        using optical encoders. Letting ( ~ , ~ , y ~ the) po-
                                                   be =                 cisely obtained, there may he unexpected obstacles which
        sition of a targeted goal, the angle to the targeted            have not been represented in the local map. The avoidance
        goal is given by                                                mode is then selected to avoid such obstacles. The details
                                                                        of the navigation and avoidance modes are described in
                                                            (3)         Ref. [4].

        Then, w’ is given by                                            4 Navigation Experiment
                                                                            The effectiveness ofthe proposednavigation technique
          o*=q(e,,-e)                                       (4)
                                                                        with real-time local map-building was demonstrated by
        where q is chosen as a positive constant to converge            navigation experiment using the Pioneer-I. Parameters
        e to e [41.
             ,                                                          used in the experiment were as follows: the size of the
                                                                        cell was IO x 10 cm and the cell coordinate was 50 x 50
        Avoidance mode: When the ultrasonic sonars de-                  cell. The threshold of the variance forjudging the reliahil-
        tect objects and the distance is shorter than a thr,ash-        ity was sma = 5000, the amount of the reliable sonar out-
        old; that is, a collision is expected, the desirable            puts for operating the map-building mode was M = 100,
        direction angle 0, for avoiding the collision is oh-            the threshold of the number of the firing sonar outputs was
        tained according to the reactive obstacle avoidance             c , ~ 5 and the distance for subgoal selection was d = 50
        behaviors [4]. Then, w’ is given by                             cm. The forward speed of the Pioneer-I was 8 cmisec
                                                                        and the communication period between the client com-
          W*   = q(@,- e)                                   (5)

                                                                   IO                          IEEE ICIT’02, Bangkok, THAILAND
      m,    ,   .   ,   ,    ,   ,   ,   ,   ._

  Fig. 8 Trajectories of Pioneer-I With map-building
                                                                    - ? k W       d     6m   :&   lib,   ?dm *& m     3 M   a 18a
puter and the Pioneer-I was IO Hz
                                                                    Fig. 9 Global map of concave wall environment
4.1 Navigation with local-map building
   Figures 7 and 8 show trajectories ofthe Pioneer-I from
the start to the goal in a concave-wall environment. When
using the reactive technique, the Pioneer-] was trapped in
the concave wall; that is, deadlocked, and could not be
navigated to the goal as shown in Fig. 7. While using
the proposed technique with the local map-building, the
Pioneer-l escaped from the concave wall according to the
two suhgoals which were given by the local map, and the
Pioneer-1 was navigated to the goal as shown in Fig. 8.

4.2   Update of global map and path-planning
                                                                     am,      ,    ,     ,   I     I      ,   I   ,    I          ,   ,

    The local map obtained can he used to build andor
update a global map of the environment. When the local
map is re-built, the location of the occupied cells are trans-
lated into the global coordinate of the environment and are
stored in a memory mounted on the client computer ofthe
Pioneer-I. The cell information ahout empty or occupied
in the global map is then merged and updated. Moreover,
suhgoals placed in the previous run can he used to plan a
desirable path for the next run since these points are one                        P-1
of landmarks navigating to the goal.
    Figure 9 shows a obtained global map when the Pioneer-
 1 moved from the start to the goal in the concave-wall en-
vironment as shown in Fig. 8. The regions drawn by red-
lines mean the occupied cells merging multiple local maps
                                                                 Fig. 10      Trajectory of Pioneer-1 according to a
and could represent walls in the environment. Points S-l
                                                                 planned path
to S-5 indicate locations of suhgoals when the Pioneer-I
moved from the start to the goal in the concave-wall envi-
ronment. To plan a desirable path, the Pioneer-] selected
two points; P-l and P-2 the Pioneer-I was effectively nav-
igated to the goal according to the points as shown in Fig.

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                                                                          -1 w


Fig. 11    Trajectory of Pioneer-I where a new obstacle             Fig. 12       Trajectory of Pioneer-l after updating global
was placed as hatched-box.                                          map

IO.                                                                 References
    Figure 11 shows the global map and the trajectory of            [I]    G. Oriolo, G. Ulivi and M. Vendittelli, "Real-Time Map
the Pioneer-I from the start to the goal where a new obsta-                Building and Navigation for Autonomous Robots in Un-
cle was placed as shown by a hatched-box. The Pionear-1                    known Environments," IEEE Truns. on Swt. Man and Cy-
moved to follow Points P-l and P-2 which were obtained                     bern., PartB,Vol. SMC-28,No.3, 1998,pp. 316-333.
in the previous run before encountering the new obsta-              [2] R. A. Brooks, "A Robust Layered Control System for a
cle. Since the avoidance mode was operated, new sub-                    Mobile Robot," IEEE J o Robot. and Automat., Vol. 2,
goals were created to avoid the obstacle as shown by the                No. I , 1986, pp. 14-23.
triangles. The global map was updated by merging the                [3] T. Skewis and V Lumelsky, "Experiments with a Mobile
new local map. Point P-2 in Fig. 11 was then replaced                   Robots Operating in a Cluttered Unknown Environment,"
                                                                        J. o f l o b o t . Syst., Vol. 11, 1994, pp. 281-300.
to one of the new-created suhgoals by taking into account
the updated global map. Thus, the proposed navigation               [4] A. Fujimori, P.N. Nikiforuk and M. M. Gupta, "Adaptive
                                                                        Navigation of Mobile Robots with Obstacle Avoidance,:'
technique was appliable to dynamic environments, where
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the location of obstacles was vaned.                                    1997, pp. 596-602.
                                                                    [SI B. Yamaguchi and R. Beer, "Spatial Learning for Naviga-
5 Concluding Remarks                                                    tion in Dynamic Environments," IEEE Trans. on Sysr. Man
                                                                        and Cybern., Part B, Vol. SMC-26, No. 3, 1996, pp. 496-
    This paper has presented a navigation technique for a               505.
sonar-equipped mobile robot in which the local map is                   D.Lee, m e Map-Building and Explorafion Srraregies of
built in real-time and is used for local path planning. 'The            a Simple Sonar-EquippedMobile Robot, 1996, Cambridge
mobile robot was navigated to the goal by the proposed                  Univ. Press.
technique even in the complicated environments which                [7] D.P. Eduardo, M. Nebot and H. Durrant-Whyte, "An Ev-
the robot was often trapped in the deadlock by the reac-                idential Approach to Map Building for Autonomous Vehi-
tive technique. Furthermore, the obtained local map could               cles," IEEE Trans. on Robot. and Automat., Vol. RA-14,
be used to build and/or update a global map of the envi-                No.4, 1998, pp. 623-629.
ronment. It was used to plan a desirable path for the next          [SI ActivMedia, Pioneer I Operation Manual, Ver. 1, 1996,
run.                                                                    ActivMedia Inc.
   The proposed navigation technique was effective even             [9] Pavlidis, T., Algorithms f o r Graphics and Image Process-
if unknown obstacles were placed in the environment; that               ing, 1982, Computer Science Press.
is, dynamic environments.

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