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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>An Omnidirectional AGV Path and Attitude Integrated Planning Method 1</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Song Yue</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Shan-liang Xue</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Nanjing University of Aeronautics and Astronautics</institution>
          ,
          <addr-line>Nanjing</addr-line>
          ,
          <country country="CN">China</country>
        </aff>
      </contrib-group>
      <fpage>100</fpage>
      <lpage>105</lpage>
      <abstract>
        <p>With the continuous development of advanced production technology, Auto Guided Vehicle (AGV) is regarded as an important part of advanced industrial production line, and the types of AGV are increasing. However,the traditional differential steering AGV cannot achieve more flexible movement and turning in narrow warehouse space, so this paper selects omnidirectional AGV as the research object.The omnidirectional AGV is free to change the attitude of the vehicle according to the demand, this brings a lot of convenience in the process of use. However, due to vehicle attitude restrictions in some stations or routes during the vehicle driving, the vehicle is only allowed to pass in a certain attitude. For example, the narrow passage only allows the vehicle to pass parallel to the route on the narrowest side of the vehicle, which brings a lot of inconvenience to the omnidirectional AGV driving.In view of the above problems,this paper proposes a comprehensive planning method for omnidirectional AGV path and attitude, which can plan the attitude adjustment stations of AGVs in the driving process according to the limitation of the AGV's attitude at the station or route in the path planning, so as to help the AGV adjust its attitude and reach the target location smoothly.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;AGV</kwd>
        <kwd>Route Planning</kwd>
        <kwd>Posture control</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1 Introduction</title>
      <p>
        In recent years, with the development and progress of intelligent technology, Automated Guided
Vehicle (AGV) [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], as a transport tool, has become the main intelligent material transport tool in modern
production system and is one of the important means to realize intelligent warehouse [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>
        Many AGVs have come into being, but most of these AGVs are differential steering type [
        <xref ref-type="bibr" rid="ref3 ref4">3-4</xref>
        ], which
cannot achieve more flexible movement and turning in narrow warehouses, so AGVs with
omnidirectional motion function have become a hot spot in current shop floor logistics research [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
      </p>
      <p>Conventional differential steering type AGV, when transporting goods, generally choose to make
the AGV to move near the storage rack first, lift the lifting mechanism to the specified height, and then,
the AGV makes the goods move towards the storage rack through the feed mechanism until they reach
the upper part of the storage rack, and finally the lifting mechanism drops to make the goods move in
place. However, this method may be risky when transporting heavy products, as the center of gravity
of the goods will deviate with the movement of the feeding mechanism, and when the projection of the
center of gravity on the plane exceeds the support surface, it will produce the danger of overturning and
cause serious safety accidents. Therefore, the safer method of delivery is to use an omnidirectional AGV,
which first lifts the goods to a specified height, then causes the AGV to move to the bottom of the shelf
and lower the lifting platform, so that the goods stay safely in the shelf position. This method can avoid
the risk of overturning due to the change of the position of the center of gravity of the goods in the
horizontal direction.</p>
      <p>Although omnidirectional AGV brought many convenience in the process of use, it can freely
change the body attitude according to demand, but due to the AGV in the process of driving part of the
station or route have body posture limit, such as the AGV between two shelves, which is a narrow
channel, only allows the AGV to the narrowest side of the body parallel to the road through, and when
the AGV needs to place the goods into the storage rack below, due to the narrow space does not support
the AGV steering, only through the side of the way to enter, which brings a lot of inconvenience for the
omnidirectional AGV driving.</p>
      <p>Although many scholars have done mature research on path planning of AGVs, few of them have
taken into account the constraints of the AGV on the body posture at stations and road sections in the
driving process. Therefore, this method proposes an omnidirectional AGV path and posture integrated
planning method, which can plan the posture adjustment nodes of the AGV during the driving process
according to the restrictions of the AGV on the body posture at the stations or road sections in the path
planning process, so as to help the AGV adjust its posture and reach the end point smoothly.
2
2.1</p>
    </sec>
    <sec id="sec-2">
      <title>Method</title>
    </sec>
    <sec id="sec-3">
      <title>Algorithm Process</title>
      <p>In this paper, the depth-first search algorithm is first used to search the topology map, and all the
paths from the starting site to the target site are obtained which are sorted according to the driving
distance. Subsequently, according to the current planning path, in the case of the vehicle attitude
restriction at the passing route, based on the greedy strategy, assuming how far the omnidirectional
AGV can travel at the farthest without changing the heading angle. The intersection of the permitted
heading angles of passing stations is calculated until the intersection is an empty set, which means that
AGV can only travel to this station at the farthest without changing the heading Angle,Then the previous
stations are traversed in reverse, and the first station that allows AGV spin is selected as the body
attitude adjustment station.Take this site as the new starting point and repeat the process until you reach
the destination. In this way, all vehicle attitude adjustment stations in the planned path can be
calculated.Finally, the planned path is segmented according to these stations, and the set of heading
angles allowed for each section of path is calculated, and the most appropriate heading Angle is selected
and sent to AGV.</p>
      <p>Start</p>
      <p>Build map
Calculate inter-site</p>
      <p>distance
DFS for Planning Path
Obtain body attitude
constraints</p>
      <p>Y
Traversing through the
stations</p>
      <p>Target Sites？</p>
      <p>N
vehicle posture seeks</p>
      <p>intersection
The intersection is
empty?</p>
      <p>N
Merging routes</p>
      <p>Delineate path
Sending control commands</p>
      <p>End</p>
      <p>Set as new starting point
Update vehicle posture
Find adjustment node</p>
      <p>Y</p>
    </sec>
    <sec id="sec-4">
      <title>Map Environment Modeling</title>
      <p>
        Topological map method is used to construct indoor map model. The topological map method is to
represent some important areas of the environment by a node, and the nodes are connected by line
segments to represent paths [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. As shown in Figure 2, Figure 2 is a schematic of a warehouse for a
particular type of product, which has a heavy mass and a long length. The map model contains two
main aspects, which are site information and route information. The sites are generally classified based
on road bifurcations or turning points and the starting and ending points of road sections where road
conditions change.
      </p>
      <p>In addition to the location of the site in the map, since omnidirectional AGV is used in this paper,
the site information also needs to represent which sites allow cart spins and which sites have restrictions
on the inbound attitude of the AGV. Take site 10 in the figure1 as an example, the site is located between
two shelves, the space is narrow, and the delivery length is long, so the AGV is not allowed to spin at
this site; then take site 9 as an example, because the AGV can not spin at site 10, so it can only be
allowed to move sideways from site 10 into site 9.</p>
      <p>Road information needs to divide all the accessible roads into several basic sections, which are used
to describe the starting and ending stops of the road, the attitude restriction of the vehicle body passing
through the road, and the narrow condition of the road. Take section 18-10 as an example, because this
section is located between two shelves, the space is narrow, so the AGV can only be allowed to pass
parallel to the road with the narrowest side of the body.</p>
      <p>Entrance
1
2
charging 4
area</p>
    </sec>
    <sec id="sec-5">
      <title>2.3 Route Planning</title>
      <p>
        In this paper, we use depth-first search algorithm to perform path planning under the body pose
constraint of each road segment. Since this paper uses the topological map method to construct the map
model, the stations in the topological map can be regarded as the vertices of the graph in graph theory,
and the connecting lines between the stations, which are also the routes, can be regarded as the edges
in the graph, and the depth-first search algorithm, as one of the commonly used algorithms in graph
theory [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ], can find out the path between two nodes that meets the requirements, and then calculate the
sum of the distances of the edges that make up the path, which can obtain each path's distance, which
meets the need of this method. The body attitude constraint described in this method generally refers to
the body direction allowed for the cart to pass a certain section.
      </p>
      <p>To calculate the distance matrix, if there are n stations in the map, then define an n ⋅ n
two-dimensional matrix e in advance. e[i, j] denotes the distance between station i and station j . If station i
to station j can be reached directly without going through any other station, then e[i, j] is equal to the
value of the distance between station to station, and if station i to station j cannot be reached directly
or i is equal to j then e[i, j] can be equal to a extremely large fixed value.</p>
      <p>Input the starting station and target station. From the starting station, iterate through the unvisited
station along the planning path.Before visiting, first determine whether the current station allows the
adjustment of the vehicle attitude, if the current station allows the adjustment of the vehicle attitude
means that regardless of the previous vehicle attitude, the car can be adjusted at the current station , so
that the car can arrive from the current station to the station to be visited; if the vehicle attitude can not
be adjusted, the set of vehicle attitude allowed by the previous section and the set of vehicle attitude of
the section to be visited to find the intersection, if the intersection is empty, the car can not arrive, give
up the station , if the intersection is not empty, the car can arrive, visit the station .When there is no
unvisited station , it goes back to the previous station and continues to try to visit other stations until all
stations have been visited.During the access, if the target station is visited, all nodes passed are recorded
and stored in the backup path, and the sum of all distances is recorded.After the access, the path with
the shortest distance is selected as the current path, and the remaining paths are stored in the backup
queue in order according to the distance, and the paths are switched from the backup queue in order
when the current path is unreachable.
2.4</p>
    </sec>
    <sec id="sec-6">
      <title>Calculate Attitude Adjustment Nodes</title>
      <p>First make a hypothesis about the farthest the car can travel from the starting point without changing
its vehicle posture.Suppose the planning path is a - b - c - d - e - f , then derive from station a .With
2.2 it is possible to obtain the set Pend of vehicle attitudes that allow the vehicle to pass each basic
section ( end indicates the identification of the end station of that basic section).The set Pb of vehicle
postures of route segment a - b is intersected with the set Pc of vehicle postures of route segment b
c . The result is S . If S is non-empty, then it means that the car can drive from station a to station c
without changing its vehicle posture.At this point, and then the intersection of S and the set Pd of
route segment c - d , if the result is empty, it means that the vehicle from station a to station d need
to change the vehicle attitude at least 1 time, if station d allows the vehicle to adjust the vehicle attitude,
then allow the vehicle to adjust the vehicle attitude of the station can be at station d , If vehicle attitude
adjustment is not allowed, then each station from station d to station a needs to be traversed in reverse,
where the first station that allows vehicle attitude adjustment is the cart at the current adjustment
station.Then this adjust vehicle attitude station is considered as the current new starting point and repeat
the above process until all stations are traversed to get all vehicle attitude adjustment stations, if all
stations are not adjustable vehicle attitude, it means the path is not reachable, jump out of section 2.4
and switch the path from the backup queue in section 2.3.</p>
      <p>The vehicle pose set described in this method, as shown in Figure 2, is set to v in the actual direction
corresponding to the top of the map, assuming that the car needs to drive from station 2 to station 1 at
this time, which is a road in the map from the bottom up, assuming that this section of the road allows
the car to move longitudinally and laterally, then the vehicle pose set allowed in the map for this section
of the road is {v, u, −v, −u} ,Where v means allow the front end of the cart to go up in the map, which
in this section of the road means going straight ahead, u means allow the front end of the cart to go
right in the map, which in this section of the road means moving sideways, - u means allow the front
end of the cart to go left in the map, which in this section of the road means moving sideways, and - v
means allow the front end of the cart to go down in the map, which in this section of the road means
driving in reverse, where v, u, −v, −u , instead of requiring the front end of the cart to always maintain
that angle, allows the cart to adjust its direction without deviating from the road in that direction.
2.5</p>
    </sec>
    <sec id="sec-7">
      <title>Calculated posture</title>
      <p>Using each vehicle attitude adjustment station as a segmentation point, the entire path is divided into
segments, and each segment of the route is noted as Roadi ( i is the serial number of each segment of
the route).Each section of the route Roadi in turn consists of a number of basic sections, and the set of
vehicle postures allowed in each basic section of Roadi is intersected to obtain the set Statusi .
Statusi is the set of body attitudes that allow the cart to pass the route, and if the body attitudes allowed
by Roadi are not unique, You can choose a body attitude from Statusi that best suits the current
direction of travel. If Statusi is empty, it means the current path is not reachable and switch the route, if
there is no other route to switch, it means the path is not reachable and the method ends.</p>
    </sec>
    <sec id="sec-8">
      <title>3 Experiments and analysis of results</title>
      <p>In order to verify the effectiveness of the method proposed in this paper, simulation experiments are
conducted under QT/C++ platform to test whether the omnidirectional AGV can adjust its attitude
flexibly and reach the end point smoothly under different tasks with the map shown in Figure 2 as an
example.</p>
      <p>Table 1 lists several types of tasks that need to be performed by omnidirectional AGVs in the
warehouse logistics process, with input starting sites and target sites, and gives the planning paths generated
according to the method in Section 2.3.</p>
      <p>When the AGV is performing charging tasks, it is stipulated that the charging interface of the AGV
is located at the rear of the vehicle, therefore, in order to facilitate charging, it is stipulated that when
the AGV drives into the charging station, i.e. station 4 point, it needs to reverse into the station. The
task execution flow is shown in Table 2.
4 3 4 0 ° Reverse the car
When the AGV performs the task of entering the warehouse, because site 10 and site 18 are located
between two shelves, the space is narrow, so the vehicle is not allowed to spin, and site 9 is also limited
because of the space, the vehicle needs to move sideways to enter. The task execution flow is shown in
Table 3.
The outbound task flow is shown in Table 4.
Table4 Outbound task flow
step Starting Site</p>
      <p>According to the experimental results, it can be found that the method proposed in this paper can,
on the basis of path planning, plan the body posture adjustment nodes of the car for the body posture
restriction conditions that may be encountered in the driving process, so as to avoid the situation that
the car cannot pass smoothly due to the body posture restriction in the driving process, and thus help
the car adjust its body posture and reach the end point smoothly.</p>
    </sec>
    <sec id="sec-9">
      <title>4 Conclusion</title>
      <p>This paper proposes a comprehensive planning method for omnidirectional AGV path and attitude,
which addresses the problem that the traditional AGV path planning method cannot flexibly adjust the
heading angle according to the body attitude restriction of omnidirectional AGVs at passing stations
and road sections. This method can plan the vehicle's attitude adjustment node for the body attitude
restriction conditions that may be encountered in the driving process, so as to give full play to the
advantages of omnidirectional AGVs and avoid the situation that the vehicle cannot pass smoothly due
to the body attitude restriction in the driving process, thus helping the vehicle to adjust its attitude and
reach the end point smoothly.</p>
    </sec>
    <sec id="sec-10">
      <title>5 References</title>
    </sec>
  </body>
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