CN107203214B - A kind of cooperative self-adapted Intelligent planning method in carrying robot COMPLEX MIXED path - Google Patents
A kind of cooperative self-adapted Intelligent planning method in carrying robot COMPLEX MIXED path Download PDFInfo
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- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
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Abstract
The invention discloses a kind of cooperative self-adapted Intelligent planning method in carrying robot COMPLEX MIXED path, this method includes:Step 1:Build global map three-dimensional system of coordinate;Step 2:Global map is divided according to floor level number, obtains the two-dimensional map and distance matrix of each floor;Step 3:Coordinate of the starting point and ending point for obtaining transport task under global map three-dimensional system of coordinate is instructed according to transport task, the distance matrix of all corridors and room in distance matrix and each floor based on each floor, path planning is carried out using Floyd algorithms, obtains Transportation Planning path;Step 4:Advance according to the path clustering carrying robot of planning, complete transport task.The present invention reduces algorithm amount of calculation, including gate inhibition, elevator interaction and Robot dodge strategy, is easy to carrying robot to perform transport task under intelligent environment by carrying out Module Division to more floor environment.
Description
Technical field
The invention belongs to robot path planning's problem, more particularly to a kind of carrying robot COMPLEX MIXED path collaboration is certainly
Adapt to Intelligent planning method.
Background technology
With the unlatching in industrial 4.0 epoch, artificial intelligence is very powerful and exceedingly arrogant, robot initially enter daily life, laboratory,
The fields such as factory, due to the fast development of science and technology, robot purposes is more extensive, and more necks are expanded to by 95% commercial Application
The non-industrial applications in domain, the effect for society are also increasing.And since middle self-propelled machine people industry development, positive growth
For global maximum robot market, robot it is " Chinese epoch " or coming.How to allow robot more efficient, more
Intelligently serviced for the mankind, be the emphasis of owner's concern, the wherein path planning of transportation robot and control is robot neck
The key problem in domain.
The path planning of mobile robot and control refer to that robot can independently perceive surrounding environment, for goal task intelligence
One relatively most short, time-consuming minimum path can be cooked up, while can be interacted with the gate inhibition on path, possesses automatic obstacle-avoiding
Function, on the premise of the safety of robot, people and transported article is ensured, smoothly complete task.
For path planning and this problem is controlled, forefathers are it is proposed that many outstanding methods, such as Chinese patent
A kind of mobile robot intensified learning initial method based on artificial potential field is disclosed in CN102819264B, by robot
Working environment virtually turns to an artificial potential field, stateful potential energy value is determined using priori so that barrier area
Domain potential energy value is zero, and target point has global maximum potential energy value, at this moment in artificial potential field the potential energy value of each state with regard to generation
Table corresponding state follows the cumulative maximum return of optimal policy acquisition.The coordinates measurement of the outstanding advantages system of this method is straight with control
Connect and form closed loop with environment, therefore enhance the adaptability and avoidance performance of system, but it is easily trapped into locally optimal solution,
Be completely dependent on priori determination, for emerging barrier, can not Real-time Feedback into system, cause for flexibly changing
Actual robot working environment there is no adaptibility to response, and can not find path between adjacent nearer barrier, so
It is not easy to be applied in practice.And for example Chinese patent CN105527965A discloses a kind of path planning based on GACA algorithm
Method and system, method are that the part optimization solution that genetic algorithm obtains is converted into the pheromones initial value of ant group algorithm, so
Optimum path search is carried out by ant group algorithm again afterwards, optimizing carries out crossover operation to qualified path after terminating, finally given
Optimal path.This method is that solve the problems, such as one of most popular method of robot path planning, is constantly entered each other by feasible solution
Row information exchanges, and finds more outstanding path, it the advantages of have strong robustness, there is high feasibility, but it is easily trapped into
Locally optimal solution, computationally intensive to cause to calculate overlong time, excessively slow reaction is unfavorable for robot and run in actual environment, made
Into the poor efficiency of work.
The content of the invention
The invention provides a kind of cooperative self-adapted Intelligent planning method in carrying robot COMPLEX MIXED path, its purpose exists
In for the deficiency of above method, for more floors, more rooms and elevator are classified as multiple modules, are set for each module
The interconnection of trunk path is put, each inside modules carry out active path regional planning, and institute's arrival in need of robot
Task point be configured, and for running into barrier in transportation robot carry out task and people avoids, ensure both sides
Safety, and each gate inhibition is numbered, when running into gate inhibition in the path of robot ambulation, gate inhibition will automatically turn on/close, high
Effect, safely solves robot core path planning problem.
A kind of cooperative self-adapted Intelligent planning method in carrying robot COMPLEX MIXED path, comprises the following steps:
Step 1:Build global map three-dimensional system of coordinate;
It is origin to deliver localized ground central point, and due east direction is X-axis, and direct north is Y-axis, and direction is Z perpendicular to the ground
Axle;
Carrying robot delivery region is floor connected regions all in a building, walkable region refer to from
The barrier region in building is deleted in all floor connected regions;
In global map three-dimensional system of coordinate, the two-dimensional plane coordinate of the floor connected region of each floor is identical, z coordinate
It is different;
Step 2:Global map is divided according to floor level number, obtains the two-dimensional map of each floor and apart from square
Battle array;
The distance matrix of each floor is made up of the neighbouring relations between all corridors and all rooms, if two rooms, room
Between it is adjacent with corridor and two corridors, then the corresponding weights in floor distance matrix be 1, be otherwise infinity;
Weights in each floor in the distance matrix of each corridor are each paths in each corridor under floor two-dimensional map
Actual range between point;
Weights in each floor in the distance matrix in each room are that in each room all roads under floor two-dimensional map
Actual range between the point of footpath is formed;
In each corridor distance matrix and room distances matrix, if barrier be present between two path points, apart from square
Corresponding weights are infinity in battle array;
The processing of division, the optimal path splicing in the global static path planning after being advantageous to, reduces path planning
The amount of calculation of model, accelerate arithmetic speed.
Step 3:The starting point and ending point for obtaining transport task is instructed in global map three-dimensional coordinate according to transport task
The lower coordinate of system, the distance matrix of all corridors and room, use in distance matrix and each floor based on each floor
Floyd algorithms carry out path planning, obtain Transportation Planning path;
Path planning is carried out using Floyd algorithms, reduces amount of calculation;
When carrying robot need move to another floor from a floor when, by path planning Task-decomposing into
Path planning in two floors;
The starting point of first path planning is transport task starting point, and terminal is the elevator position of first floor;
The starting point of second path planning is the elevator position of second floor, and terminal is transport task terminating point;
The elevator of first floor and the elevator of second floor are same elevator;
Step 4:The Transportation Planning path clustering carrying robot obtained using step 3 is advanced, and completes transport task.
Further, during carrying robot advances according to the path planning obtained, carrying robot reaches gate inhibition
During preceding path point, door open command is first sent, the unlatching situation of gate inhibition is detected using Kinect sensor, after confirming that door is opened,
By reaching next path point after gate inhibition, after sending instruction of closing the door, next path point is continued to;
Carrying robot reach elevator before path point when, first send door open command, then examined using Kinect sensor
The unlatching situation of elevator is surveyed, after confirming that door is opened, into elevator.
Further, carrying robot is known in real time during the advance of transport task is performed using Kinect sensor
In front of other path whether someone or other barriers, there is barrier in the range of two meters in front of the existing path of carrying robot
When, carry out avoidance according to following operation:
A) when carrying robot runs into people in corridor, obtained by the spacer of Kinect sensor combination ceiling
Position relationship between carrying robot and people, is kept out of the way;
Direction is kept out of the way in planning in the two-dimensional coordinate for be currently located floor, and the direction of keeping out of the way according to planning is kept out of the way;
The direction kept out of the way direction and refer to possess maximum retreat distance on the vertical line of the interpersonal line of carrying machine,
Edge is kept out of the way direction and moved ahead in walkable region, after people leaves 3 meters of scopes of robot, backtracking normally travel circuit,
Go to next path point;
B) when carrying robot runs into people in a room, if carrying robot in read path point, keeps itself position
Put motionless, after people leaves the path of carrying robot, carrying robot continues to move ahead;If carrying robot is to next
During path point is advanced, then along the previous path point of backtracking, and stay in previous path point and wait people to exit to next path point
Path, be further continued for going to next path point.
C) when carrying robot runs into emerging static-obstacle thing, carrying robot is scanned using Kinect sensor
And remote control center is sent instructions to, static-obstacle thing is identified in global map temporarily, and update the area that can walk
In domain and all distance matrixs can not tie point, plan the optimal path in current floor again using Floyd algorithms, concurrently
Carrying robot is given, around static-obstacle thing, is moved on;
D) when carrying robot runs into other transportation robots, both halt simultaneously, and remote control center is to surplus
The higher carrying robot of remaining electricity, which is sent, meets dynamic barrier instruction, is sent to another carrying robot and continues normally travel
Instruction;
The carrying robot for meeting dynamic barrier instruction is received according to A) or B) situation works as another carrying robot
Make dynamic barrier and carry out dynamic obstacle avoidance, another robot normally travels according to path profile.
Further, carrying robot reaches next path point from current path point in accordance with the following methods:
First, the coordinate (x1, y1) of current path point and the angle, θ c of carrying robot are read;
Then, calculated and gone to using the distance between current path point coordinates and next path point coordinates and 2 points
The angle of the carrying robot of next path point;
Finally, advance according to the distance between new carrying robot angle and two path points, control carrying robot.
Further, the carrying robot take thing, put thing during perform following operation and prevent from colliding desktop:
During carrying robot takes thing, puts thing, carrying machine human body does not rotate, and is completed when taking thing or putting thing
Afterwards, it is forwarded to up to after next path point, carrying machine human body receives control instruction and carries out pose adjustment.
To prevent transportation robot when taking object point or putting object point directly to next path point is gone to, machine human body
Collide, occur unexpected with taking thing/put thing platform.
Further, carrying robot carries out real-time Communication for Power during moving ahead with remote control center:
When carrying robot can not continuously be communicated with remote control center three times, a upper path is returned to along original route
Point waits, until being communicated again with remote control center;
When remote control center can not continuously receive the signal that carrying robot is sent three times, alarm is sent.
Further, the adjacent positioned piece is at intervals of 3m.
Spacer is arranged in robot working environment, is awaited orders a little in robot, takes object point, puts object point, elevator point, gate inhibition
The place arrangement spacer such as select, be advantageous to robot and carry out taking thing on the basis for ensureing self-position precision, put thing, Men Jinjiao
Mutually, elevator interactive operation;Simultaneously on the driving path of robot, one path point is set every 3m, is testing robot
Can timely calibrating position under the intelligent environment of room.In laboratory 1.5m is controlled according to a path point2Space is arranged, and is ensured real
The walkable region of Yan Shizhong robots can be all capped.
Beneficial effect
1st, by Module Division, the operand of algorithm is greatly reduced, the operation efficiency of Floyd algorithms is improved, saves
Time of the robot in path planning;
2nd, the interaction schemes of gate inhibition and elevator make carrying robot performed under the intelligent environments such as laboratory transport task into
For possibility, the simple work of lab assistant is advantageously reduced, improves laboratory operational efficiency.
3rd, Robot dodge strategy can allow carrying robot in complex environment normal work, ensure carrying robot, transport article
And Laboratory Instruments, the safety of personnel.
Brief description of the drawings
Fig. 1 is the path point schematic diagram of certain floor;
Fig. 2 is the schematic flow sheet of the method for the invention.
Embodiment
Below in conjunction with example and accompanying drawing, the present invention is described further.
Step 1:Build global map three-dimensional system of coordinate;
It is origin to deliver localized ground central point, and due east direction is X-axis, and direct north is Y-axis, and direction is Z perpendicular to the ground
Axle;
Carrying robot delivery region is floor connected regions all in a building, walkable region refer to from
The barrier region in building is deleted in all floor connected regions;
In global map three-dimensional system of coordinate, the two-dimensional plane coordinate of the floor connected region of each floor is identical, z coordinate
It is different;
Step 2:Global map is divided according to floor level number, obtains the two-dimensional map of each floor and apart from square
Battle array;
The distance matrix of each floor is made up of the neighbouring relations between all corridors and all rooms, if two rooms, room
Between it is adjacent with corridor and two corridors, then the corresponding weights in floor distance matrix be 1, be otherwise infinity;
Weights in each floor in the distance matrix of each corridor are each paths in each corridor under floor two-dimensional map
Actual range between point;
Weights in each floor in the distance matrix in each room are that in each room all roads under floor two-dimensional map
Actual range between the point of footpath is formed;
In each corridor distance matrix and room distances matrix, if barrier be present between two path points, apart from square
Corresponding weights are infinity in battle array;
The processing of division, the optimal path splicing in the global static path planning after being advantageous to, reduces path planning
The amount of calculation of model, accelerate arithmetic speed.
Step 3:The starting point and ending point for obtaining transport task is instructed in global map three-dimensional coordinate according to transport task
The lower coordinate of system, the distance matrix of all corridors and room, use in distance matrix and each floor based on each floor
Floyd algorithms carry out path planning, obtain Transportation Planning path;
Path planning is carried out using Floyd algorithms, reduces amount of calculation;
When carrying robot need move to another floor from a floor when, by path planning Task-decomposing into
Path planning in two floors;
The starting point of first path planning is transport task starting point, and terminal is the elevator position of first floor;
The starting point of second path planning is the elevator position of second floor, and terminal is transport task terminating point;
The elevator of first floor and the elevator of second floor are same elevator;
Step 4:The Transportation Planning path clustering carrying robot obtained using step 3 is advanced, and completes transport task.
During carrying robot advances according to the path planning obtained, carrying robot reaches the path point before gate inhibition
When, door open command is first sent, the unlatching situation of gate inhibition is detected using Kinect sensor, after confirming that door is opened, after gate inhibition
Next path point is reached, after sending instruction of closing the door, continues to next path point;
Carrying robot reach elevator before path point when, first send door open command, then examined using Kinect sensor
The unlatching situation of elevator is surveyed, after confirming that door is opened, into elevator.
Carrying robot is during the advance of transport task is performed, using in front of Kinect sensor Real time identification path
Whether someone or other barriers, when there is barrier in the range of two meters in front of the existing path of carrying robot, according to following
Operation carries out avoidance:
A) when carrying robot runs into people in corridor, obtained by the spacer of Kinect sensor combination ceiling
Position relationship between carrying robot and people, is kept out of the way;
Direction is kept out of the way in planning in the two-dimensional coordinate for be currently located floor, and the direction of keeping out of the way according to planning is kept out of the way;
The direction kept out of the way direction and refer to possess maximum retreat distance on the vertical line of the interpersonal line of carrying machine,
Edge is kept out of the way direction and moved ahead in walkable region, after people leaves 3 meters of scopes of robot, backtracking normally travel circuit,
Go to next path point;
B) when carrying robot runs into people in a room, if carrying robot in read path point, keeps itself position
Put motionless, after people leaves the path of carrying robot, carrying robot continues to move ahead;If carrying robot is to next
During path point is advanced, then along the previous path point of backtracking, and stay in previous path point and wait people to exit to next path point
Path, be further continued for going to next path point.
C) when carrying robot runs into emerging static-obstacle thing, carrying robot is scanned using Kinect sensor
And remote control center is sent instructions to, static-obstacle thing is identified in global map temporarily, and update the area that can walk
In domain and all distance matrixs can not tie point, plan the optimal path in current floor again using Floyd algorithms, concurrently
Carrying robot is given, around static-obstacle thing, is moved on;
D) when carrying robot runs into other transportation robots, both halt simultaneously, and remote control center is to surplus
The higher carrying robot of remaining electricity, which is sent, meets dynamic barrier instruction, is sent to another carrying robot and continues normally travel
Instruction;
The carrying robot for meeting dynamic barrier instruction is received according to A) or B) situation works as another carrying robot
Make dynamic barrier and carry out dynamic obstacle avoidance, another robot normally travels according to path profile.
Carrying robot reaches next path point from current path point in accordance with the following methods:
First, the coordinate (x1, y1) of current path point and the angle, θ c of carrying robot are read;
Then, calculated and gone to using the distance between current path point coordinates and next path point coordinates and 2 points
The angle of the carrying robot of next path point;
Finally, advance according to the distance between new carrying robot angle and two path points, control carrying robot.
The carrying robot takes thing, put thing during perform following operation and prevent from colliding desktop:
During carrying robot takes thing, puts thing, carrying machine human body does not rotate, and is completed when taking thing or putting thing
Afterwards, it is forwarded to up to after next path point, carrying machine human body receives control instruction and carries out pose adjustment.
To prevent transportation robot when taking object point or putting object point directly to next path point is gone to, machine human body
Collide, occur unexpected with taking thing/put thing platform.
Carrying robot carries out real-time Communication for Power during moving ahead with remote control center:
When carrying robot can not continuously be communicated with remote control center three times, a upper path is returned to along original route
Point waits, until being communicated again with remote control center;
When remote control center can not continuously receive the signal that carrying robot is sent three times, alarm is sent.
The adjacent positioned piece is at intervals of 3m.
Spacer is arranged in robot working environment, is awaited orders a little in robot, takes object point, puts object point, elevator point, gate inhibition
The place arrangement spacer such as select, be advantageous to robot and carry out taking thing on the basis for ensureing self-position precision, put thing, Men Jinjiao
Mutually, elevator interactive operation;Simultaneously on the driving path of robot, one path point is set every 3m, is testing robot
Can timely calibrating position under the intelligent environment of room.In laboratory 1.5m is controlled according to a path point2Space is arranged, and is ensured real
The walkable region of Yan Shizhong robots can be all capped.
Instantiation:
Carrying robot receives order, and article is extracted from path point 12, reaches path point 76 and places article, intermediate path
Track is path point 12-14-16-17-33-34-35-36-37-38-98-97-96-72-73-74-76, as shown in figure, its
During middle path point 12,14,15,17 is 102 between 1 building, path point 33,34,35,36,37,38 is in 1 building corridor, Er Qielu
Footpath point 38 is path point before elevator door, and path point 98,97,96 is in 4 buildings corridors, should during 72,73,74,76 405 between 4 buildings
Path intermediate demand passes through 3 gate inhibitions, and using an elevator, path point is path point 17,35,96 to gate inhibition in front of the door.
Carrying robot is run after taking object point to obtain article along order path, when carrying robot reaches path point 17,
Door open command is first sent, the unlatching situation of gate inhibition is then detected using Kinect sensor, after confirming that door is opened, after gate inhibition
After reaching next path point 33, after sending instruction of closing the door, ensuing path point is continued to, similarly passes through its latter two door
Prohibit.When robot reaches path point 38, door-opened elevator instruction is first sent, the unlatching situation of elevator is then detected using Kinect,
After confirming that door is opened, into elevator.After reaching 4 buildings, there is dustbin barrier near path point 97, use Kinect sensor
Depth distance identifies that location transmission is to distal end in a coordinate system by Obstacle Position, by static-obstacle thing temporarily in global map
In be identified, and update in walkable region and all distance matrixs can not tie point, planned again using Floyd algorithms
Optimal path in current floor, and carrying robot is sent to, around dustbin, move on, thing path point is put in arrival, is put
Lower article, task are completed.
Specific embodiment described herein is only to spirit explanation for example of the invention.Technology belonging to the present invention is led
The technical staff in domain can be made various modifications or supplement to described specific embodiment or be replaced using similar mode
Generation, but without departing from the spiritual of the present invention or surmount scope defined in appended claims.
Claims (7)
1. a kind of cooperative self-adapted Intelligent planning method in carrying robot COMPLEX MIXED path, it is characterised in that including following step
Suddenly:
Step 1:Build global map three-dimensional system of coordinate;
It is origin to deliver localized ground central point, and due east direction is X-axis, and direct north is Y-axis, and direction is Z axis perpendicular to the ground;
The carrying robot delivery region is floor connected regions all in a building, and walkable region refers to from all
Floor connected region in delete building in barrier region;
Step 2:Global map is divided according to floor level number, obtains the two-dimensional map and distance matrix of each floor;
The distance matrix of each floor is made up of the neighbouring relations between all corridors and all rooms, if two rooms, room with
Corridor and two corridors are adjacent, then the corresponding weights in floor distance matrix are 1, are otherwise infinity;
Weights in each floor in the distance matrix of each corridor be under floor two-dimensional map in each corridor each path point it
Between actual range;
Weights in each floor in the distance matrix in each room are all path points in each room under floor two-dimensional map
Between actual range form;
In each corridor distance matrix and room distances matrix, if barrier between two path points be present, in distance matrix
Corresponding weights are infinity;
Step 3:The starting point and ending point for obtaining transport task is instructed under global map three-dimensional system of coordinate according to transport task
Coordinate, the distance matrix of all corridors and room, is calculated using Floyd in distance matrix and each floor based on each floor
Method carries out path planning, obtains Transportation Planning path;
When carrying robot needs to move to another floor from a floor, by path planning Task-decomposing at two
Path planning in floor;
The starting point of first path planning is transport task starting point, and terminal is the elevator position of first floor;
The starting point of second path planning is the elevator position of second floor, and terminal is transport task terminating point;
The elevator of first floor and the elevator of second floor are same elevator;
Step 4:The Transportation Planning path clustering carrying robot obtained using step 3 is advanced, and completes transport task.
2. according to the method for claim 1, it is characterised in that advanced in carrying robot according to the path planning obtained
Cheng Zhong, when carrying robot reaches the path point before gate inhibition, door open command is first sent, utilizes Kinect sensor detection gate inhibition
Unlatching situation, after confirming that door is opened, by reaching next path point after gate inhibition, after sending instruction of closing the door, continue to down all the way
Footpath point;
When carrying robot reaches the path point before elevator, first send door open command, then detect elevator using Kinect and opening
Situation is opened, after confirming that door is opened, into elevator.
3. according to the method for claim 2, it is characterised in that carrying robot is performing the advance process of transport task
In, using in front of Kinect sensor Real time identification path whether someone or other barriers, when the existing path of carrying robot
When there is barrier in the range of two meters of front, avoidance is carried out according to following operation:
A) when carrying robot runs into people in corridor, delivered by the spacer of Kinect sensor combination ceiling
Position relationship between robot and people, is kept out of the way;
Direction is kept out of the way in planning in the two-dimensional coordinate for be currently located floor, and the direction of keeping out of the way according to planning is kept out of the way;
The direction kept out of the way direction and refer to possess maximum retreat distance on the vertical line of the interpersonal line of carrying machine, edge are moved back
Keep away direction to move ahead in walkable region, after people leaves 3 meters of scopes of robot, backtracking normally travel circuit, go to
Next path point;
B) when carrying robot runs into people in a room, if carrying robot in read path point, keeps self-position not
Dynamic, after people leaves the path of carrying robot, carrying robot continues to move ahead;If carrying robot is to next path
During point is advanced, then along the previous path point of backtracking, and the road that previous path point waits people to exit to next path point is stayed in
Footpath, it is further continued for going to next path point;
C) when carrying robot runs into emerging static-obstacle thing, carrying robot is concurrent using Kinect sensor scanning
Send instruction to be identified static-obstacle thing in global map temporarily to remote control center, and update walkable region and
In all distance matrixs can not tie point, plan the optimal path in current floor again using Floyd algorithms, and be sent to
Carrying robot, around static-obstacle thing, move on;
D) when carrying robot runs into other transportation robots, both halt simultaneously, and remote control center is electric to residue
The higher carrying robot of amount, which is sent, meets dynamic barrier instruction, and continuing normally travel to another carrying robot transmission refers to
Order;
The carrying robot for meeting dynamic barrier instruction is received according to A) or B) another carrying robot is worked as start by situation
State barrier carries out dynamic obstacle avoidance, and another robot normally travels according to path profile.
4. according to the method described in claim any one of 1-3, it is characterised in that carrying robot is in accordance with the following methods from current
Path point reaches next path point:
First, the coordinate (x1, y1) of current path point and the angle, θ c of carrying robot are read;
Then, calculated using the distance between current path point coordinates and next path point coordinates and 2 points go to it is next
The angle of the carrying robot of path point;
Finally, advance according to the distance between new carrying robot angle and two path points, control carrying robot.
5. according to the method for claim 4, it is characterised in that the carrying robot takes thing, put thing during perform with
Lower operation prevents from colliding desktop:
During carrying robot takes thing, puts thing, carrying machine human body does not rotate, after the completion of taking thing or putting thing,
It is forwarded to up to after next path point, carrying machine human body receives control instruction and carries out pose adjustment.
6. according to the method for claim 5, it is characterised in that carrying robot move ahead during with remote control center
Carry out real-time Communication for Power:
When carrying robot can not continuously be communicated with remote control center three times, upper path point etc. is returned along original route
Treat, until being communicated again with remote control center;
When remote control center can not continuously receive the signal that carrying robot is sent three times, alarm is sent.
7. according to the method for claim 3, it is characterised in that the adjacent positioned piece is at intervals of 3m.
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