CN112947475A

CN112947475A - Laser navigation forklift type AGV vehicle-mounted system and method

Info

Publication number: CN112947475A
Application number: CN202110301652.9A
Authority: CN
Inventors: 秦齐; 万熠; 梁西昌; 侯嘉瑞; 刘自若; 贺翔; 李亚男; 荣培植; 吴付旺; 巩方彬; 陈飞
Original assignee: Shandong University
Current assignee: Shandong University
Priority date: 2021-03-22
Filing date: 2021-03-22
Publication date: 2021-06-11

Abstract

The invention discloses a laser navigation forklift type AGV vehicle-mounted system and a control method, wherein the system comprises an electric forklift body, a vehicle-mounted main controller is arranged on the electric forklift body, and the vehicle-mounted controller is connected with a positioning navigation module, a path planning module, a safety obstacle avoidance module, an audible and visual alarm module, a motion execution module, an automatic charging module, a wireless communication module and a task management scheduling module; the positioning navigation module describes the surrounding environment in a laser SLAM mode, integrates information of an I MU, a wheel type odometer and a camera sensor, and completes drawing construction and positioning of the AGV forklift.

Description

Laser navigation forklift type AGV vehicle-mounted system and method

Technical Field

The invention relates to the field of unmanned laser forklift control, in particular to a vehicle-mounted system and a method of an unmanned laser forklift.

Background

With the rapid development of warehouse logistics automation and the disappearance of domestic population dividends, Automated Guided Vehicles (AGVs) gradually become important components of intelligent logistics systems by virtue of the advantages of high efficiency, strong flexibility and the like. Wherein, fork truck formula AGV is as the representative, not only can realize the material handling function, can realize the function of material stack moreover, replaces the manpower basically completely, realizes automaticly. At present, mainstream fork truck AGV in market is with electric fork truck as the main part, installs sensors such as laser radar in the electric fork truck main part to install optics auxiliary device such as reflector panel additional in surrounding environment, assist laser radar and fix a position, and then realize the control to AGV. However, there are the following problems:

1. the positioning mode of current laser navigation fork truck formula AGV installation reflector panel is higher to the surrounding environment requirement, and the reflector panel is easily polluted, and the reflectivity of object has certain influence to the accuracy of laser radar location around, because the requirement of reflector panel installation, uses limitedly in the outdoor, and adopts single sensor location more, and it is relatively poor to avoid dynamic obstacle ability.

2. The existing AGV path planning method mostly has the problems of long path searching time, more redundant nodes and the like, and influences the working efficiency of the AGV. And the problem of crossing jam and the like exists for the dispatching of multiple AGVs.

3. Only various sensors are installed on a forklift main body, a vehicle-mounted system of the forklift main body is mainly used for receiving information and sending instructions, a laser SLAM module, a path planning module, a motion control module and the like are not integrated, and the transportability is poor.

Disclosure of Invention

In order to solve the technical problems in the prior art, the invention provides a laser navigation forklift type AGV vehicle-mounted system and a control method, and the system and the control method have the advantages of high integration level, simple architecture and the like.

The technical scheme adopted by the invention is as follows:

in a first aspect, the embodiment of the invention provides a laser navigation forklift type AGV (automatic guided vehicle) vehicle-mounted system, which comprises an electric forklift body, wherein a vehicle-mounted main controller, a positioning navigation module, a path planning module, a safety obstacle avoidance module, an audible and visual alarm module, a motion execution module, an automatic charging module, a wireless communication module and a task management scheduling module are arranged on the electric forklift body;

the vehicle-mounted main controller is an industrial personal computer, and the positioning navigation module, the path planning module, the safety obstacle avoidance module, the sound and light alarm module, the motion execution module, the automatic charging module and the wireless communication module are respectively connected with the main controller; the positioning navigation module abandons the traditional reflector positioning mode, adopts a laser SLAM mode to describe the surrounding environment, integrates sensor information such as IMU, wheel-type odometer and camera, and completes map building and AGV forklift self positioning.

The path planning module can perform collision detection, calculate the distance between the AGV forklift and surrounding obstacles, and is used for planning a shortest collision-free path from the starting position to the target station for the AGV.

The safety obstacle avoidance module adopts a two-stage combined protection measure combining hardware and software and matching contact protection with non-contact protection, and comprises 2 professional laser obstacle avoidance scanners arranged on the head of the vehicle, a three-region protection mode, a protection region and two warning regions, obstacle avoidance detection photoelectricity arranged at the tail fork tip part of the vehicle, a bumper and an obstacle avoidance contact switch arranged on the head of the vehicle and a contact switch arranged at the fork tip part of the vehicle;

and the sound-light alarm module is used for alarming and prompting when a fault occurs.

The motion execution module adopts an electro-hydraulic hybrid driving mode by the walking, steering and lifting descending of the AGV, and the lifting of the fork adopts hydraulic control.

The automatic charging module is used for charging the vehicle-mounted battery, and the working efficiency of the AGV is improved. The wireless communication module is used for data communication with the remote control center, and plays a role in data transmission and data transfer.

And the task scheduling module is used for managing and scheduling the tasks of a plurality of AGV. The overall system is based on the ROS operating system.

In a second aspect, based on the foregoing system, an embodiment of the present invention further provides a method, where the map building method of the positioning navigation module is as follows:

step 1: the system collects speed and acceleration information through an IMU, and completes primary estimation on the self attitude of the AGV through attitude resolving and complementary filtering;

step 2: the wheel type odometer collects speed information to complete the dead reckoning of the AGV, so that the position of the AGV is estimated, and attitude estimation is completed by integrating attitude estimation and position estimation;

and step 3: the multi-line laser radar adopts a point cloud segmentation matching technology, establishes a point cloud description model of the surrounding environment based on a point cloud segment and a classified target method, and scans and matches the point cloud description model with the estimated pose to obtain a matched pose;

and 4, step 4: the camera identifies the mark pose and the mark size;

and 5: matching the pose with the laser radar to obtain a high-precision pose by dynamic weighting;

step 6: outputting the pose to a central controller to adjust the rotating speed and the rotating angle of the wheel;

and 7: and judging whether the target task point is reached, if so, finishing guidance, and if not, starting the next scanning period.

Further, the method for planning the path by the path planning module is as follows:

step 1: firstly, dividing grids according to the map precision;

step 2: adding the starting point into an open list;

and step 3: searching nodes in 8 directions by taking the starting point as a center;

and 4, step 4: adding the jumping points meeting the conditions into an open list;

and 5: searching a grid point of the minimum value in the open list and marking as an X point;

step 6: judging whether X is a target point, if so, ending the path search, and if not, deleting the X from the open list and adding the X into the closed list;

and 7: nodes can be searched in the straight line direction and the oblique line direction, when the two directions can be expanded, the expansion in the straight line direction is preferentially carried out, and the expansion in the straight line direction is firstly completed and then the expansion in the diagonal line direction is carried out; searching a first jumping point N in a straight line direction or a diagonal line direction;

and 8: deleting the N points in the closing list;

and step 9: judging whether the N point is in the open list or not, if not, adding the N point into the open list, if so, updating the value of the N point in the open list, and then performing the next round of search;

step 10: and after the search is finished, traversing the nodes in the closed list, and sequentially connecting all the nodes together to obtain a final path. And according to the finally generated path, the navigation frame is used for outputting speed information, so that the motion control of the AGV can be realized.

The beneficial effects of the above-mentioned embodiment of the present invention are as follows:

the laser navigation forklift type AGV vehicle-mounted system and the control method provided by the invention improve the related algorithm and have the advantages of high integration level, simple architecture and the like. The traditional positioning and mapping method of the reflector is abandoned, the SLAM algorithm is adopted, sensor data such as IMUs, mileometers and cameras are fused, the laser positioning accuracy is improved, the environmental adaptability is improved, and the working range of the AGV is expanded. And a related path planning algorithm is improved, path searching nodes are reduced, path searching time is shortened, and AGV autonomous navigation efficiency is improved. A novel AGV multi-machine scheduling method is provided, the problem of intersection congestion is effectively relieved, and the phenomenon of detour is reduced while conflict is avoided.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.

FIG. 1 is a schematic diagram of the overall system framework of the present invention;

FIG. 2 is a flow diagram of a positioning and mapping module of the present invention;

FIG. 3 is a flow chart of a path planning module of the present invention;

FIG. 4 is a flow chart of an obstacle avoidance module of the present invention;

FIG. 5 is a flow chart of an automatic charging module of the present invention;

FIG. 6 is a flow chart of the motion control module of the present invention;

FIG. 7 is a flow chart of the management scheduling of the present invention.

Detailed Description

It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an", and/or "the" are intended to include the plural forms as well, unless the invention expressly state otherwise, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof;

as described in the background art, the present invention provides a laser navigation forklift type AGV vehicle-mounted system and a control method thereof to solve the above technical problems.

In a typical embodiment of the present invention, as shown in fig. 1 and fig. 2, the embodiment discloses a laser navigation forklift type AGV vehicle-mounted system, which includes an electric forklift body, and a vehicle-mounted main controller, a positioning navigation module, a path planning module, a safety obstacle avoidance module, an audible and visual alarm module, a motion execution module, an automatic charging module, a wireless communication module, and a task management scheduling module are disposed on the electric forklift body.

The vehicle-mounted main controller is an industrial personal computer, and the positioning navigation module, the path planning module, the safety obstacle avoidance module, the sound and light alarm module, the motion execution module, the automatic charging module and the wireless communication module are respectively connected with the main controller; the positioning navigation module abandons the traditional reflector positioning mode, adopts a laser SLAM mode to describe the surrounding environment, integrates sensor information such as IMU, wheel type odometer and camera, and completes map building and AGV forklift self positioning.

The safety obstacle avoidance module adopts hardware and software to combine together, and the barrier scanner is kept away to 2 specialty laser that install additional including the locomotive portion to contact protection and non-contact protection complex second grade joint safeguard procedures, three regional protection modes, two warning areas in a protected area, the fender that rear of a vehicle fork point portion was installed is detected photoelectricity, the bumper that the locomotive was installed additional with keep away the contact switch that barrier contact switch and fork point portion were installed additional.

The motion execution module adopts an electro-hydraulic hybrid driving mode by the walking, steering and lifting descending of the AGV, and the lifting of the fork adopts hydraulic control. The automatic charging module is used for charging the vehicle-mounted battery, and the working efficiency of the AGV is improved.

The wireless communication module is used for data communication with the remote control center, and plays a role in data transmission and data transfer. And the task scheduling module is used for managing and scheduling the tasks of a plurality of AGV. The overall system is based on the ROS operating system.

The positioning navigation module abandons the traditional reflector positioning mode, adopts a laser SLAM mode to describe the surrounding environment, integrates sensor information such as IMU, wheel type odometer and camera, and completes map building and AGV forklift self positioning. The path planning module can perform collision detection, calculate the distance between the AGV forklift and surrounding obstacles, and is used for planning a shortest collision-free path from the starting position to the target station for the AGV. The safety obstacle avoidance module adopts hardware and software to combine together, and the barrier scanner is kept away to 2 specialty laser that install additional including the locomotive portion to contact protection and non-contact protection complex second grade joint safeguard procedures, three regional protection modes, two warning areas in a protected area, the fender that rear of a vehicle fork point portion was installed is detected photoelectricity, the bumper that the locomotive was installed additional with keep away the contact switch that barrier contact switch and fork point portion were installed additional. And the sound-light alarm module is used for alarming and prompting when a fault occurs. The motion execution module adopts an electro-hydraulic hybrid driving mode by the walking, steering and lifting descending of the AGV, and the lifting of the fork adopts hydraulic control. The automatic charging module is used for charging the vehicle-mounted battery, and the working efficiency of the AGV is improved. The wireless communication module is used for data communication with the remote control center, and plays a role in data transmission and data transfer. And the task scheduling module is used for managing and scheduling the tasks of a plurality of AGV. The overall system is based on the ROS operating system.

The laser radar mapping and positioning module is different from a traditional single-line laser radar mapping, abandons a reflector mapping mode, adopts a multi-line laser radar mapping method, and specifically comprises the following steps:

step 1: the system collects speed and acceleration information through the IMU, completes the preliminary estimation of the self attitude of the AGV through attitude calculation, complementary filtering and the like,

and step 3: the multiline laser radar adopts a point cloud segmentation matching technology, establishes a point cloud description model of the surrounding environment based on a point cloud segment and a classified target method, scans and matches the point cloud description model with the estimated pose to obtain the matched pose,

and 4, step 4: the camera identifies the position and the size of the mark,

and 5: matching the pose with the laser radar to obtain a high-precision pose by dynamic weighting,

step 6: outputs the pose to a central controller to adjust the rotating speed and the rotating angle of the wheel,

Therefore, multi-sensor fusion positioning and map building is realized, the running pose information of the AGV is fed back in real time, the normal walking of the AGV is ensured, and certain precision is kept. The flow is shown in fig. 2.

Furthermore, in the embodiment, the path planning module is used for planning a collision-free path from a starting position to a target station for the AGV, and in order to solve the problems of long path search time, more search redundant nodes and the like existing in the existing path planning method, a new path planning method is applied, instead of a traditional point-by-point judgment method, expansion calculation is performed in four directions or eight directions around the starting point serving as a center, a key point is selected as a jumping point, a jumping point judgment method is adopted, a jumping point meeting conditions is selected according to a rule by taking the starting point as the center, and the jumping point is searched in the next search direction by taking the directions of the original jumping point and the new jumping point as the destination, so that a calculation and judgment link for non-key nodes in the traditional algorithm is omitted, and the algorithm efficiency is improved. The flow is shown in fig. 3. The algorithm maintains two node lists, namely an open list and a closed list, wherein the open list stores nodes which are not traversed, and the closed list stores nodes which are traversed, and the specific steps are as follows:

step 1: firstly, dividing grids according to the map precision;

step 2: adding the starting point into an open list;

step 6: judging whether X is a target point, if so, ending the path search, and if not, deleting X from the open list, and adding X into the closed list;

and 7: the nodes can be searched in the straight line direction and the oblique line direction, when the two directions can be expanded, the expansion in the straight line direction is preferentially carried out, and the expansion in the straight line direction is firstly completed and then the expansion in the diagonal line direction is carried out. Searching a first jumping point N in a straight line direction or a diagonal line direction;

and 8: deleting the N points in the closing list;

Further, the safety obstacle avoidance module in the embodiment adopts two-level combined protection measures of hardware and software, and is divided into a contact type and a non-contact type. The first-level safety system adopts multiple non-contact sensors, and comprises two professional laser obstacle avoidance scanners which are additionally arranged on a vehicle head, wherein the scanning angles of the laser scanners are 270 degrees, the laser scanners are respectively arranged at two corners of the vehicle head, the vehicle body is just covered on the surrounding area, and no safe dead angle exists. The obstacle avoidance detection photoelectricity is additionally arranged at the tip of the tail fork, and the goods in-place detection photoelectricity is additionally arranged at the root of the fork. The second level adopts contact safety system, including installing the bumper additional at the locomotive to install pull switch additional behind the bumper, install contact switch additional at rear of a vehicle fork point portion, install limit for height contact switch etc. additional on the portal. If the warning area detects the obstacle, the vehicle decelerates and crawls, and if the stopping area detects the obstacle. Stopping immediately, if no obstacle is detected around, keeping the AGV forklift in a working state, and if the anti-collision rubber strip touches the obstacle, stopping immediately, wherein the flow chart is shown in fig. 4, and the specific steps are as follows:

step 1: starting the obstacle avoidance system to work;

step 2: whether the laser radar warning area detects the obstacle or not, if the obstacle is detected, the speed is reduced and the vehicle is driven slowly, and if the obstacle is not detected, normal operation is continued;

and step 3: whether the laser radar stopping area detects an obstacle or not, if the obstacle is not detected, normal operation is continued, and if the obstacle is detected, the vehicle is stopped immediately;

and 4, step 4: detecting whether the barrier is moved away, if so, continuing normal work, and if not, keeping the barrier in place;

and 5: if the ultrasonic sensor detects an obstacle, the operation is normal if the obstacle is not detected, and if the obstacle is detected, the operation is immediately stopped,

step 6: detecting whether the barrier is moved away, if so, continuing normal work, and if not, keeping the barrier in place;

and 7: whether the anti-collision rubber strip detects an obstacle or not, if the obstacle is not detected, the anti-collision rubber strip continues to work normally, and if the obstacle is detected, the vehicle stops immediately;

and 8: and detecting whether the barrier is removed, if so, continuing normal operation, and if not, keeping the barrier in place.

Furthermore, in this embodiment, the automatic charging module detects the battery level through detecting the battery I/O port to control the contactor of the charging brush plate, so as to control the on/off of the charging. The on-vehicle brush and the disconnection of battery that charge of operation in-process, only can close the contactor when the AGV reaches the controller on the AGV after the charging station, be on-vehicle brush and the battery switch-on that charges, the side plate electrode with fill electric pile and be in the same place. The automatic charging module flow is shown in fig. 6, and includes the following steps:

step 1: detecting the current state of the AGV;

step 2: if the AGV is in an idle state, detecting whether the electric quantity of the AGV is lower than 50%, if the electric quantity of the AGV is lower than 50%, charging the charging pile, and if the electric quantity of the AGV is higher than 50%, standing by in a stopping area;

and step 3: detecting whether the battery is charged for two hours or the battery power is higher than 95%, and if the battery power is higher than 95%, driving to a stop area for standby; if not, continuing to charge;

and 4, step 4: if the AGV is in a working state, detecting whether the electric quantity of the AGV is lower than 30%, and if the electric quantity of the AGV is lower than 30%, completing a cycle of work and then charging the charging pile; if the working speed is not lower than 30%, continuing working, and waiting to the stop area after the working is finished;

and 5: judging whether the charging is carried out for one hour or the electric quantity is higher than 95%, and if the electric quantity is higher than 95%, driving to a stop area for standby; if not higher than 95%, the charging is continued.

Furthermore, the motion execution module in the embodiment is used for automatically controlling the actions of the forklift, mainly comprises a driving unit and an execution unit, and comprises motion control of straight movement, steering, fork lifting and the like. The motion control flow is shown in fig. 6.

Step 1: the AGV enters a standby state;

step 2: whether a task calls or not is judged, if no task calls exist, standby is carried out in a stopping area, and if the task calls exist, the station direction is judged;

and step 3: if the station is at the initial station, the station is in the station-out direction, and if the station is out from the left side, the station is sequentially retreated, slowly moved, retreated, rotated to the left and then accelerated and retreated; if the vehicle leaves from the right side, the vehicle is retreated slowly, retreated to the right, rotated to the right and then accelerated.

And 4, step 4: when entering a target station, if entering from the left side, firstly slowing down and slowly moving, then turning from backward to forward, and then turning to the left; if the vehicle enters from the right side, the vehicle decelerates and slowly moves, then turns from backward to forward, and then turns to the right after going forward;

and 5: judging whether the specified station is reached, and if the specified station is not reached, instructing to adjust by a controller; if the forklift reaches the designated station, the forklift is stopped first, and then the fork action is executed;

step 6: judging whether the fork action is finished or not, and if the fork is not in place, adjusting the command of the controller; and if the pallet fork is in place, carrying out the next cycle of work.

Further, in this embodiment, AGV acts as the executor of system, accomplishes the turnover transport of goods, and AGV needs work under the supervision of task management scheduling module, and this system adopts wifi wireless communication, constitutes star network connection between task management module and the AGV, mainly accomplishes functions such as rational distribution, AGV walking planning, traffic control of AGV task, still possesses functions such as supervise equipment running state simultaneously. The system dynamic scheduling flow chart is shown in the following chart. The main idea is as follows: if for the syntropy conflict, then judge the car distance between two AGV, if the AGV car distance is less than safe distance, then slow down the back car or the car before accelerating, if conflict in opposite directions, then judge two AGV who enters into earlier and dash into the district, when having an AGV enter into the conflict district, then let another AGV park the waiting outside the conflict district, leave the conflict district until the AGV that has entered into the conflict district. The program circularly runs, and the dynamic scheduling of the AGV system can be realized, and the specific steps are as follows:

step 1: the upper computer starts monitoring the AGV state;

step 2: the upper computer issues a task instruction;

and step 3: judging the priority of the task in the task queue;

and 4, step 4: allocating proper AGV for the task;

and 5: the AGV starts working, whether the current AGV is in the range of 3 meters in front of the conflict area or not is judged, and if not, the AGV continues to run at the normal speed;

step 6: if the current AGV is within the range of 3 meters in front of the conflict area, continuing to judge the conflict type, judging whether the conflict is in the same direction, if the conflict is in the same direction, judging whether the distance between two vehicles in the conflict area is smaller than a safety distance, if the distance is not smaller than the safety distance, the current AGV runs at a normal speed, if the distance is smaller than the safety distance, continuing to judge whether the current AGV is in front of another AGV, if the distance is in front, accelerating the current AGV, and if the distance is in back, decelerating the current AGV;

and 7: if the AGV does not conflict in the same direction, judging whether the AGV is in a direction conflict or not, and if the AGV is not in the direction conflict, driving the AGV at the normal speed; if the two AGVs conflict with each other, judging the positions of the two AGVs, if the current AGV enters the conflict area firstly and the other AGV is within 2 meters of the conflict area, and if the current AGV enters the conflict area, suddenly stopping the other AGV; if another AGV enters the conflict area before the current AGV and the current AGV is within two meters before the conflict area, the current AGV is suddenly stopped; and if the other AGV enters the conflict area before the current AGV and already leaves the conflict area, canceling the sudden stop of the current AGV, otherwise, driving the current AGV at the normal speed.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A laser navigation forklift type AGV vehicle-mounted system is characterized by comprising an electric forklift body, wherein a vehicle-mounted main controller is arranged on the electric forklift body and is connected with a positioning navigation module, a path planning module, a safety obstacle avoidance module, an audible and visual alarm module, a motion execution module, an automatic charging module, a wireless communication module and a task management scheduling module;

the positioning navigation module describes the surrounding environment in a laser SLAM mode, integrates IMU, wheel type odometer and camera sensor information, and completes drawing construction and AGV forklift self positioning.

2. The laser navigation forklift type AGV vehicle-mounted system according to claim 1, wherein the path planning module selects key points as jumping points, selects the jumping points meeting the conditions according to rules by taking a starting point as a center in a jumping point judgment mode, and searches the jumping points by taking the directions of the original jumping points and the new jumping points as the next searching direction until reaching the end point.

3. The laser navigation forklift type AGV vehicle-mounted system according to claim 1, wherein said safety obstacle avoidance module includes two of a contact type protection module and a non-contact type protection module.

4. The laser navigation forklift type AGV car-mounted system according to claim 3, wherein the contact type protection module comprises a bumper mounted on the car head, an obstacle avoidance contact switch mounted at the tip of the rear fork and a height limit contact switch mounted on the upper end of the door frame.

5. The laser navigation forklift type AGV vehicle-mounted system according to claim 3, wherein said non-contact type protection module comprises a laser obstacle avoidance scanner installed on the head of the electric forklift body.

6. The laser navigation forklift type AGV vehicle-mounted system according to claim 5, wherein said two laser obstacle avoidance scanners are installed at two corners of the front of the vehicle, and the scanning angle of the laser scanners is 270 degrees.

7. The laser navigation forklift type AGV vehicle-mounted system according to claim 1, wherein the motion execution module is used for walking, steering and lifting and descending of the fork of the AGV, an electro-hydraulic hybrid driving mode is adopted, and lifting of the fork is controlled hydraulically.

8. The control method of the laser navigation forklift type AGV vehicle-mounted system based on any one of claims 1 to 7, wherein the map building method of the positioning navigation module is as follows:

and 4, step 4: the camera identifies the mark pose and the mark size;

9. The method for controlling the AGV system according to claim 8, wherein the path planning module plans the path by the following steps:

step 1: firstly, dividing grids according to the map precision;

step 2: adding the starting point into an open list;

and 8: deleting the N points in the closing list;