Robot inspection scheduling method based on topological path and behavior tree

Abstract

The invention relates to a robot inspection scheduling method based on a topological path and a behavior tree, and the method comprises the steps: constructing a topological map comprising a plurality of inspection points and a preset path, generating an inspection list, and enabling a remote platform to issue an inspection task of a single inspection point to an inspection robot according to the inspection list; the inspection robot executes an inspection task based on the behavior tree and feeds an inspection result back to the remote platform; if the inspection result is successful, the remote platform inquires an inspection list and determines whether all inspection tasks are completed or not, if yes, inspection is ended, and if not, the previous steps are repeated; if the inspection result is failure, performing exception handling; and according to the abnormal recovery condition, judging whether to continue to complete the unexecuted inspection task or give up inspection for resetting. The method has the beneficial effects that a longer route is segmented into a plurality of shorter routes by using a topological route, so that the shape of the route can be well restrained, and the robot can reach a farther inspection point according to an expected route.

Description

Technical Field

[0001] The present invention belongs to the field of patrol scheduling, and particularly relates to a robot patrol scheduling method based on a topological path and a behavior tree. Background Art

[0002] With the development of robot technology, it has gradually become a trend to use robots for patrol inspection in power plants. The content of the patrol inspection mainly includes obtaining readings of various meters in the station, obtaining the states of disconnecting switches, obtaining temperature and humidity information, obtaining gas concentration, etc. The operating state and fault conditions of equipment are found through the above data. The patrol inspection work is generally jointly completed by a remote monitoring platform and a patrol inspection robot. The basic process is that the remote monitoring platform sends patrol inspection instructions to the patrol inspection robot, and the patrol inspection robot cruises along a preset path, arrives at each task point one by one, and uses various sensors to obtain the concerned index data. Then, based on a preset threshold, it judges whether the index parameters are abnormal and whether to issue an alarm or prompt manual intervention.

[0003] On the patrol inspection robot side, the current mainstream technology is to use a state machine to control the patrol inspection process. With the increase in patrol inspection points, the change in patrol inspection content, and the emergence of various abnormal situations, the patrol inspection process based on the state machine is huge and complex, showing poor scalability and poor usability. Another technology mentions using a behavior tree method for process control, mainly describing how to use a behavior tree for robot behavior control. This technology is divorced from the specific business scope and does not involve the patrol inspection field and specific patrol inspection methods. Another technology mentions a multi-point patrol inspection method based on a behavior tree. In this method, all patrol inspection point information and operation content are stored in the robot. The remote platform issues a start patrol inspection instruction, and the robot navigates to each patrol inspection point one by one according to the stored patrol inspection information for operation. After completing all patrol inspection point tasks, it gives the remote platform a feedback of successful patrol inspection; when an abnormality is encountered during the patrol inspection, after manual reset, it generally cannot continue the patrol inspection and needs to start the patrol inspection task from the beginning. The supervision and intervention ability of the remote platform during the patrol inspection process in this method is weak; and when the distance between two patrol inspection points is far, the route planned by the navigation module may not match the expectation, and the route planned each time may be different. This method cannot constrain the patrol inspection route between two patrol inspection points. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a robot patrol scheduling method based on a topological path and a behavior tree.

[0005] In a first aspect, there is provided a robot patrol scheduling method based on a topological path and a behavior tree, including: Step 1, construct a topological map including multiple patrol inspection points and a preset path and generate a patrol inspection list, and the remote platform issues a patrol inspection task for a single patrol inspection point to the patrol inspection robot according to the patrol inspection list; Step 2: The inspection robot executes the inspection task based on the behavior tree; Step 3: The inspection robot feeds back the inspection result to the remote platform; Step 4: If the inspection result is successful, the remote platform queries the inspection list to determine whether all inspection tasks are completed. If so, the inspection ends; otherwise, steps 1-3 are repeated; Step 5: If the inspection result is a failure, abnormal handling is performed; Step 6: According to the abnormal recovery situation, it is judged whether to continue to complete the unexecuted inspection tasks or to abandon the inspection for reset.

[0006] Preferably, in step 1, the construction of the topological map including multiple inspection points and a preset path and the generation of the inspection list include: Construct an environmental map; Complete the deployment of inspection waypoints and inspection tasks; Store the inspection task list at the remote platform end.

[0007] Preferably, in step 1, during the construction of the environmental map and the deployment of inspection waypoints, several passing waypoints are inserted among the inspection points to constrain the shape of the overall route.

[0008] Preferably, in step 1, the selection of the passing waypoints includes: setting one passing waypoint at the inflection point of the turning area, setting one passing waypoint at a preset distance in the straight area, and setting two passing waypoints at both ends of the narrow area.

[0009] Preferably, in step 2, the behavior tree includes a status detection node, a topological path planning node, a navigation node, and a job execution node.

[0010] Preferably, the status detection node includes a hardware self-check sub-node, a software self-check sub-node, and a power self-check sub-node; the navigation node includes a navigation task sub-node, a navigation monitoring sub-node, and a non-empty judgment sub-node; The status detection node and the navigation node belong to sequential nodes, and the sequential nodes execute the sub-nodes in sequence until a sub-node returns a failure or all sub-nodes return successfully; the topological path planning node and the job execution node belong to execution nodes, and the execution nodes are action nodes or conditional nodes.

[0011] In a second aspect, a robot inspection scheduling system based on a topological path and a behavior tree is provided for executing any of the methods in the first aspect, including: a remote platform and an inspection robot; the remote platform and the inspection robot are communicatively connected.

[0012] In a third aspect, a computer storage medium is provided, in which a computer program is stored; when the computer program runs on a computer, the computer is enabled to execute the method according to any one of the first aspect.

[0013] In a fourth aspect, an electronic device is provided, including: a memory for storing a computer program; a processor for executing the computer program to implement the method according to any one of the first aspect.

[0014] The beneficial effects of the present invention are as follows: 1. The present invention uses a topological route to segment a long route into multiple shorter paths, which can well constrain the shape of the route, so that the robot can reach a far patrol point according to the expected route.

[0015] 2. The present invention uses a behavior tree to complete the patrol task and can dynamically adjust the behavior tree according to business requirements, and its scalability is better than that of a state machine.

[0016] 3. The present invention controls the robot to perform patrol at each patrol point through a remote platform. Since the platform does not issue all patrol points at one time, but sends them one by one and waits for the execution result one by one, the supervision ability of the patrol process is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic diagram of the node types of the behavior tree; Figure 2 It is a flowchart of the deployment work before patrol; Figure 3 It is a patrol flowchart; Figure 4 It is a schematic diagram of a topological map example; Figure 5 It is a schematic diagram of the patrol behavior tree. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] The present invention will be further described below with reference to embodiments. The description of the following embodiments is only used to help understand the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several modifications can still be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

[0019] Embodiment 1: To solve the problems of the prior art, Embodiment 1 of the present application provides a robot patrol scheduling method based on topological paths and behavior trees, mainly describing how the remote monitoring platform and the patrol robot cooperate to better complete the patrol task and how to optimize the path between patrol points.

[0020] Specifically, as Figure 3 shown, the method includes: Step 1: Construct a topological map including multiple inspection points and a preset path, and generate an inspection list. The remote platform issues an inspection task for a single inspection point to the inspection robot according to the inspection list.

[0021] In terms of the inspection task process planning, the robot needs to construct a map of the environment before inspection, determine the inspection waypoints and inspection tasks, and export an inspection list for the remote platform to load and use. The specific process is as Figure 2 shown.

[0022] In terms of path optimization, this method uses the method of inserting several waypoints between inspection points to constrain the shape of the overall route, avoiding situations such as path variability and inconsistency with the expected route when planning paths for two relatively far inspection points. The topological path planning algorithm is used to select the inserted inspection points and generate the corresponding inspection paths.

[0023] Specifically, in the stage of environmental map construction and determination of inspection waypoints, several waypoints are set according to the road conditions on the power plant site between two inspection points that are far apart, so as to better constrain the shape of the route. When selecting waypoints, one waypoint is set at the inflection point in the turning area, one waypoint is set every 5 - 8 meters in the straight area, and two waypoints are set at both ends in the narrow area; and the waypoints should avoid all restricted areas and should not be set on the edge of the road as much as possible. The distance between the waypoint and the road edge should be greater than the width required for the robot to pass through, ensuring that the robot can pass normally. In addition, when the width of the road is less than the width required for the robot to pass through, other detour waypoints need to be set to avoid the current area and go to the destination. The selection of waypoints is relatively crucial. If the waypoints are set improperly, the robot may not be able to pass through the section where the waypoint is located normally, or may plan a route that does not match the expectation. When setting waypoints, the corresponding point position information is stored in each waypoint, including the waypoint number, waypoint type, spatial coordinates and attitude, operation content. Topological line segments are connected between waypoints, and the corresponding path information is stored on the line segment, including the speed used for traveling on this section, the method of stopping and avoiding obstacles, the movement mode, the weight of this section, etc. In this way, a topological map with path information and point position information can be constructed. Among them, the weight of the section can be modified dynamically. When the robot cannot pass through certain areas during a certain inspection (for example, a certain area needs to be repaired and maintained for several days), the weight of the waypoints contained in this area is set to infinity. At this time, the robot will plan a suitable path to avoid the current area to complete the inspection task. After completing the above operations, the corresponding waypoints and path information are stored in the form of a graph when used. This graph is called the topological map of the site. For a sample, refer to Figure 4 shown.

[0024] Specifically, after the construction of the topological map is completed, when a remote platform designates a certain inspection task for the robot, based on the information such as the starting point number and the target point number of the task and the existing topological map, using the A* algorithm, Dijkstra's algorithm or any other weighted path planning algorithm, the shortest path from the starting point to the target point can be planned. Since the path weight of this topological map represents the passability of the road section, the shortest path is also the optimal path. In Figure 4 , assuming that the starting point of a certain task is A and the target point is E, according to the algorithm, the shortest path can be obtained as A - B - C - D - E, where points B, C, and D are waypoints; after obtaining the shortest topological path, the robot dynamically plans the travel route, speed, etc. based on the traditional grid map information and road section constraint information, first moves from point A to point B, then to point C, then to point D, and then to point E for specific inspection operations; the robot can continue to the next point without pausing when passing through the waypoints, and the robot also has a relatively low accuracy requirement for whether the waypoints are reached.

[0025] Step 2: The inspection robot executes the inspection task based on the behavior tree.

[0026] Step 3: The inspection robot feeds back the inspection results to the remote platform.

[0027] Step 4: If the inspection result is successful, the remote platform queries the inspection list to determine whether all inspection tasks have been completed. If so, the inspection ends; if not, steps 1 - 3 are repeated.

[0028] Step 5: If the inspection result is a failure, abnormal handling is performed.

[0029] Step 6: According to the abnormal recovery situation, it is judged whether to continue to complete the unexecuted inspection tasks or abandon the inspection for reset.

[0030] Embodiment 2: Based on Embodiment 1, Embodiment 2 of the present application provides a more specific robot inspection scheduling method based on topological paths and behavior trees, including: Step 1: Construct a topological map including multiple inspection points and preset paths and generate an inspection list, and the remote platform issues the inspection task of a single inspection point to the inspection robot according to the inspection list.

[0031] The construction of the topological map including multiple inspection points and preset paths and generating an inspection list includes: Construct an environmental map; Complete the deployment of inspection waypoints and inspection tasks; Store the inspection task list at the remote platform end.

[0032] In addition, the remote platform can store the coordinates of the inspection points and the operation tasks locally and then send them to the robot one by one. Alternatively, the remote platform can store the inspection numbers locally and store the coordinates of the inspection points and the operation tasks on the robot side. In either case, the inspection work can be carried out normally according to the above business process.

[0033] Step 2: The inspection robot executes the inspection task based on the behavior tree.

[0034] Behavior trees are tree-like structures that are traversed in a specific order starting from the root node until a terminal state (success or failure) is reached. Behavior trees execute from the root node to the child nodes in discrete update steps (called ticks) at a set frequency (usually 100 - 200hz). When the behavior tree is updated, typically at a specific rate, its child nodes are recursively updated according to the way the tree is constructed. After a node's update step, it returns a status to its parent node, which can be Success, Failure, or Running. Behavior trees contain two types of nodes: Control nodes and Execution nodes. Control nodes are internal nodes that define how to traverse the behavior tree based on the status of their child nodes, including Sequence, Fallback, Parallel, and Decorator nodes: The Sequence node executes its child nodes in order until one returns Failure or all return Success; the Fallback node executes its child nodes in order until one returns Success or all return Failure; the Parallel node executes all its child nodes in "parallel". The Parallel node returns Success when at least M child nodes (between 1 and N) are successful and returns Failure when all child nodes fail; the Decorator node modifies a single child node using a custom policy. The Decorator has a set of rules to change the status of the "decorated node". For example, the "Invert" decorator changes Success to Failure. Execution nodes are the leaves of the behavior tree and can be Action nodes or Condition nodes. A Condition node can only return Success or Failure in a single update step, while an Action node can span multiple update steps and can return Running until they reach a final state. The above nodes of the behavior tree are represented by Figure 1 the shapes shown.

[0035] Regarding the behavior tree, when the robot receives an inspection task from the remote platform that includes a set of target coordinates and poses, and one or more operation contents, it executes the behavior tree once. After the execution is completed, the robot returns to the remote platform whether the execution of the behavior tree was successful or failed, as well as the error code in case of failure.

[0036] Specifically, to complete the inspection task of an inspection point, it is necessary to sequentially execute four steps: robot status self-check, path planning, navigation, and operation execution. Moreover, each step needs to be successfully completed in order to successfully complete the inspection task of that point. According to the functional requirements, a behavior tree is generated as shown in Figure 5 Figure. The root node of this behavior tree is a sequence node, which contains four child nodes, namely: Status Check, Topological Path Planning (Plan), Navigation, and Robot Action. Among them, the Status Check node and the Navigation node are sequence nodes, and the Topological Path Planning node and the Robot Action node are action nodes. According to the sequential attribute, these four child nodes are executed sequentially. If all child nodes return successfully, the inspection point task is successfully completed. If any one of them returns a failure, the inspection point task fails.

[0037] Specifically, the StatusCheck node is responsible for the robot's self-check, including HardwareCheck, SoftwareCheck, and PowerCheck. HardwareCheck includes checking whether the chassis motors are working properly and whether each sensor is working properly. When one or more of the above are abnormal, generally, a hardware engineer is required to perform hardware detection and repair. The robot returns a failure and prompts for repair. SoftwareCheck mainly detects whether each hardware driver, navigation module, and sensor module are successfully started. When one or more of the above are abnormal, a software engineer is required to perform inspections and fault recovery. The robot returns a failure and prompts for repair. PowerCheck mainly focuses on whether the battery is fully charged. If the battery is insufficient, the task is interrupted and the robot autonomously goes to the charging pile to charge. According to the functional requirements, the StatusCheck node contains 3 sub-nodes, including the HardwareCheck sub-node, the SoftwareCheck sub-node, and the PowerCheck sub-node. Among them, the HardwareCheck node is an action node that executes the corresponding hardware detection logic; the SoftwareCheck node is an action node that executes the corresponding software detection logic; the PowerCheck node is a selection node that contains 2 sub-nodes, namely the ThresholdCheck node and the SetGoalToCharge node, and both sub-nodes are action nodes. The ThresholdCheck node mainly obtains the current battery percentage and the current voltage from the robot, and judges whether the current battery is sufficient to complete the current inspection point task by comparing with the preset threshold. The SetGoalToCharge node is mainly responsible for changing the coordinates of the inspection target point of the robot to the coordinates of the charging point. According to the selected attribute, as long as one of the 2 sub-nodes is executed successfully, the PowerCheck returns a success. When the battery is sufficient and the battery judgment returns a success, the SetGoalToCharge node is skipped and a success is directly returned. When the battery is insufficient, the ThresholdCheck node returns a failure and the SetGoalToCharge node is executed. If the charging task is successfully set, the PowerCheck node also returns a success, and it is marked in the blackboard of the behavior tree that the target point has been replaced by the charging point; if the charging task setting fails, the PowerCheck node returns a failure and the StatusCheck node also returns a failure, and the entire behavior tree execution fails. The remote platform prompts the user to perform corresponding processing according to the failure reason of the behavior tree.

[0038] Specifically, after the StatusCheck node returns a success, the robot enters the topological path planning stage, executes the logic of the Plan node, and generates a topological path. The internal design of the Plan node is based on the aforementioned topological path section. If the path planning is successful, a list of waypoints will be obtained and stored in the blackboard of the behavior tree, and the Plan node returns a success; if the planning fails, it means that there is no suitable path to the inspection point currently, the Plan node returns a failure, and the current behavior tree execution fails.

[0039] Specifically, when the path planning node returns successfully, the robot retrieves the waypoint coordinates from the list and calls its own navigation module to navigate to each waypoint one by one until the list is empty. The Navigation node is a sequence node that contains three child nodes. Among them, the NavMissionHandle node and the NavMonitor node are selection nodes, and the CheckNavPathList node is an action node. The CheckNavPathList node is modified by a non-empty judgment node (NotEmpty) with an attribute.

[0040] The NavMissionHandle node contains two child nodes: the IsBusyCheck node for judging the navigation status and the NavPositionSend node for sending the navigation task. Among them, the IsBusyCheck node is a conditional node, and the NavPositionSend node is an action node. Since the navigation task generally takes a long time and it takes a long time to get the feedback of success or failure, the behavior tree uses an asynchronous method to wait for the feedback. Before issuing the navigation task, the IsBusyCheck node queries the navigation status of the robot. If it is in the middle of navigation, it returns "running". When the next update step comes, it re-enters the behavior tree to judge the navigation status until it is in the idle state. When the robot is in the idle state, the NavPositionSend node obtains the information of the next target waypoint from the blackboard of the behavior tree and sends it to the navigation module to start a new navigation task and waits for the navigation task feedback.

[0041] The NavMonitor node includes two child nodes: the NavStatusQuery node for querying the navigation feedback and the NavCancel node for canceling the navigation task. Among them, the NavStatusQuery node is an action node and is modified by a timeout node (TimeOut) with an attribute. The NavCancel node is an action node. When the navigation task is successfully feedback after being issued, the NavStatusQuery node returns success. When the feedback times out or the feedback information is failure, the NavStatusQuery node returns failure, and the NavCancel node executes the process of canceling the navigation task and returns failure regardless of whether the cancellation is successful or not, and the entire behavior tree fails.

[0042] When both the navigation task node and the navigation monitoring node return successfully, the waypoint list check node (CheckNavPathList) performs a check on the waypoint list. When the waypoint list is not empty, the waypoint list check node returns successfully and becomes running after passing through the decorator non-empty judgment node. When the next update step arrives, the navigation node re-executes the navigation task node to start the process of moving to the next waypoint. When the waypoint list is empty, the waypoint list check node returns failure and becomes successful after passing through the decorator non-empty judgment node. Therefore, the navigation node also returns successfully.

[0043] When the navigation node returns successfully, the robot reaches the destination and starts task execution operations. According to the demand configuration, it can collect harmful gas concentration information, dust concentration information, meter image information, temperature and humidity information, etc. The task operation node (RobotAction) contains multiple interfaces for interacting with each sensor, calls the corresponding interfaces one by one, and stores the interfaces in the database for subsequent user reference according to the index. After the task operation node finishes execution, the current behavior tree returns successfully.

[0044] In addition, the nodes in the behavior tree can be added, deleted, or their functions can be changed according to the needs.

[0045] Step 3: The inspection robot feeds back the inspection results to the remote platform.

[0046] Step 4: If the inspection result is successful, the remote platform queries the inspection list to determine whether all inspection tasks have been completed. If so, the inspection ends; if not, steps 1 - 3 are repeated.

[0047] Step 5: If the inspection result is a failure, abnormal handling is performed.

[0048] Step 6: According to the abnormal recovery situation, it is judged whether to continue to complete the unexecuted inspection tasks or to abandon the inspection for reset.

[0049] It should be noted that the parts that are the same or similar to those in Embodiment 1 in this embodiment can be referred to each other and will not be elaborated in this application.

[0050] Embodiment 3: Based on Embodiment 2, Embodiment 3 of the present application provides a robot inspection scheduling system based on a topological path and a behavior tree, including: a remote platform and an inspection robot; the remote platform and the inspection robot are communicatively connected.

[0051] In terms of the inspection task process planning, after the deployment is completed, the inspection task list is stored on the remote platform side. The remote platform issues the inspection task for one inspection point at a time. The inspection robot executes the inspection task based on the behavior tree and feeds back the results to the remote platform. After receiving the successful feedback, the platform queries the inspection list to determine whether all inspection tasks have been completed. If not, it issues the next inspection task until all inspection tasks are completed. When the remote platform receives the failure feedback, indicating that an abnormality has occurred in the inspection task, it calls the exception handling process or prompts the user for manual recovery, and decides whether to continue with the unexecuted inspection tasks or abandon the inspection and perform a reset based on the exception recovery situation. During the inspection process, the remote platform can modify the inspection list autonomously according to the on-site situation or requirements, and selectively skip several inspection points. This system strengthens the supervision of the remote platform over the inspection process and enhances the fault tolerance of the inspection system. The specific process is shown in Figure 2.

[0052] It should be noted that the system provided in this embodiment is the system corresponding to the method provided in Embodiment 2. Therefore, for the parts that are the same or similar in this embodiment and Embodiment 2, they can be referred to each other and will not be elaborated in this application.

[0053] In summary, this application can replace the traditional manual inspection method, automate the inspection of each point, not only simplify the methods of collecting and displaying multi-sensor data, but also increase the route constraints during the inspection process. In addition, it strengthens the supervision ability of the remote platform during the inspection process and enhances the fault tolerance of the inspection system.

Claims

1. A robot patrol scheduling method based on topological paths and behavior trees, characterized in that, Including: Step 1: Construct a topological map including multiple inspection points and a preset path, and generate an inspection list. The remote platform issues the inspection task of a single inspection point to the inspection robot according to the inspection list; Step 2: The inspection robot executes the inspection task based on the behavior tree; Step 3: The inspection robot feeds back the inspection result to the remote platform; Step 4: If the inspection result is successful, the remote platform queries the inspection list to determine whether all inspection tasks are completed. If so, the inspection ends; if not, steps 1-3 are repeated; Step 5: If the inspection result is failed, perform exception handling; Step 6: According to the exception recovery situation, judge whether to continue to complete the unexecuted inspection tasks or abandon the inspection and perform reset.

2. The robot patrol scheduling method based on topological paths and behavior trees according to claim 1, wherein In step 1, the construction of the topological map including multiple inspection points and a preset path and the generation of the inspection list include: Construct an environmental map; Complete the deployment of inspection waypoints and inspection tasks; Store the inspection task list at the remote platform end.

3. The robot patrol scheduling method based on topological paths and behavior trees according to claim 2, wherein, In step 1, during the construction of the environmental map and the deployment of inspection waypoints, several waypoints are inserted among the inspection points to constrain the shape of the overall route.

4. The robot patrol scheduling method based on topological path and behavior tree according to claim 3, wherein, In step 1, the selection of the waypoints includes: setting one waypoint at the inflection point of the turning area, setting one waypoint at a preset distance in the straight area, and setting two waypoints at both ends of the narrow area.

5. The robot patrol scheduling method based on topological path and behavior tree according to claim 4, characterized in that In step 2, the behavior tree includes a status detection node, a topological path planning node, a navigation node, and a job execution node.

6. The robot patrol scheduling method based on topological paths and behavior trees according to claim 5, characterized in that The status detection node includes a hardware self-check sub-node, a software self-check sub-node, and a power self-check sub-node; the navigation node includes a navigation task sub-node, a navigation monitoring sub-node, and a non-empty judgment sub-node; The status detection node and the navigation node belong to sequential nodes. The sequential nodes execute the sub-nodes in sequence until a sub-node returns a failure or all sub-nodes return successfully; the topological path planning node and the job execution node belong to execution nodes, and the execution nodes are action nodes or conditional nodes.

7. A robot patrol scheduling system based on topological paths and behavior trees, characterized in that, Used to execute the method according to any one of claims 1 to 6, including: a remote platform and an inspection robot; the remote platform and the inspection robot are communicatively connected.

8. A computer storage medium, characterized in that, The computer storage medium stores a computer program; when the computer program runs on the computer, the computer is caused to execute the method according to any one of claims 1 to 6.

9. An electronic device, characterized in that, Including: A memory for storing a computer program; A processor for executing the computer program to implement the method according to any one of claims 1 to 6.

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