How to work a plot of land with at least two agricultural robots

Abstract

The present invention relates to a method for working a plot by at least two agricultural robots (R1, R2, ..Ri) functioning autonomously and independently according to commands and / or instructions transmitted by a common central management and control system (SC), which subdivides the plot (P) into at least two band-shaped different working areas (Z1, Z2...Zj) with opposite edges and pond areas (F, F') extending along each edge of the bands (Z1, Z2...Zj). A feature of the present invention is that each pound area (F, F') is subdivided into pound area portions (small portions) (PF1, PF1'; PF2, PF2'; ...PFj, PFj'), each pound area portion faces the edge of each band forming the work zone (Z1, Z2, ...Zj), and at least a portion of the pound area portion (PF1, PF1'; PF2, PF2'; ...PFj, PFj') is temporarily and exclusively assigned to a robot (R1, R2, ...Ri) that is passing through or about to pass through a specified pound area portion (PF1, PF1'; PF2, PF2'; ...PFj, PFj') or that has started, is performing, or has completed work on a specified pound area portion (R1, R2, ...Ri).

Description

[Technical Field]

[0001] The invention relates to the field of agricultural machinery, more particularly to the soil work or plant cultivation of agricultural plots, and concerns a method for automatic and simultaneous work by a fleet of at least two agricultural machines or robots, and an agricultural assembly for carrying out this method. [Background technology]

[0002] In the agricultural sector, it is known that when a fleet of autonomous agricultural machines (robots) works on a plot, it is important to distribute the work within the plot to ensure system efficiency, as well as to avoid the risk of collisions between different agricultural machines as much as possible.

[0003] A parcel P is typically divided into a "main field" CP (the most suitable usable area SU) and a zone de fourriere (enclosing area, storage space) surrounding the main field CP and its adjacent perimeter (hereafter referred to as the "pound area") (see Figure 1). (In Figure 1, the pound area is the entire perimeter of the main field.) Conventionally, this pound area is located at least at both ends of the parcel's working lines or paths, and is used by machines to make U-turns, and more generally when moving from one working line to another in the main field.

[0004] In a known conventional way, each autonomous vehicle in a fleet communicates with each other (directly by radio frequency or via a central system) to keep track of the other autonomous vehicles' positions. Another solution is the master-slave type, where the slave robot replicates the path of the master robot.

[0005] However, these known solutions always require a two-way communication exchange and require permanent communication between the robots, which inevitably results in complex data flows and connections between the machines and the network.

[0006] Other known master-slave solutions require the slave robot to depend on the master robot, reducing efficiency as the two machines cannot actually operate independently and can only work in pairs or groups. Additionally, each robot must be managed via a permanent communication link.

[0007] Yet another solution suggests dividing the work area into work zones of fixed width corresponding to the working width of the agricultural robots working on it (each zone is worked in one pass), allocating the work zones to different robots and allocating / reassigning these work zones in real time according to the progress of each robot's work. Such a solution is disclosed in [Patent Document 1] (European Patent Publication No. EP 3,508,045) or [Patent Document 2] (US Patent Application Publication No. US 2019 / 0146513).

[0008] In the latter case, when a robot wants to go to a new zone through the pond area (after finishing a task in a particular zone), or when it wants to make a U-turn in the pond area at the end of one zone, or when its passage is blocked by an obstacle (especially another robot), a robot passing through or at the exit of that zone must wait for the passage to clear or find an alternative route to reach its goal or perform an operation (selection of the shortest alternative route). In this case, passage through a zone or work queue where a portion of the adjacent pond area at the end is blocked is temporarily prohibited, and passage is not allowed even if the robot needs to change zones.

[0009] As a result, all known solutions, especially the last one, complicate the management of the fleet (prioritization, collision avoidance, etc.) in the pond area in the case of several agricultural robots. [Prior art documents] [Patent documents]

[0010] [Patent Document 1] European Patent No. EP3,508,045 [Patent Document 2] U.S. Patent Application Publication No. US2019 / 0146513 Summary of the Invention [Problem to be solved by the invention]

[0011] The object of the present invention is to provide a solution that overcomes the above-mentioned drawbacks and in particular eliminates collision management as much as possible and allows effective coordination of different robots without the need for communication between the robots. [Means for solving the problem]

[0012] The object of the present invention to achieve the above object is to provide a method for dividing a work area to be worked into at least two separate work zones (zones delimited) so as to cover substantially the entire usable surface area of ​​the work area, i.e. the usable area, before the start of work in the work area or gradually during the work. the method further comprising: subdividing a work area into a plurality of work zones (travails), each work area comprising a portion of the work area in the form of a band having two opposite edges at each end thereof, with a pound area zone extending along adjacent edges of each of the two opposite edges of each band; subdividing each pound area zone into a plurality of pound area portions opposite each other and contiguous with each end edge of the band forming the work area; and temporarily and exclusively assigning at least a portion of a pound area portion to a robot that is about to traverse or is traversing a given pound area portion or that has begun, is performing, or completed work in a work area associated with that pound area portion, and wherein the movement and / or movement of at least a portion of the other robots may be influenced by the temporary and exclusive assignment through the central management and control system.

[0013] The present invention will be better understood from the following description of preferred embodiments, but the invention is not limited to the following examples. [Brief explanation of the drawings]

[0014] [Figure 1] The figure shows that the section P consists of a main field CP and a pound area that is adjacent to it and covers all or part of its periphery. In [Figure 1], the entire perimeter of the main field is the pound area. [Figure 2] For a rectangular parcel, the parcel field is subdivided into pound areas that surround its entire perimeter, and then the pound areas are subdivided into portions (small portions). [Figure 3] A diagram showing the results after the partitions in [Figure 2] are alternately assigned to uniform work areas in the same or repeating pattern of type ABC, ABC, .... [Figure 4] Diagrams representing the divisions of [Fig. 2] and [Fig. 3], where the whole field is allocated alternately to uniform working areas according to different or repeating patterns similar to [Fig. 3], but with bands of different sizes (narrower widths) (at the ends). [Figure 5] The entire field is allocated with alternating uniform work areas according to the same pattern as in [Figure 4] or a repeating pattern (types ABC, ABC, ...), but there are no horizontal pound areas (only pound areas at both ends of the work column) and the (end) bands have different sizes. [Figure 6] FIG. 2 shows a block diagram of an example of an agricultural assembly for carrying out the method of the present invention, showing the main components (central control system - autonomous robotic agricultural machine). [Figure 7] Illustrates a section where the main field is being handled by four different robots, demonstrating that competition / conflict between the robots can be managed by the method of the present invention (exclusive allocation of parts of the pond area). DETAILED DESCRIPTION OF THE INVENTION

[0015] As shown in Figures 2 to 6, the present invention relates to a method for simultaneously working a plot (P) by a flotilla of at least two agricultural machines or robots (R1, R2, ..., Ri) operating autonomously and independently according to instructions and / or commands transmitted from a common central management and control system (SC).

[0016] In the method of the present invention, before the start of work on the section (P) or gradually during the work, the section (P) is subdivided into at least two different working zones (Z1, Z2, ..., Zj), which together cover substantially the entire usable or useful area (SU) of the section (P), also called the main field CP, and each working zone (Z1, Z2, ..., Zj) consists of a portion of the working section in the form of a band (bande), which has two opposite edges (EB, EB') at both ends, and a zone of one pond area (F, F') extends along the edges (EB, EB') adjacent to the two opposite edges of each band (Z1, Z2, ..., Zj).

[0017] The method of the present invention is characterized in that the zone of each pond area (F, F') is subdivided into pond area portions (PF1, PF1'; PF2, PF2'; ...; PFj, PFj'), which are opposite each other and contiguous with one of the two end edges (EB and EB') of one of the bands forming the working areas (Z1, Z2, ..., Zj), and at least one of the pond area portions (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') is temporarily and exclusively assigned to a robot (R1, R2, ..., Ri) that is about to traverse or is traversing a given pond area portion or that has started, is performing, or completed work in the working area associated with that pond area portion, and the movement and / or movements of at least some of the other robots are influenced by said temporary and exclusive assignment through said central management and control system.

[0018] Of course, if there are lateral (side) pound areas FL, FL' extending on both sides of the main field CP along the direction of the work row, the method of the present invention can also be applied to portions or zones of the lateral (side) pound areas FL, FL'. Each portion of these lateral (side) pound areas FL, FL' is treated as a pound area portion PF.

[0019] That is, by exclusively allocating portions of a pond area to specific agricultural robots at specific times through a central management and control system, the present invention facilitates the management of a fleet of robots operating simultaneously in the same area, and in particular greatly facilitates the handling of potential collisions and limits crossings between the robots. Furthermore, each robot does not need to know the location of the other robots, and in particular does not need to communicate with each other.

[0020] In general, it is within the scope of the present invention to give a portion of a pound area (or at least a part of that portion) to a specific robot that needs it, temporarily and exclusively, at least while that robot is present there. The method of exclusive allocation, with access prohibited to other robots, of the present invention is preferably performed with at least some foresight (before a robot actually accesses the portion reserved for that robot) and by applying various rules (prioritization, chronological order, corresponding to the type of robot...) depending on the user's selection.

[0021] In a first simple example, the method of the present invention allows a portion or part of a pound area (PF1, PF1'; PF2, PF2'; ..; PFj, PFj') to be given temporarily and exclusively to the robot (R1, R2, ... Ri) that first enters or is about to enter that portion or part of the pound area.

[0022] In a second variant, portions or parts of specific pound areas (PF1, PF1'; PF2, PF2'; ..; PFj, PFj') are given to specific robots (R1, R2, ... Ri) according to predetermined logical prioritization rules applied by a common central management and control system (MS). In the case of agricultural robots of different sizes, priority can be given to larger robots.

[0023] Of course, two portions of two pond areas PF and PF' located at both end edges EB and EB' of the same working area Z can also be temporarily and exclusively assigned to two different robots (for example, a robot that makes a U-turn at the first portion and returns to working area Z, and another robot that moves between the two zones to the other portion).

[0024] According to the characteristics of the invention, the method involves exclusively allocating portions of the pond area (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') to specific robots (R1, R2, ..., Ri), followed by the coordination and control (pilotage) of the operations and movements of the other robots operating in that section (P) by the common central management and control system (SC), applying, if necessary, pre-programmed allocation rules at the level of the CS. This control of the other robots can, for example, consist in updating a temporary no-go zone of access for other robots likely to pass through the exclusively allocated portion.

[0025] The width of the pond area (F, F') depends on the width of the associated working area, its depth (the longitudinal dimension of the associated working band) and the width of the lateral pond area portions (FL, FL').

[0026] In particular, if a portion of the pond area PF is sufficiently deep, the portion of the pond area surrounding the portion (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') temporarily and exclusively assigned to a particular robot (R1, R2, ..., Ri) can be associated only with the band portion (BF) of the portion of the pond area immediately adjacent to the edge (EB, EB') of the associated work area. In other words, the complementary band portion of BF (the complementary portion of BF to PFj) can be free to move and access (and vice versa—BF free to move). In another variant, as shown in Figure 7, a portion of the pond area (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') can be temporarily and exclusively assigned to a portion (RF) located within that portion, such as a waiting area, parking lot, refueling area, or maintenance area for a particular robot (R1).

[0027] Due to the features of the present invention, the temporary and exclusive allocation of portions (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') of the pound area to different robots (R1, R2, ..., Ri) is advantageously carried out gradually according to the progress of the work of the working robots in the working areas (Z1, Z2, ..., Zj) of a given section (P).

[0028] That is, depending on the option chosen, the working areas (Z1, Z2, ..., Zj) can either all be established before the start of work on the relevant section (P) (pre-division of the section), or they can be defined gradually as work on the section (P) progresses. They may (or may not) all have the same width Lz (especially if the robots are identical), except for the end bands or final BT, which may have a smaller width.

[0029] If a partition (P) has a perimeter pound area and includes two end pound area zones (F, F') located at the edges (EB, EB') of the working area (Z1, Z2, ..., Zj) and two lateral pound area zones (FL, FL') connected to the two end pound area zones, then a portion or the entirety of each of the two lateral pound area zones (FL, FL') can be assigned to the robot (R1, R2, ..., Ri) that first enters the corresponding lateral pound area zone.

[0030] According to an advantageous feature of the invention, each working area (Z1, Z2, Zj) can be exclusively assigned to one of the agricultural robots (R1, R2, Ri) at least during a work phase (performed by that robot), and advantageously, the width (Lz) of the working area (Z2, Z1, Zj) is at least equal to the working width (Lr) of the agricultural robot (R1, R2, Ri) to which it is exclusively assigned, preferably an integer multiple thereof.

[0031] In addition, the exclusive allocation of the sections (P) of the working areas (Z1, Z2, Zj) that have not yet been worked to the various agricultural robots (R1, R2, Ri) that are currently working is gradually carried out according to the degree of completion of the work currently being carried out in the various working areas by each of the agricultural robots assigned to them.

[0032] Furthermore, after initially allocating a first dedicated working area to each agricultural robot, at a predetermined point during the work of the plot (P), the allocation of future working areas forming the not-yet-worked portion (PRP) of the plot (P) to each agricultural robot is carried out sequentially during the work of each agricultural robot assigned to it in each working area according to the progress of the work.

[0033] It is advantageous to allocate all working areas (Z1, Z2, Zj) to different agricultural robots (R1, R2, Ri) before or at the start of the work of the section (P), allocating one agricultural robot per zone, and then, during the realization of the work of the section (P), to reallocate the working areas where work remains to be done among the different agricultural robots, intervening at predetermined times depending on the behavior, availability and / or evolution of the state of each robot, as well as the actual or foreseeable future progress of the work at that moment in the working areas of each robot exclusively assigned to it.

[0034] The subdivision of the plot (P) and the exclusive allocation of the working areas (Z1, Z2, Zj) of each agricultural robot (R1, R2, Ri) are advantageously carried out in such a way as to minimize crossing of each robot at the pond area (F) when the working areas are exchanged, when one or more portions of the pond area facing and extending contiguously with one of the two end edges (EB and EB') of the specific working areas (Z2, Z1, ..., Zj) forming the band are temporarily and exclusively allocated to the specific robot (R1, R2, Ri) to which they are temporarily and exclusively assigned, or to a specific robot to which at least one or more portions of the pond area are preferentially reserved.

[0035] As with exclusive work areas, portions of adjacent pound areas do not have to directly contact each other.

[0036] The definition, exclusive allocation and management of tasks in a workspace can be carried out, for example, according to the method described in French patent application no. FR2009696 filed today by the applicant.

[0037] Figure 7 shows a relatively complex example of collision / conflict management. In this example, two robots, R1 and R2, are moving forward for their next (future) move. R1 is leaving the parking area (RF) and heading toward its assigned work area (Z1). R2 is leaving the work area (Z2) where it just completed its task and heading toward the parking area (RF) in a portion of the pond area (PF3), which is continuous with the work area (Z3) where robot R3 has just completed its move. Work area (Z4) will be worked on by robot R4, and robots R3 and R4 are about to turn in portions of the pond area (PF3 and PF4). In this situation and configuration, priority can be given to the robot that moves first. In this illustration, robot R1 moves first, temporarily and exclusively reserving all portions of the pond area (PF1, PF2, and PF4) that it must cross to reach Z1. Therefore, R2 and R4 initially wait in their respective work areas. Since (R1) never passes through the pound area portion (PF3), R3 can make a U-turn. (PF4) is temporarily reserved for (R1)'s passage, and (R4) waits until (R1) passes before making a U-turn. However, in this case, unless logic other than temporal prioritization applies (e.g., robot size or importance, type of task to be performed, etc.), (PF4) will be released before (PF2) before (R1) passes, so it can execute before (R2) arrives at (PF3) at (RF).

[0038] The present invention further relates to an agricultural assembly for automated work on a plot (P), comprising a fleet of at least two autonomously and independently working machines or agricultural robots (R1, R2, ... Ri) equipped with suitable work tools, and a common central management and control system (SC) capable of communicating with said robots, sending and receiving instructions and / or commands, and returning robot operation and / or status information, as shown in Figure 6.

[0039] Each robot is equipped with a positioning device or satellite positioning, and the central management and control system (SC) has means for subdividing the area (P) to be worked on into at least two working areas (Z1, Z2, ..., Zj) before and / or during the start of work on that area (P).

[0040] The working areas together cover substantially the entire surface of the compartment. Each working area (Z1, Z2, ..., Zj) consists of a portion of the compartment having band-like end edges (EB, EB') and a ponding area (F, F') extending along the two adjacent band-like edges (EB or EB'). Optionally, lateral ponding areas (FL, FL') may also be present.

[0041] In the present invention, a common central management and control system (SC) subdivides each pound area region (F, F') into pound area portions (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') that are opposite and contiguous to one of the two end edges (EB and EB') of the band that forms one work zone (Z1, Z2, ..., Zj), and temporarily and exclusively controls at least a part of the pound area portions (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') to be a predetermined pound area portion. The robots (R2, R2, ..., Ri) are capable of assigning to the robots (R2, R2, ..., Ri) that are about to cross or have crossed the portions (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') of said pond area, or that have started, are performing or are going to complete work in the work zones (Z1, Z2, ..., Zj) associated with the portions (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') of said pond area.

[0042] Said assembly preferably implements said method in order to ensure the management of a fleet of robots (R1, R2, Ri) during the operation of a section (P).

[0043] The invention is of course not limited to the illustrations of the attached drawings and the described embodiments, in particular modifications in terms of the construction of the individual elements or substitution of technical equivalents without departing from the field of protection of the invention.

Claims

1. 1. A method for simultaneously working in a plot (P) with autonomous and independent movement by a fleet of at least two agricultural machines or robots (R2, R1, . . . , Ri) according to instructions and / or commands transmitted by a common central management and control system (SC), comprising: The work area (P) to be worked on is subdivided, before the start of work in the work area (P) or gradually during the work, into at least two separate work zones (Z1, Z2, ..., Zj), which together cover substantially the entire usable surface area or useful area (SU) of the work area (P), and each work zone (Z1, Z2, ..., Zj) is made up of a band-shaped fraction of the work area having two opposite edges (EB, EB') at each end, and each of and one pound area (F, F') extending along adjacent edges (EB or EB') at the two opposite edges of the bands (Z1, Z2, ..., Zj), each of said pound areas (F, F') being subdivided into a plurality of pound area portions (PF1, PF1'; PF2, PF2'; ...; PFj, PFj'), each portion facing and contiguous with one of the two opposite edges (EB, EB') of one of the bands forming the working area (Z1, Z2, ..., Zj), temporarily and exclusively assigning at least a fraction of the pound area portions (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') to a robot (R1, R2, ..., Ri) that is crossing or about to cross a given pound area portion (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') or that is about to start, perform, or complete work in a work area (Z1, Z2, ..., Zj) associated with a given pound area portion (PF1, PF1'; PF2, PF2'; ...; PFj, PFj'); The actions and / or movements of at least some of the other robots may be affected by said temporary and exclusive assignment through said central management and control system. A method characterized by:

2. A method as described in claim 1, in which one portion of a pound area or a part of that portion (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') is temporarily and exclusively assigned to one specific robot (R1, R2, ..., Ri) in accordance with predetermined prioritization logic rules applied by the common central management and control system (SC).

3. 3. A method according to claim 1 or 2, in which a portion of a pound area or a part of that portion (PF1, PF1'; PF2, PF2'; . . . ; PFj, PFj') is temporarily and exclusively assigned to a particular robot (R1, R2, ..., Ri) by applying pre-programmed assignment rules at the level of a common central management and control system (SC), after which the operations and movements of other robots operating in that area (P) are coordinated and controlled by the central management and control system (SC).

4. 4. A method according to any one of claims 1 to 3, wherein the temporary and exclusive allocation of a portion of a pound area or a fraction of a portion thereof (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') to a particular robot (R1, R2, ..., Ri) concerns only a band fraction (BF) of a portion of the pound area that is immediately adjacent to the edge (EB, EB') of the working area concerned.

5. A method according to any one of claims 1 to 4, in which the temporary and exclusive allocation of one portion (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') of the pond area to different robots (R2, R1, ..., Ri) is carried out gradually as work progresses in the working area (Z1, Z2, ... Zj) of the partition (P) considered by that robot.

6. 6. A method according to any one of claims 1 to 5, wherein, at least during a work phase, each working area (Z2, Z1, Zj) is temporarily and exclusively assigned to one of the agricultural robots (R2, R1, Ri), the width (Lz) of the majority of the working area (Z1, Z2, Zj) being equal to or greater than the working width (Lr) of the agricultural robot (R1, R2, Ri) exclusively assigned thereto, and during the process of carrying out work in the section (P), the temporary and exclusive assignment of the working areas (Z1, Z2, Zj) in which work still remains to be done to each agricultural robot (R1, R2, Ri) is made gradually according to the degree of completion of the work currently underway in each working area of ​​each exclusively assigned agricultural robot.

7. A method as described in claim 6, wherein the width (Lz) of the majority of the working area (Z1, Z2, Zj) is equal to an integer multiple of the working width (Lr) of the agricultural robot (R1, R2, Ri) exclusively assigned thereto.

8. 8. A method according to claim 6 or 7, characterized in that, before or at the start of work on the section (P), one agricultural robot is assigned to one working area, and each agricultural robot (R1, R2, Ri) is assigned to all working areas (Z1, Z2, Zj), and during the work on the section (P), a reallocation between the agricultural robots in working areas where work remains to be done is intervened depending on changes in behavior, the availability and / or status of each robot, or the actual or foreseeable progress of work in working areas that are still to be worked at a given time by each robot exclusively assigned to them.

9. A method according to any one of claims 1 to 8, wherein the subdivision of the plot (P) and the exclusive allocation of the working areas (Z1, Z2, Zj) to each agricultural robot (R1, R10, Ri) is carried out so as to minimize the crossing of the robots at the pond area (F) when changing the working area, and the exclusive allocation of a predetermined working area (Z2, Z1, Zj) to a specific robot (R2, R1, Ri) is carried out temporarily and exclusively to the specific robot, or is carried out in advance at the time of reservation, in which a portion of the opposing pond area that is contiguous with one of the two end parts (EB, EB') of the band-shaped working area (Z1, Z2, .., Zj) is allocated to the specific robot.

10. The system comprises a group of workers of at least two agricultural machines or robots (R1, R2, . . . Ri) equipped with appropriate working tools, which function autonomously and independently, and a common central management and control system (SC) capable of sending instructions and / or commands to each robot and transmitting and receiving information on the operation and / or status of each robot, each robot being equipped with a positioning device or a satellite positioning device, and the central management and control system (SC) gradually determines the robots to be worked on before and / or during the work in this section (P).

1. An agricultural assembly comprising means for dividing the plot (P) into at least two separate working areas (Z1, Z2, ..., Zj), the working areas together covering substantially the entire plot, each working area (Z1, Z2, ..., Zj) consisting of a band-shaped fraction of the plot having two opposite edges (EB, EB') and a pond area (F, F') extending along the adjacent edges (EB or EB') connected to each of the two opposite ends of the band, The central management and control system (SC) can subdivide each pound area region (F, F') into pound area portions (PF1, PF1'; PF2, PF2'; . . .; PFj, PFj') each located consecutively opposite one of the two edge portions (EB and EB') of the band forming the working area (Z1, Z2, . . ., Zj), and can assign at least one pound area portion (PF1, PF1'; PF2, PF2'; . . .; PFj, PFj') to a predetermined pound area portion. An agricultural assembly characterized in that it further has means for temporarily and exclusively assigning to robots (R1, R2, ..., Ri) that are about to cross or have crossed (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') or to robots (R1, R2, ..., Ri) that have started, are performing or have completed work in a work area (Z1, Z2, ..., Zj) related to portions (PF1, PF1'; PF2, PF2'; ...; PFj, PFj') of a predetermined pound area.

11. Agricultural assembly according to claim 10 for implementing the method according to any one of claims 1 to 9 for managing a team of workers of robots (R1, R2, Ri) during the work of one plot (P).

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