JP4066922B2 - Robot stop location determination method and robot stop location determination apparatus - Google Patents

Description

  The present invention relates to a method for determining a stop position of a robot that can be used when creating a work plan that minimizes the cost of the mobile robot, for example, when a work having a plurality of work places is performed by a mobile robot. The present invention relates to a robot stop position determination device.

In a work where there are a plurality of work points, the position where the mobile robot is stopped (ie, the stop point) has conventionally been appropriately determined by the work plan creator (ie, the worker) according to the experience so far. Also, when a mobile robot is operated at a stop point, the robot arm is empirically taught to the mobile robot.
On the other hand, in recent years, research for obtaining a travel route (including a stop point) of a mobile robot by calculation has been made, and Non-Patent Document 1 is known as an example. In this research, the travel route is calculated by paying attention to the evaluation criteria of the operability of the arm of the mobile robot, and the route plan (work plan) is realized. Although not directly related to the present invention, Patent Documents 1 and 2 are known as technologies in related fields.
Koji Nagatani, Tomonobu Hirayama, Akio Gofuku, Yutaka Tanaka, "Working place planning for mobile manipulators that maintain operability (7th Robotics Symposia Proceedings pp.329-334 (2002-03))" JP-A-5-104465 JP-A-6-337709

  However, in the case of a configuration in which the operator empirically determines the stop position of the mobile robot, there has been a problem that the cost cannot be minimized because optimization has not been performed. In addition, in the research of Non-Patent Document 1, no consideration is given to various cost evaluations, and the work performed while moving the mobile robot is considered, but the mobile robot is placed at a predetermined location. No consideration is given to work that is stopped and executed (that is, work that requires high accuracy).

  Accordingly, an object of the present invention is to determine a robot stop point determination method and a robot stop point determination method capable of obtaining an optimal stop point of a mobile robot by calculation using a cost as an evaluation criterion in a work having a plurality of work points. To provide the equipment.

The robot stop location determination method according to the present invention includes a step of setting a region in the movable work space of the robot arm of the robot as a work determination region for a plurality of operations, and disposing grid points at set intervals in each work determination region. Determining whether or not work by the robot can be performed at each grid point and setting workable areas corresponding to the plurality of work, and overlapping of the plurality of workable areas is optimal. The overlapping of the plurality of workable areas so that all work can be performed in a minimum number of workable areas by solving as a collective covering problem, and the plurality of workable areas in the region where the overlapping overlap of the work area in combination so that optimal, seek working position the work completion time is the minimum cost The Rukoto, in which a step of determining the minimum stop position. According to this stop location determination method, the stop location of the robot is optimized in the work where there are a plurality of work locations.

Further, in the case of the above-described method, the method includes the step of optimizing the work order of the robot arm of the robot at each stop position so that the work can be performed in the shortest time by solving the stacker / crane problem. preferable. Further, by calculating the travel route of the traveling carriage of the robot between the respective stopping points by the Dijkstra method of graph search, the work execution time at each stopping point is minimized, and the travel distance of the traveling carriage is reduced. It is even more preferred to have the step of determining to be minimal .
On the other hand, the robot stop location determination apparatus of the present invention uses a region in the movable work space of the robot arm of the robot as a work determination region for a plurality of operations, and arranges grid points at set intervals in each work determination region Means for determining whether the work by the robot can be performed at each grid point and setting workable areas corresponding to the plurality of work, and overlapping of the plurality of workable areas. so as to optimize, i.e., by solving a set covering problem, it means for combining overlapping of the plurality of work area so as to be able to perform all operations in the minimum number of work area, the plurality of work in the region where the overlapping overlap of the work area in combination so that optimal region, this determining the working position of the work completion time is the minimum cost Accordingly, it has the characteristics to a location that includes a means for determining the minimum stop position.

In the case of this configuration, it is preferable to provide means for optimizing the work order of the robot arm of the robot at each stop so that the work can be performed in the shortest time by solving the stacker / crane problem . In addition, by calculating the travel route of the traveling carriage of the robot between the stop points by the Dijkstra method of graph search, the work execution time at each stop point is minimized, and the travel distance of the traveling carriage is reduced. It is an even more preferable configuration to include a means for determining to be the minimum .

Hereinafter, an embodiment in which the present invention is applied to a “method for planning an optimal operation of a mobile robot (mobile manipulator) that performs a plurality of tasks” will be described with reference to the drawings. First, FIG. 2 is a block diagram showing an electrical configuration of the mobile robot 1 used in this embodiment.
As shown in FIG. 2, the mobile robot 1 includes a robot controller 2, a robot arm 3, a traveling carriage 4, and a power supply system 5. The mobile robot 1 is a well-known mobile robot (for example, a special robot). The mobile robot described in application 2000-262876 may be used). The robot controller 2 includes a memory 6, a CPU 7, and a control driver 8.

  The robot controller 2 is configured to control the robot arm 3 and the traveling carriage 4 based on teaching data given from the teaching pendant 9 or teaching data given from a personal computer (PC) 10. The teaching pendant 9 is detachably connected to the robot controller 2 via a cable. The PC 10 is detachably connected to the robot controller 2 via a cable, or is connected via a wireless LAN.

The PC 10 is a computer that actually calculates the “optimum motion planning method for the mobile robot 1 that performs a plurality of tasks” according to this embodiment, and includes a simulation program for executing the calculation. In this case, the PC 10 is an offline simulator. And PC10 comprises the stop location determination apparatus of a mobile robot.
Further, the PC 10 functions as a means for disposing a region in the movable work space of the robot arm 3 of the mobile robot 1 as a work determination region for a plurality of operations and arranging grid points at set intervals in each work determination region. A function as means for determining whether or not work by the mobile robot 1 can be performed at each grid point and setting workable areas corresponding to the plurality of work, and the plurality of workable areas And a function as a means for determining the minimum stop position by obtaining a work position with the lowest cost in the overlapping area of the combined workable areas. A function as means for optimizing the work sequence of the robot arm 3 of the mobile robot 1 at each stop point; The travel path between, and a function as a means for determining such cost is minimized.

Next, a system (that is, a simulation program) of the “optimum operation planning method of the mobile robot 1 that performs a plurality of tasks” according to the present embodiment will be specifically described with reference to FIGS. 1 and 3 to 9 as well.
First, the setting conditions of the system of this embodiment will be described.
Here, “operation” means that a plurality of objects scattered in the work environment are held and transported by the manipulator (robot arm 3) of the mobile robot 1.

“Work information” is a set of an initial configuration and a target configuration of the hand of the manipulator (robot arm 3) when performing the work.
In addition, it is assumed that environmental information such as obstacle arrangement is known. Work can be performed in any order. The input value of the system is work information for each work. The output of the system is a plurality of work points, a work order at each work point, and a movement route (travel route) between the work points.

The traveling carriage 4 has nonholonomic characteristics that can travel only in a specific direction at a certain position and orientation.
Also, due to stability and accuracy problems, the work while moving is not performed. It is assumed that the traveling distance and the number of movements of the traveling carriage 4 are better. This is because not only the traveling time but also time correction is required for the position of the traveling carriage 4 after movement, and errors are likely to occur due to positioning.

In the present embodiment, the problems to be solved by the system are divided into the following three.
The first problem is how to allocate a plurality of tasks to a plurality of work locations, that is, an allocation problem.
The second problem is a traveling problem in which order a plurality of operations are performed and in which order a plurality of work points are to be visited.

The third problem is an operation planning problem of how to generate a trajectory from the initial configuration to the target configuration of the robot arm 3 (manipulator) hand and the traveling carriage 4.
In order to solve these problems, the highest-priority evaluation index in this embodiment is “minimizing the number of movements of the traveling carriage 4, that is, minimizing the number of work points”. Then, after satisfying this evaluation index, “Which is the best combination of the minimum number of work points that can be obtained? The problem “whether it should be performed” is integrated to derive an optimal solution.

  Hereinafter, the work flow of the system of this embodiment will be described in detail with reference to the flowchart of FIG. First, in step S1, grid points are arranged in the work determination area. Here, the work determination area is an area (three-dimensional space) in the movable work space of the robot arm 3 of the mobile robot 1 and may be called a determination target area. The process for arranging grid points in this work determination area will be described below.

  As shown in FIG. 7A, it is assumed that there are six works, for example, and work information is given to each. In the figure, although it is expressed by a two-dimensional plane, it is actually a three-dimensional position and orientation. For simplicity, the work information is represented by two circles and an arrow connecting them. This means that the robot arm 3 hand moves from the first circle (initial configuration) to the circle at the tip of the arrow (target configuration).

  In this case, if the determination as to whether or not the six tasks T1 to T6 shown in FIG. 7A can be performed is performed over the entire work environment, the amount of calculation becomes enormous. An area within a certain distance R and also within the certain distance R from the target configuration is extracted as a determination target area (work determination area). For example, the hatched area shown in FIG. 7B is the determination target area of T1. The distance R may be determined as appropriate based on the distance that the arm of the robot arm 3 reaches to the maximum extent. Then, grid points at set intervals are arranged in the determination target area (work determination area) (see FIG. 7C).

  Next, the process proceeds to step S2, and it is determined whether or not the robot arm 3 can perform the work when the traveling vehicle 4 takes a configuration corresponding to each grid point arranged in the determination target region. The determination condition at this time is whether the initial or target configuration of the hand can be achieved (first condition), whether the hand trajectory that achieves the work without interfering with the obstacle can be realized (second condition), or has the hand There are three conditions, i.e., whether the operability can exceed a certain value (third condition).

  In this case, the third condition is to prevent the work from being unattainable due to the position and orientation error of the traveling carriage 4 or the position and orientation error of the work target. The second condition is determined by solving an operation planning problem for the robot arm 3. Furthermore, regarding the operability of the third condition, here, among the lattice points satisfying the first condition and the second condition, only those in which all six neighbors satisfy the condition for (x, y, θ) are satisfied. Deal with it by selecting.

  Specifically, the subroutine shown in the flowchart of FIG. 3 is executed. First, in step S201, the first condition (whether the initial / target configuration of the hand can be achieved) is examined for the first grid point. If the first condition is satisfied, the process proceeds to “YES”, and the second condition (whether a hand trajectory for achieving the work is realizable) is examined (step S202). If the second condition is satisfied, the process proceeds to “YES”, and the third condition (whether the hand can have maneuverability of a certain value or more) is examined (step S203). If the third condition is satisfied, the lattice point is set as a workable point (step S204).

On the other hand, in the above steps S201, S202, and S203, if each condition is not satisfied, the process proceeds to “NO”, and the lattice point is set as an unworkable point (step S205).
Then, the process proceeds to step S206, and it is determined whether or not the determination as to whether or not the work is possible has been completed for all grid points in each work determination area (determination target area). Here, when the determination is completed, the process proceeds to “YES”, and the determination process ends. If the determination is incomplete, the process proceeds to “NO”, returns to step S201, and continues to determine the next grid point.

  Thereby, a determination result as to which work can be performed at each grid point is obtained. Based on the determination result, by gathering the grid points where the same work can be performed, information indicating in which area each work T1 to T6 can be performed, that is, workable areas (work location areas) A1 to A6 is obtained. (Refer FIG.7 (d)). In this case, the workable area is an area (three-dimensional space) including a work place where the work can be performed regardless of the position and orientation of the traveling carriage 4 of the mobile robot 1. You may call it.

  Next, the process proceeds to step S3 in FIG. 1, and the smallest workable area capable of performing all work is determined. Specifically, a subroutine shown in the flowchart of FIG. 4 is executed. First, the process proceeds to step S301, and an overlapping area is redefined in the workable area. In this case, since the workable areas A1 to A6 obtained as described above overlap (there are overlapping portions) as shown in FIG. 8, each overlapping area is defined as A7 to A12. When each area has a work that can be performed as an element, the area is redefined as including an area in which an arbitrary element is added to the element. For example, it is assumed that the workable area A1 includes A7, A8, and A9, and A7 includes A9.

  In the case of the example shown in FIG. 8, twelve areas are configured. In general, when the number of operations is n, the number of areas is maximum.

である。
次に、図４のステップＳ３０２へ進み、それらの領域の中からどれを選択すれば、最少数の領域で全作業を遂行することができるかを調べる。この問題は、集合被服問題（Set Covering Problem）として解く。

It is.
Next, the process proceeds to step S302 in FIG. 4, and it is checked which one of these areas can be selected to perform all the operations in the minimum number of areas. This problem is solved as a Set Covering Problem.

Here, the set clothing problem is a problem of covering the rows of the 0-1 matrix a _ij having m rows and n columns, each of which is given a cost, with a minimum cost by combining a subset of the columns.
x _j = 1: When column j (cost c _j > 0) is in the solution,
x _j = 0: When defined as other than that, the set clothing problem is expressed as follows.

そこで、行を作業番号、列を各作業可能領域の番号とすれば、上記ステップＳ３０２の問題は、作業可能領域の組合せによって全作業を被覆する問題となり、集合被服問題の一種と捉えられる。ただし、以下の特徴を有する。

Therefore, if the row is the work number and the column is the number of each workable area, the problem of step S302 becomes a problem that covers all work by the combination of workable areas, and is regarded as a kind of collective clothing problem. However, it has the following characteristics.

-Cost is non-existent (or) uniform and minimizes the subset required for coverage, not cost.
・ It is necessary to list solutions.
In this embodiment, this problem is called a “Least Set Covering Problem”.

Now, the matrix a _ij generated from the area configured in FIG. 8 is shown in the following equation (1). For ease of viewing, only one element is shown.

この問題を集合被服問題として解いた場合、以下の３つの解が得られる。

When this problem is solved as a collective clothing problem, the following three solutions are obtained.

ここで、３つ目の解に着目する。この領域の組合せでは、Ａ９，Ａ１１のどちらでも作業Ｔ４を遂行可能である。Ｔ４をＡ９で遂行する場合は、Ａ１１ではＴ３のみを遂行することになる。このとき、Ａ３がＡ１１を含んでいるため、この解は１つ目の解に吸収される。逆に、Ｔ４をＡ１１で遂行する場合は、この解は２つ目の解に吸収される。つまり、解は２つに集約されることになる。よって、本問題において得られるべき解は、１つ目と２つ目のみである。

Here, pay attention to the third solution. In this combination of areas, the operation T4 can be performed by either A9 or A11. When T4 is performed at A9, only T3 is performed at A11. At this time, since A3 includes A11, this solution is absorbed by the first solution. Conversely, when T4 is performed at A11, this solution is absorbed by the second solution. That is, the solutions are aggregated into two. Therefore, only the first and second solutions should be obtained in this problem.

This results in the least set-clothing problem as a Set Partitioning Problem. A set partitioning problem is one in which the inequality sign ≧ of the constraint condition of the set clothing problem becomes equal sign =, and each row is covered by only one subset of solutions. By treating it as a set partitioning problem, the number of combinations of workable areas is reduced and the amount of calculation is reduced.
This feature is caused by the region configuration method redefined in step S301. If this redefinition is not performed, A1 is defined as a region from which A7 to A8 have been removed, that is, a region where only operation T1 can be performed, and A7 is similarly defined as a region from which A9 has been removed, that is, operation T1. And T5 can only be performed, and A4 cannot be performed. The third solution cannot be absorbed by other solutions, and work such as T4 that is included in the solution region overlaps. It gives rise to the problem of which to carry out. Therefore, the redefinition in step S301 is effective.

The set partitioning problem is generally an NP-difficult problem, and various approximate solution derivation methods have been proposed. On the other hand, since this problem is small in scale and has the above-described features, it is possible to derive an optimal solution within a realistic time by a simple branch-and-bound operation described below.
(1) A column having the maximum number of covered rows is used as a parent. Adopt parents as part of the solution.
(2) Delete the line covered by the parent. This is because the rows covered by the parent no longer need to be covered.

(3) If a column covering the same row as the parent is adopted, set partitioning is not performed.
(4) Repeat the above operation until all lines are covered.
(5) Delete the parent row, select a new parent, and repeat the operation. The solution is one that can be coated with the same number of columns required for the coating already obtained. Since the number of covering rows of the parent becomes smaller, it is possible to determine whether or not covering with the minimum number of columns is possible. End when you can't.

As a result, a set of a minimum number of workable areas can be obtained (see step S303 in FIG. 4).
Next, the process proceeds to step S4 in FIG. 1, and the work order of the robot arm 3 that can be executed in the shortest time on each grid point in each region is determined, and the work execution time is calculated. Specifically, when the traveling cart 4 takes the configuration of each grid point in each area, the work can be performed in the shortest time by achieving the hand configuration given as multiple work information in any order. This is derived by solving the Stacker Crane Problem. In this case, the cost is the work execution time. The total cost in the order of the solutions is the cost required to realize all the work to be performed in that area.

In step S5, a graph connecting the lattice points in the region is generated, and a set of lattice points having the minimum cost (that is, the shortest work execution time) is determined. In this case, first, the order of going around the work locations is listed. From the two solutions obtained in step S3, the order of going around the work location is:
A3-A9-A12, A3-A12-A9, A9-A3-A12,
A7-A11-A12, A7-A12-A11, A11-A7-A12
There are six types. In general, if there are m solutions for n locations, m * n! / There are two permutation types.

  Then, the regions are connected in the order obtained as described above. At that time, each lattice point in the region is connected to each lattice point in the next region. Thereby, a graph with each grid point as a node is constructed (see FIG. 9). As many graphs as the number of permutations are generated, only two graphs are shown in FIG. 4A shows the case of A9-A3-A12, and FIG. 4B shows the case of A7-A11-A12. Further, the number of grid points in each region is set to 3 for easy viewing.

  Next, a combination of lattice points is determined, which is executed according to a subroutine of the flowchart shown in FIG. First, in step S501, one grid point is selected in each work area. Then, the process proceeds to step S502, and for each set of workable areas, an arc connecting the selected grid points in the other areas is created. In step S503, a closed loop arc is generated at each lattice point.

  In step S504, the cost is assigned to all arcs. In this case, the work execution cost (the work execution time at the lattice point, that is, the total cost obtained as described above) is assigned to the closed-loop arc (see type-1 in FIG. 9). Further, the travel cost of the traveling cart 4 (the travel distance (route length) required for the traveling cart 4 to move) is assigned to the arc between the grid points (see type-2 in FIG. 9).

Here, as a method for deriving the path, for example, a known document (T. Kito, J. Ota, R. Katsuki, T. Mizuta, T. Arai, T. Ueyama, T. Nishiyama: Smooth Path Planning by Using Visibility Graph-like Methode, Proc. Of IEEE Int. Conf. On Robotics and Automation, to appear, (2003))
May be used.

  Then, the process proceeds to step S505, and the arc of the minimum cost, that is, the cost minimum solution of the constructed graph is calculated by, for example, the Dijkstra method of the graph search while considering the traveling order of the traveling carriage 4. Thereby, the combination of the optimal work location, the work sequence at the work location, and the movement route connecting the work locations is derived. In this case, when there are a plurality of graphs, the minimum costs are compared, and the one with the lowest cost is determined as the final solution.

  Subsequently, the process proceeds to step S6 in FIG. 1, and the solution derived by the above-described calculation, that is, the minimum stop location (optimal work location), the work sequence at each stop location (work location), and each stop location (work location). ) Between the travel routes (movement routes). These output data are given from the PC 10 to the robot controller 2 of the mobile robot 1. The robot controller 2 is configured to control the robot arm 3 and the traveling carriage 4 based on the given data.

Next, control (subroutine) for reducing the amount of calculation for determining the combination of lattice points (steps S501 to S505) described above will be described with reference to the flowchart shown in FIG. First, conditions for reducing the amount of calculation will be described. As described above, as many search graphs as the number of permutations are generated.
Therefore, in order to reduce the calculation amount, a condition that “workable areas (work location areas) are sufficiently separated from each other” is assumed. “Sufficiently separated” means “the degree to which the traveling cart 4 selects any position and orientation in each region is not affected by the difference in work execution time and movement time, and the order in which the work points are connected”. It is. This assumption makes it possible to determine the work site circulation order first.

  Specifically, in step S601 in FIG. 6, one representative grid point is calculated in each work area. For example, the lattice point near the center of gravity in the work area is set as the representative lattice point (in this case, the stop point of the traveling carriage 4 is set as the representative lattice point, so the solution is a semi-optimal solution). Subsequently, the process proceeds to step S602, where for each set of workable areas, the representative grid points are connected by arcs, the arc straight line length is assigned as a cost, and this is solved as a traveling sales problem (Traveling Salesman Problem). A traveling order that minimizes the moving cost of the carriage 4 is calculated. In this case, only two search graphs need be generated from each solution, in the above-described example. As a solution for the traveling sales problem, a known solution may be used as appropriate.

Then, the process proceeds to step S603, and the circulation order is determined for each set of work areas. Subsequently, the process proceeds to step S604, and a set of work areas that is the minimum cost among the set of work areas is calculated. Note that many of the above assumptions are valid in an actual factory environment, and therefore, it is an effective calculation amount reduction technique.
In the present embodiment having such a configuration, for a plurality of operations, the area in the movable work space of the robot arm 3 of the mobile robot 1 is set as a work determination area, and lattice points at set intervals are set in each work determination area. A placement step (see step S1 in FIG. 1), and it is determined whether or not the work by the mobile robot 1 can be performed at each lattice point, and workable areas corresponding to the plurality of work are set. A step (see step S2 in FIG. 1), a step (see step S3 in FIG. 1) for combining the plurality of workable regions so that the overlap is optimal, and in the region where the combined workable regions overlap And determining the minimum stop point by obtaining the work point with the minimum work cost (see steps S4 and S5 in FIG. 1). Sea urchin was constructed.

  According to this stop location determination method, when the mobile robot 1 performs a task having a plurality of work locations, the worker simply optimizes the cost as an evaluation criterion by giving the work information of each task to the PC 10. Further, the minimum stop point of the mobile robot 1 can be obtained from the PC 10. Accordingly, the cost (that is, the work execution time) can be reduced as compared with the case where the worker determines the stop position of the mobile robot empirically.

Moreover, in the said Example, it comprised so that the step (refer step S4 of FIG. 1) of optimizing the work order of the robot arm 3 of the mobile robot 1 in each stop location of the mobile robot 1 might be provided. According to this configuration, since the work order of the robot arm 3 can be optimized, the cost (that is, the work execution time) can be further reduced.
Furthermore, in the said Example, it comprised so that the travel route (movement route) between each stop location of the mobile robot 1 might be provided with the step (refer step S5 of FIG. 1) which determines so that cost may become the minimum. According to this configuration, since the travel route (movement route) of the mobile robot 1 is the route with the minimum cost, the cost (that is, the work execution time) can be further reduced.

  In the above embodiment, the present invention is applied to a system for determining the stop position of the mobile robot 1, but the present invention is not limited to this, and the present invention is applied to a system for determining the base position of a fixed robot. You may comprise so that it may apply (that is, it applies as an optimization method of a base position).

Flowchart of a work flow showing an embodiment of the present invention Mobile robot block diagram Flowchart of a subroutine for determining whether or not work can be performed at grid points Subroutine flowchart for determining the combination of workable areas Subroutine flowchart for determining the combination of grid points Flowchart of another subroutine (reducing the amount of calculation) that determines the combination of grid points (A) is a diagram showing a plurality of tasks, (b) is a diagram showing a task determination area, (c) is a diagram showing a state where grid points are arranged in the task determination area, and (d) is a diagram showing a work possible area. Diagram showing overlap of workable areas Diagram showing search graph structure

Explanation of symbols

In the drawings, reference numeral 1 denotes a mobile robot, 2 denotes a robot controller, 3 denotes a robot arm, 4 denotes a traveling carriage, 7 denotes a CPU, 9 denotes a teaching pendant, and 10 denotes a PC (a stop point determination device for a mobile robot).

Claims (6)

For a plurality of tasks, a region in the movable work space of the robot arm of the robot is set as a task determination region, and a grid point at a set interval is arranged in each task determination region;
Setting a working area corresponding the to the plurality of working operations by pre-km bots determines whether or not it is possible to carry out at each grid point,
The overlap of the plurality of workable areas so that the overlap of the plurality of workable areas is optimal, that is, by solving as a collective covering problem, all work can be performed in the minimum number of workable areas. comprising the steps of: combining,
Determining a minimum stop location by obtaining a work location that minimizes the work execution time, which is a cost , in an overlapping region of the work enable regions combined so that the overlap of the plurality of work enable regions is optimal; and A method for determining a stop point of a robot. 2. The method according to claim 1, further comprising: a step of optimizing a work order of the robot arm of the robot at each stop so that the work can be performed in the shortest time by solving a stacker / crane problem. The robot stop location determination method described. By calculating the travel route of the traveling carriage of the robot between the stop points by the Dijkstra method of graph search, the work execution time at each stop point is minimized, and the travel distance of the carriage is minimized. The robot stop position determining method according to claim 1, further comprising a step of determining so as to be . With respect to a plurality of tasks, a region in the movable work space of the robot arm of the robot is set as a task determination region, and means for arranging lattice points at set intervals in each task determination region;
Means for determining whether or not work by the robot can be performed at each lattice point and setting workable areas corresponding to the plurality of work;
The overlap of the plurality of workable areas so that the overlap of the plurality of workable areas is optimal, that is, by solving as a collective covering problem, all work can be performed in the minimum number of workable areas. A means of combining
Means for determining a minimum stop point by obtaining a work point that minimizes a work execution time, which is a cost , in an overlapping region of the workable regions combined so that the overlap of the plurality of workable regions is optimal ; An apparatus for determining a stop position of a robot. 5. The apparatus according to claim 4, further comprising means for optimizing the work order of the robot arm of the robot at each stop so that the work can be performed in the shortest time by solving a stacker / crane problem. The stop position determination apparatus of the described robot. By calculating the travel route of the traveling carriage of the robot between the stop points by the Dijkstra method of graph search, the work execution time at each stop point is minimized, and the travel distance of the carriage is minimized. 6. The stop position determining apparatus for a robot according to claim 4, further comprising means for determining to be

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