JPH1039909A - Work scheduling method for plural robots - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce labor required for work scheduling by automating work scheduling for plural robots. SOLUTION: For spot welding by means of plural robots, welding spot information expressed by the respective shaft values of robots is inputted from robot emulator data 41 and according to previously set limitation conditions, the grouping of welding spots is performed (a2). It is previously discriminated whether or not interference is to generate between the groups and the result is outputted as group data 43. For solutions such as the distribution of groups to the respective robots, the operating order of groups for respective robots and the bonding in the welding order of respective welding spots in the groups, initial values are generated while using the approximate solution method of the traveling sales-man problem (a3). Concerning the solution, an optimizing method based on an SA parameter 45 is applied and while evaluating cycle time considering the interference, the solution is improved (a4).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a work planning method for a plurality of industrial robots, which can easily determine a work sequence for efficiently performing a work on a work using a plurality of industrial robots. About.

[0002]

2. Description of the Related Art Conventionally, various works in factories and the like,
For example, spot welding, handling such as assembly,
Industrial robots are used for painting and cutting. In a spot welding line at an automobile factory or the like, a plurality of robots are arranged in one process in order to improve production capacity, and the robots often work simultaneously within an overlapping operation range. In such a case, the positions at which the operating robots work at the same time overlap, and it is necessary to consider the interference between the robots that causes a collision between the arm and the tool. When interference occurs between the robots, the lower priority robots wait for interference avoidance according to a predetermined priority order, and the cycle time required for the robot operation becomes longer. If there is a large difference in the cycle time between multiple robots,
The work time required for the process is determined according to the robot having the longest cycle time, and the robot having the short cycle time has play. Determining the work order of each robot while satisfying specifications such as the number of robots, cycle time, required number of works, and work space is complicated and requires a great deal of labor. For this reason, the work order is often determined based on experience specific to a skilled person, and it is not easy to revise the work order in response to changes in line specifications or products.

Japanese Patent Application Laid-Open No. 2-273807 discloses a method of creating teaching data for a plurality of robots, in which each work area of a plurality of robots is divided into predetermined small areas, a simulation is performed for each work order, and the robots interfere with each other. Prior art for selecting a work order not to be performed is disclosed. In this prior art, a simulation is performed for each work order while changing the work order of the small regions based on work position data of each small region and shape data and motion performance data of each robot. Teaching data can be obtained by selecting a work order in which the robots do not interfere with each other from the work situation data of each robot obtained from the simulation.

[0004]

When performing a work plan for a plurality of robots, a method may be considered in which all combinations of each robot and each work are calculated, and a combination having a short cycle time and causing no interference is selected. . For example, if the number of robots is r, the number of works is n, the movement time from work j to work k is Cjk, and the work time of work j is Wj, the work plan optimization problem is formulated as the following equation 1. can do.

[0005]

(Equation 1)

Here, Xijk is a variable that takes a value of 0 or 1, and has the relationship of the following equations (2) and (3).

[0007]

(Equation 2)

At this time, the total number of combinations in the work plan is expressed by the following formula (4).

[0009]

(Equation 3)

Assuming that three standard robots and 90 welding points are used as an additional punching process of the spot welding line, the number of combinations is calculated by the following equation (4).
¹⁴² , which is a huge number of combinations that cannot be calculated. Furthermore, it is impossible to actually obtain a solution because the robot's interference must be considered.

In the prior art of Japanese Patent Application Laid-Open No. 2-273807,
Group your work into smaller areas, reduce the solution search range,
Although efficient search can be achieved, grouping is performed by skilled workers based on shape data such as work and experience, and all combinations of divided small areas are checked to select work orders that do not interfere Therefore, the number of small areas is 5
Degree is the limit. In addition, since the purpose is to select a work order that does not cause interference, it is not suitable for a work plan in which interference frequently occurs. In order to reduce the frequency of occurrence of interference, it is necessary to reduce the degree of overlap of the work areas of the robot, and it becomes difficult to improve the production efficiency by arranging the robots densely. Further, since the simulation is performed for each combination of all the divided small areas and the robot, the time required for the work planning becomes long.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a work planning method for a plurality of robots, which can make a work plan for grouping works automatically and within a realistic time.

[0013]

According to the present invention, in a work planning method for a plurality of robots arranged so that at least a part of a work area overlaps, a plurality of works to be performed by the plurality of robots are determined in advance. A grouping step of dividing the group into a number equal to or greater than the number of robots based on constraints, and whether a possible combination of the group and the robot interferes with the operation of the robot between other combinations. An interference investigation step of conducting an investigation to judge according to a predetermined criterion, the allocation of groups to each robot, the order of work of the group allocated to each robot, the direction in which the work in each group is performed, and the An initial feasible solution routine that determines an initial feasible solution according to a predetermined method as a solution indicating a priority of performing work preferentially when interference occurs And a solution change step of changing the contents of the solution by changing the distribution of groups to each robot, a work order between groups, a direction in each group, and a priority of the robot, and an initial possible solution determination step. For the solution determined in the above or the solution changed in the solution change stage, an evaluation value is calculated according to the criteria determined in advance for the robot's work, including work required for avoidance when interference occurs, according to the result of the interference research stage A value calculation step;
The evaluation value is calculated in the evaluation value calculation step for the initial feasible solution determined in the initial feasible solution determination step, and the solution change in the solution change step and the evaluation of the solution in the evaluation value calculation step are performed according to a predetermined optimization method. And a step of repeatedly searching for a solution having the best evaluation value. According to the present invention, a plurality of tasks to be performed by a plurality of robots in the group stage are divided into groups of a number equal to or larger than the number of robots based on predetermined constraint conditions. The solution indicating the work order of the group, the direction of the work in the group, and the priority of performing the work in a case where interference occurs between the robots, based on the initial feasible solution set in the initial feasible solution setting stage. In the best solution search stage, the best solution is searched, and a work plan that minimizes the evaluation value of the time required for the work can be performed. Since the work is grouped, the search range of the solution can be reduced, and the search can be made more efficient. In the evaluation value calculation stage for evaluating the solution, evaluation is performed in consideration of interference between groups,
In the best solution search stage, it is not necessary to verify the presence or absence of the interference by the simulator, and it is possible to reduce the work time required for the work planning.

In the best solution search step of the present invention, a solution in which only an evaluation value inferior to the evaluation value already obtained in the evaluation value determination step is obtained is determined in advance so as to be adopted with a certain probability. It is characterized by using an optimization technique. According to the present invention, in the best solution search stage, for example, a simulated annealing method or the like is used as a predetermined optimization method, a solution having an evaluation value that is not always good is adopted with a certain probability, and the search for a solution becomes a local solution. Falling can be prevented.

Further, in the initial feasible solution determination step of the present invention, a predetermined approximate solution of the traveling salesman problem is used. According to the present invention, an initial feasible solution in which the best solution is easily obtained can be obtained in the initial feasible solution determination stage by using a predetermined approximate solution of the traveling salesman problem such as the nearest neighbor method.

In addition, according to the present invention, it is determined whether or not it is necessary to add a work position for avoiding interference to each group divided in the grouping step. The work position is added as an avoidance point, and if avoidance is possible at the work points at both ends of an existing group even if avoidance is required, the work positions at both ends are set as avoidance points. According to the present invention, when interference avoidance is required for each group, avoidance points are set at both ends of each group, so that evaluation when interference occurs can be easily performed.

Further, in the present invention, in the initial possibility solution determination step, a work time having an initial value of 0 is set for each robot, and the movement time from the initial position of each robot to the avoidance point of the group is determined by the robot. Calculate from the athletic performance data of, and distribute the group with the shortest travel time to each robot,
Allocate all the groups to the robot by repeating the selection of the group that adds the working time in the group and the calculated travel time to the robot's working time, and the selection of the robot that sequentially selects the group for the robot with the shortest working time It is characterized by doing. According to the present invention, in the initial possible solution determination stage, a work time with an initial value of 0 is set for each robot, and selection of a group for each robot and selection of a robot with a small time and time are repeatedly performed. ,
It is possible to determine an initial feasible solution in which the deviation of the working time between the robots is small.

Further, in the grouping step of the present invention, a work dividing step of dividing the work into groups according to the movable range of each robot and the type of work tool, and inputting space information about the work and the jig and tool to be used. In the information input step, enter whether or not the tool or tool interferes with the work or tool while the tool moves between the work positions in a predetermined order in each group divided in the work division step. The method is characterized in that it includes a group dividing step of dividing a group in work before and after passing when it is determined according to the spatial information to be performed and when it interferes with a work or a tool. According to the invention, in the grouping stage,
In the work division stage, the work is divided into groups according to the robot's movable range and the type of work tool, and the movement of the tool between work positions in the group interferes with the work or jig according to the spatial information input in the information input stage When it is determined that the group is divided, the group in which interference does not occur when moving between the work positions in the group can be easily determined.

The present invention also provides a method of grouping based on the angle difference between the tool direction vectors at the robot tip and the grouping based on the angle difference between the tool insertion direction vectors for the groups divided by the work dividing step. ,
For work included in the group, an order determination using an approximation algorithm of traveling route generation and grouping based on a moving distance between work positions are performed as processing. According to the present invention, the groups divided in the grouping stage include the difference in the angle between the tool direction vectors at the robot tip, the difference in the angle between the tool insertion direction vectors, and the approximation of the tour degree generation for the work included in the group. Since the grouping is performed according to the order in which the algorithm is used and whether or not the moving distance between the work positions is long, the work in the group can be performed efficiently, and if a solution can be obtained for the group, An efficient work plan can be performed as a whole.

In the information input step of the present invention, B-
It is characterized by inputting spatial information of a work and a tool by rep expression. According to the present invention, since the space information of the work and the jig is input as a list by the B-rep expression, it is possible to easily and efficiently input the three-dimensional space information including the unevenness.

Further, in the present invention, the determination as to whether or not the interference is made is based on the vector from the tool movement start point to each point on the map and the tool movement vector with respect to the mapping of the object onto each coordinate axis plane. Is calculated, and when there is a vector having a different sign of the outer product, it is determined that interference occurs. According to the present invention, the determination as to whether or not interference occurs during the movement of the tool is determined by using a vector from the starting point of the movement of the tool to each point on the mapping with respect to the mapping of the object to each coordinate axis plane. This is done by calculating the cross product of the tool and the movement vector. The mapping with the same sign of the outer product is on one side with respect to the mapping of the moving vector, and the vector with the different sign of the outer product is on the other side with respect to the moving vector. And the object can be determined to cause interference.

[0022]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows an arrangement of a robot and a work to be subjected to an operation planning method for a plurality of robots according to an embodiment of the present invention. The robots 1, 2, and 3 (hereinafter sometimes abbreviated as "R1,""R2," and "R3") have spot welding guns 4, 5, and 6 as tools, respectively. Is controlled. Each of the robots 1, 2, 3 has a plurality of hit points 20 as shown in FIG.
To perform spot welding.

The robots 1, 2, and 3 are, for example, multi-axis industrial robots, and the positions of the tips of the spot welding guns 4, 5, and 6, which are tools, are calculated based on the angles of the respective axes. The position of the hit point 20 is represented in advance as a value of each axis of the robot by a teaching operation, and the robot working posture is obtained as a robot simulator or a manually input file. Robot working range, spot welding guns 4, 5,
Data such as six types are also obtained as files. The result of the work plan performed by the external computer is transferred to the control device 10. In the work plan, work positions considered to be suitable for continuous work are grouped as one group based on a file on the hit points 20 and a file on the robot. By grouping the hit points 20, the solution search range in the work plan can be reduced. The grouping of the dots 20 can be performed by manually editing the file by the operator, but in the present embodiment, the groups are automatically grouped by the following method.

An example in which three spot welding robots 1, 2 and 3 as shown in FIGS. 1 and 2 target 90 hit points 20 in 14 groups will be described. A work position data file is prepared for each robot from the robot simulator. The file contents include x, y, z coordinates for each work position, and each axis value of each robot corresponding to each work position x, y, z. Motion performance data for each robot 1 and 2, welding gun type,
The initial priority of the robot is set in advance and prepared as a work robot data file.

The following Table 1 shows an example of the constraints of the movable range of each robot and the workable gun.

[0026]

[Table 1]

Here, each of the robots 1, 2, 3 is R1, R
2, R3, respectively, and 1 to 14 indicate groups of hit points 20, and each robot gives a logical value "1" to a combination violating the constraint condition for each group. A logical value “0” is given to the combination that satisfies the condition. FIG. 3 shows a state in which the hit points 20 are divided into groups 21, 22 and the like in accordance with the constraint conditions in Table 1 and grouped. Further, when grouping is performed based on the difference between the tool direction and the insertion vector of the spot welding guns 4, 5, and 6, which are the tools at the tip of the robot, the grouping result is as shown in FIG. The group 21 shown in FIG. 3 is divided into groups 31 and 32. The order of spot welding within the group is determined by applying an approximate algorithm for generating a traveling route to the group shown in FIG. According to the determined order within the group, if there is a movement in which the movement distance when performing the movement between the hit points 20 becomes a certain value or more, the group is divided before and after the movement. In this manner, the group 22 in FIGS.
It is divided into four. Next, a B-rep expression of the vehicle body and the jig is input. The group is divided when it interferes with the vehicle body or with the jig / tool due to movement between multiple points. FIG. 6 shows the result after checking the interference with respect to the movement between all the hit points. The avoidance points are set at both ends of each of the groups G1 to G14, and the working posture of the tool at the avoidance points and the working time in the group are determined. And output to a group file.

Next, an inter-group interference determination is performed on candidates satisfying the constraints for the robots 1, 2, and 3 to work on the groups G1 to G14. The results of the determination are shown in Table 2 below.

[0029]

[Table 2]

FIG. 7 shows an overall operation flow of the work planning method for a plurality of robots according to the present embodiment. Step a
The operation is started from 1 and in step a2, the above-described grouping process is performed. In this process, the robot simulator data 41 in which the dot information for each dot 20 is represented as each axis value, the robot performance data including the driving performance data of each robot, the priority, and the initial value represented as each axis value 42 are used. The result of the grouping is output as group data 43 including each axis value of the work time and the start point. Next, in step a3, an initial value is generated. To generate the initial value, the robot data 42 and the group data 4
3 is used. The initial value generation result is output as an initial value result 44 indicating the distribution of the groups to the robots, the order of the tasks in the group, and the connection that is the work direction in the group. Next, at step a4, as a solution improvement, an SA parameter 45 which is a parameter for executing robot data 42, group data 43, simulated annealing (hereinafter abbreviated as "SA") and the like.
And the group data 43 to calculate the cycle time in consideration of the interference, and search for the best solution. The solution improvement result 46 regarding the distribution of the groups to the robots, the work order of the groups, the priorities of the robots, and the combination of the work order in the group, etc., is output as a file, and the operation ends in step a5.

In the initial value generation processing in step a3, as described above, the group data 4
3 and the robot data 42 are read. Each of the robots 1, 2, and 3 is uniquely assigned a number in advance. Here, the work time is determined for each of the robots 1, 2, and 3, and the initial value is set to 0. Robot 1, which has the shortest working time
When the working time is the same for a plurality of robots 1, 2, and 3, robots 1, 2, and 3 with lower numbers are selected.
3 is selected. For the selected robots 1, 2, 3, all groups G1 not assigned from the current values
The travel time to the start point of G14 is calculated, and the group with the shortest travel time among them is allocated as the next work group.

For example, when the robot 1 is selected and it is determined that the work of the group G3 is to be performed next, it is denoted as R1: G3. For the robot 1, the sum of the movement time of the group G3 to the start point of the group and the work time in the group is added to the work time. Similarly, the robots 1, 2, and 3 having the shortest current working time are selected, and the groups G1 to G14 in which the moving time to the starting point is the shortest are selected as the next working group. When all the groups G1 to G14 are assigned to the robots 1, 2, and 3 by repeating such selection, a final result as shown in Table 3 below is obtained as an initial feasible solution. R1 has the highest initial priority, followed by R2, and R3 has the lowest. () Indicates the direction of the work in the group, and is set in advance as “order” or “reverse”. The initial possible solutions as shown in Table 3 are output as an initial distribution file indicating the work allocation of each robot, an initial order file indicating the work order of each robot, and an initial combination file indicating the direction of the work in each group.

[0033]

[Table 3]

In the solution improvement process in step a4 of FIG. 7, the solution is improved using the cycle time in consideration of the interference as an evaluation value. A file in which the initial temperature, the temperature reduction rate, the loop / stage, and the total number of loops are set as the SA parameter 45 is prepared using the SA method for solution improvement. In the SA method,
The degree to which a solution having a cycle time longer than the already evaluated cycle time is adopted to prevent the solution from falling into a local solution is expressed as “temperature”. A file indicating the presence or absence of interference between groups is prepared as shown in Table 2 above. First, the initial value result 44 is read, and the evaluation value of the initial value is calculated. The calculation method is as shown in Table 3 in advance.
The robots 1, 2, and 3 are assigned an initial priority, and the robot with the highest priority performs work without being affected by other robots. The next highest priority robot is checked according to the interference table to determine whether the highest priority robot causes interference with the work, and if interference occurs, the work is postponed. Such processing is repeated until no interference occurs, and the processing is executed for all robots. The robot with the lowest priority checks all robots for interference. Thus, the cycle time of each robot can be obtained, and the longest cycle time among the robots is the evaluation value of the solution.

Since the initial value is always adopted as the current solution, an evaluation value for the initial value is stored. Next, as a change process, a random number value is generated, and any one of distribution change, order change, combination change, or priority change is selected. In the distribution change, the processing of the group distributed to a certain robot is changed to another robot. A group is randomly selected from groups that can be processed by other robots, and the group is deleted from the distribution and order of the robots to which the selected group belongs. The robot that can process the group is determined according to the random number value, and the selected group is added to the determined robot allocation and order. The selected group is added to the end of the order of the group allocated to the determined robot. The following Table 4 shows the group G2 belonging to the robot R1 in the initial state,
2 shows a state in which the distribution has been changed.

[0036]

[Table 4]

In order change, the work order between groups allocated to a certain robot is changed. The robot to be changed is selected based on a random value. The order can be changed by a method of changing the order of adjacent groups to the reverse order or a method of randomly exchanging groups. In this order change, only the order between groups is changed, so that the changed work order is stored. For example, when the order of the groups G3 and G7 of the robot R1 is changed from the initial state, the result is as shown in Table 5.

[0038]

[Table 5]

In the connection change, the work direction in the group is changed. The group to be changed according to the random number is determined to be 1 or 2. The work direction in the determined group is changed to the current reverse direction, and the state is stored. For example, if the connection of the groups G10 and G14 of the robot R3 is changed from the initial state, the result is as shown in Table 6 below.

[0040]

[Table 6]

In the priority change, the priority of the robot is changed. A permutation is created by random numbers, and the order according to the created permutation is set as a new priority. The determined priority is stored. For example, when the priority is changed to the order of R3, R1, and R2, the following table 7 is obtained.

[0042]

[Table 7]

In the solution improvement, an evaluation value is calculated using a solution obtained by performing any of the change processes. If the changed solution has a smaller evaluation value represented by the cycle time than the current solution, the changed solution is regarded as the current solution. At this time, if the evaluation value is the smallest among the evaluation values so far, it is stored as the best solution. Even if the evaluation value is large, it is determined whether or not the solution changed according to the SA method described later is set as the current solution. Such change processing is performed by using the SA parameter 45.
Is repeated for the number of loops included in. In addition, the temperature is changed by multiplying the temperature by the parameter of the decrease rate for each loop number / stage. The best solution after the whole number of loop iterations is obtained as a final result as shown in Table 8, for example.

[0044]

[Table 8]

FIG. 8 shows an operation of dividing a group by checking for interference with a jig or a vehicle body at the grouping stage in step a2 of FIG. The operation is started from step b1, and in step b2, grouping is performed according to the movable range where each robot can hit and the type of welding gun. Next, in step b3, a B-rep expression of the vehicle body and the jig is input. Next, in step b4, it is determined whether or not there is a dot group that passes through the jig when the welding gun moves between the dots in each group. If there is a dot group that passes through the jig, in step b5, the group is divided between the dots that pass through the jig. If it is determined in step b4 that there is no hit point group to which a jig is added when moving between hit points, it is determined in step b6 whether there is no hit point group to add a vehicle body by moving between hit points. If there is a hit point group that passes through the vehicle body, the hit point group is divided between the hit points that pass through the vehicle body in step b7. If it is determined in step b6 that there is no hit point group in which the movement between hit points passes through the vehicle body, the operation ends in step b8.

FIG. 9 shows an operation of judging the presence or absence of interference between the groups of the two robots 1 and 2. The operation is started from step c1, and in step c2, it is determined whether or not there is an assignment for which interference determination has not been attempted in the assignment between the robot and the hit point group. If it is determined that there is an assignment for which no determination has been attempted, in step c3, one of the assignments between the robot and the hit point group for which no interference determination has been attempted is selected. Next, in step c4, the robot 2
It is determined whether or not there is a set of hit points for which interference determination has not been attempted in the hit point group assigned to. If there is a set of hit points, in step c5, a set of hit points s and t for which no interference determination has been attempted is selected from the hit point groups assigned to the robot 2. Next, in step c6, the hit points s,
Line segments s and t are drawn between t. In step c7, line segments rs and rt are drawn between the hit points s and t and the installation position of the robot 2. In step c8, the surface of the triangle generated by the line segments st, rs, and rt is defined as a.

In step c9, it is determined whether or not there is a hit point in the hit point group assigned to the robot 1 that has not yet been subjected to the interference determination with respect to the surface a. If there is a hit point, at step c10, a hit point u which has not yet attempted to determine the interference with the surface a is selected from the hit point group assigned to the robot 1. Next, in step c11, a line segment ru is drawn between the hit point u and the installation position of the robot 1. In the next step c14, an interference determination between the line segment ru and the surface a is performed. In step c13, it is determined whether or not the line segment ru and the surface a interfere. In the case of interference, the current hit point group assignment for the robots 1 and 2 in step c14 is as follows:
It is determined that this involves interference between the robots, and the process returns to step c2. If it is determined in step c2 that there is no assignment for which the interference determination has not been attempted yet in the assignment between the robot and the hit point group, the operation is terminated in step c15. If it is determined in step c4 that there is no set of hit points for which no collision determination has been made in the hit point group assigned to the robot 2, the process returns to step c2. Step c9
If it is determined that there is no hit point in the hit point group assigned to the robot 1 for which interference determination has not been performed on the surface a, the process returns to step c4. In step c13,
When it is determined that the line segment ru does not interfere with the surface a, the process returns to step c9.

FIG. 10 shows the relationship between the robot corresponding to the operation of FIG. 9 and the hit point group. Surface a shown with diagonal lines
Is a triangular surface formed between the installation position r of the robot 2 and the hit points s and t in the hit point group 2.
In contrast, it is determined whether or not a line segment ru between the hit point u of the hit point group 1 and the installation position of the robot 1 causes interference.

FIG. 11 shows the operation of the initial value generation processing shown in step a3 of FIG. 7 in more detail. Initial value generation is started from step d1, and in step d2, the current position of each robot is set as the robot initial position. In step d3, the current working time of each robot is set to zero. Step d4
Then, it is determined whether or not the distribution to each robot has been completed for all the groups. When it is determined that the distribution has not been completed, in step d5, a robot having a shorter total working time is selected from the robots. In step d6, it is determined whether or not there is a group satisfying the constraint condition for the selected robot. When it is determined that the robot does not exist, the next robot is selected in step d7, and the process returns to step d6. When it is determined in step d6 that there is a group that satisfies the constraint condition, a group having the shortest moving time from the current position is selected for the robot selected in step d8. In step d9, among the hit points of the selected group, the hit point on the opposite side to the robot is changed to the current position of the robot. In step d10,
The working time and the moving time for the points within the group are added to the current working time of the robot. When step d10 ends, the process returns to step d4. When it is determined in step d4 that the distribution for all the groups is completed, the initial value result 44 is output as a file in step d11, and the operation of generating the initial value is ended in step d12.

FIG. 12 shows the operation of the solution improvement processing in step a of FIG. 7 in more detail. The operation is started from step e1, and initialization for solution improvement operation is performed in step e2. Next, SA processing is executed in step e3, the changed solution is evaluated in step e4, and it is determined whether to adopt the solution. If adopted, the data is registered as a database in step e5, and if not adopted, the previous data is reset in the database in step e6. When step e5 or step e6 ends, it is determined in step e7 whether the number of loops, which is the end condition, is satisfied. If it is determined that the end condition is not satisfied, a random number X is generated in step e8. In step e9, a change in the order of the groups, a change in the distribution of the groups to the robots, a change in the work order within the group, a change in the priority order among the robots, and a change in the priority order among the robots are determined by the generated random numbers.
Repeat execution. If it is determined in step e7 that the termination condition is satisfied, the best solution having the best evaluation value is output with reference to the database, and the operation is terminated in step e11.

FIG. 13 shows the operation of the subroutine for executing the SA in step e3 of FIG. The operation is started from step f1, the necessary initialization is performed in step f2, and the cycle time calculation in consideration of the interference is performed in step f3. In step f4, it is determined whether or not the current cycle time obtained by the calculation is smaller than the previous cycle time registered in the database. When it is determined that it is not smaller, a numerical value as shown in the following Expression 5 is calculated in step f5, and it is determined whether or not the calculated value is larger than the random number value.

Exp (− (f (x ′) − f (x)) / Tk) (5) When it is determined in step f4 that the current cycle time is smaller than the previous cycle time, a new solution is adopted. Also, when it is determined in step f5 that the value represented by the fifth equation is larger than the random value, the current solution is adopted,
In step f6, the current cycle time f (x ') is substituted for the previous cycle time f (x). Step f
When it is determined in step 3 that the value of the fifth equation is smaller than the random number, it is not adopted, and the process proceeds to step f7 when step f6 ends. In step f7, it is determined whether or not the number of loops in FIG. 12 has reached an integral multiple of the stage. If it is determined that the temperature has reached, the temperature Tk is multiplied by the temperature reduction rate m in step f8. Here, 0 <m <1. When the operation in step f8 ends, or when it is determined in step f7 that the number of loops is not an integral multiple of the stage, the subroutine ends in step f9, and the process returns to step e3 in FIG.

FIG. 14 shows a comparison result between the SA method and the local search method which is a general approximation algorithm. FIG.
(A), (b), and (c) are 42.8 as initial feasible solutions.
The process of improving the solution according to the SA method when solutions having cycle times of 2 seconds, 52.55 seconds and 40.65 seconds are respectively set is shown. FIG. 14 (d) shows the state shown in FIG.
The process of solution improvement by the local search method based on the same initial solution as (b) and (c) is shown. According to the SA method, FIG.
As shown in FIGS. 4 (a), (b), and (c), a good solution can be obtained as a whole without depending much on the initial solution.
For example, as shown in FIG.
From the initial solution of 2.25 seconds, an improvement of about 10 seconds is made, and a final result of 31.83 seconds can be obtained. On the other hand, in the local search method shown in FIG. 14D, it is found that once the solution is stable, it is difficult to improve the solution even if the simulation is repeated.

FIG. 15A shows a work plan determined by the present embodiment, and FIG. 15B shows a work plan determined by a skilled person as a Gantt chart. The space between each group indicates the avoidance of interference,
The shaded portion indicates the travel time. In the present embodiment employing the SA method, a result is obtained in which the cycle time is reduced by about 1 second from the work plan determined by the skilled worker.

FIG. 16 shows a method of determining whether or not the vector of the movement between the oblique lines passes through a structure such as a jig or a vehicle body in step b4 or step b6 in FIG. The operation starts from step g1, and in step g2, a plane f parallel to the xy plane of the structure is selected. Step g
In 3, the plane f is mapped in xy parallel. In step g4,
At the start of the movement, the hit point S and the target hit point D are mapped on the xy plane.
At step g5, it is determined whether or not the vector from the mapping point of the hit point S to the mapping point of the hit point D interferes with the surface F. If there is interference, at step g6, the plane f is mapped parallel to xz. In step g7, the movement start point S and the target point D are mapped on the xz plane. In step g8, it is determined whether or not the vector from the mapping point of the hit point S to the mapping point of the hit point D interferes with the surface y. If it is determined that interference occurs, the process proceeds to step g9, where the surface f is mapped on the yz plane. At step g10, the movement start point S and the target point D are mapped on the yz plane. In step g11, it is determined whether or not a vector from the mapping point of the hit point S to the mapping point of the hit point D interferes with the surface f. If it is determined that interference occurs, step g1
At 2, it is determined whether or not the concave shape is on the surface f. If there is a concave shape, a surface w of the space formed by the concave shape is selected in step g13. Next, in step g14, the face w
It is determined whether or not there is interference between the hit points S and D. When it is determined that there is interference, it is determined in step g11 that there is no interference between the structure and the movement vector.
The operation ends at 16.

If it is determined in step g12 that the concave shape is not on the surface f, it is determined in step g17 that there is interference, and the operation is terminated in step g16. Step g14
When it is determined that there is no interference between the surface w and the hit points S and D, it is determined in step g18 whether or not the surface f has a concave shape that has not yet been confirmed. If there is any unconfirmed concave shape, the process returns to step g13. If there is no unconfirmed concave shape, it is determined in step g17 that there is interference, and the operation ends in step g16. Step g15
If it is determined that the vector from the mapping point of the hitting point S to the mapping point of the hitting point D does not interfere with the surface f, the process proceeds to step g19, and it is determined whether there is any unconfirmed surface. If there is any surface that has not been confirmed, the process returns to step g2. If there is no unconfirmed surface, the process proceeds to step g15, where it is determined that there is no interference, and step g16 is performed.
To end the operation. Step g8 and step g11
When it is determined that the light does not interfere with the surface f, the process returns to step g19.

FIG. 17 shows an operation of judging interference between a vector and a surface in the operation of FIG. The operation starts from step h1, and in step h2, a vertex list V1 is generated by removing the concave vertices from the entire vertex list Va of the plane.
The concave shape mentioned here includes a shape as shown in FIG. In the shape shown in FIG. 18, the vertex a is irrelevant at the time of interference determination. By eliminating such vertices from the vertex list for performing cross product calculation, it is possible to reduce the calculation.

In step h3, a vector from the mapping point of the hit point S to the vertex vm of the vertex list V1 is set as a vector Sm. In step h4, all the vectors Sm and the hit points S
Calculate the cross product Gm of the vector between the mapping points of D. At Step h5, it is determined whether or not the proposition (Gα> 0 and Gβ <0) holds for certain points α and β in the vertex list V1. When it is determined that the proposition is satisfied, it is determined in step h6 that interference occurs. When it is determined that the proposition is not satisfied, it is determined in step h7 that interference does not occur, and the operation is terminated in step h8.

FIG. 19 shows the principle by which the interference can be determined in step h5 by calculating the cross product. The sign of the cross product of the vector SD and another vector starting from the hit point S differs depending on whether the other vector is on the right or left side of the vector SD. For the vector SD,
The cross products of vectors to points S1, S2, S3, and S4 originating from S are represented by F (S1), F (S2), and F (S
3) and F (S4), the following relationships expressed by the sixth to ninth expressions are established. If F (S1)> 0, F (S2)> 0, F (S3) <0, F (S4) <0 ... (6) If F (S2)> 0, F (S1)> 0, F (S3) ) <0, F (S4) <0 (7) If F (S3)> 0, F (S4)> 0, F (S1) <0, F (S2) <0 (8) F (S4) > 0, F (S3)> 0, F (S1) <0, F (S2) <0 (9) That is, if there are vectors having different signs of the outer product,
It is determined that the vector SD interferes with the graphic having the vertices of S1, S2, S3, and S4.

FIGS. 20 to 25 show a process of judging whether or not the image vector from the hit point S to the hit point D passes through the concave surface f. FIG. 20 shows a spatial relationship between the hit points S and D and the surface f. 21A shows the mapping of the surface f on the xy plane, and FIG. 21B shows the mapping of the hit points S and D on the xy plane. (C) shows a combination of vectors for interference detection by cross product calculation. (A) of FIG.
FIG. 6 shows a mapping of a surface f onto an xz plane, and FIG.
Is mapped on the xz plane, and (c) shows a state in which interference is detected by cross product calculation. FIG.
Shows the mapping of the surface f to the yz plane, and (b) shows the hit point S · D.
(C) shows the state of interference detection by outer product calculation.

FIG. 24 shows a state in which the movement vector from the hit point S to the hit point A has a concave shape on the surface. FIG.
(A) shows the surface w corresponding to the concave shape, and (b) shows the spot S
It shows a state in which it is determined whether or not the movement vectors from to pass through the plane w. Passage is determined in the same manner as in the method shown in FIGS. In this case, it is determined that the movement vector does not pass through the surface w and does not interfere with the surface w.
In the determinations shown in FIGS. 21 to 23, since the passage is determined including the concave portion, if it is determined that the movement vector passes through the surface w, it is determined that the surface f does not substantially pass. You. However, in the determination in FIG.
It is determined that the movement vector does not pass through
As shown in (1), it is determined that the movement vector passes through a non-concave portion of the surface f, and it is concluded that there is interference.

FIG. 26 shows the principle of a method of expressing a structure by B-rep. Structure A has ridge lines e5, e6, e
, E13, e14, e15, e16. .. And vertices v5, v6, v7, v8,
... and so on. The direction symbol is U for the upper direction and D for the lower direction. The width direction and the depth direction are indicated by E, W; N, S, respectively. The structure A shown in FIG. 26 is expressed as a tree structure as shown in FIG.

The tree structure shown in FIG. 27 can be expressed as the following list. objct (01, [f1, f2, ..., f13]) ... (10) face (f1, [f11, f12]) ... (11) face (f2, [f13]) ... (12) edge (e5, v5, v6,1) ... (13) edge (e6, v6, v8,1) ... (14) edge (e7, v7, v8,1) ... (15) edge (e8, v8, v5, -1) ... (16) Vertex (v1) ... (17) vertex (v2) ... (18) vertex (v3) ... (19) For example, in Expressions 13, 14, and 15, "1" is used.
The portion marked with “-1” in Equation 16 is that the ridge lines e5, e6, and e7 are convex while the ridge line e
8 indicates that it is concave. B-re in equations 10 to 19
For the p expression, the direction symbols U, D, N, W,
S and E are set, and a list of direction symbols when the edge line is a vector is added.

FIG. 28 shows the B-rep expression of the following Expression 20 and the shape of the surface expressed by the direction symbol list of Expression 21. fLp (f98, [e50, e51, e52, e53, e54, e55, e56, e57]) ... (20) dLp (f98, [S, E, N, W, N, E, N, W] ... (21) By adding the direction symbol list, various feature shapes can be extracted.

In this embodiment, as the evaluation value, the optimization method, and the approximate solution to the traveling salesman problem, the work time in consideration of interference, the simulated annealing method, and the nearest neighbor method are used. It is not limited to these. For example, an evaluation value based on the moving distance, the number of interferences, or a combination thereof can be used. As an approximate solution, 2 Opt
Method, the Greedy method, and the Farthest Insertion method can also be used.

In the embodiment described above, the case where the present invention is applied to a work plan in the case of performing spot welding on the body of an automobile by three robots has been described. It can be widely applied to work plans such as general, painting and cutting.

[0067]

As described above, according to the present invention, work is grouped, and the order of work and the distribution of work to robots are
Since it is performed in groups, it is possible to greatly reduce the number of searching for solutions for the combination of robot and task, and to easily and automatically obtain the best solution without a large difference from the optimal solution in a realistic time. it can. Since the best solution can be obtained automatically, knowledge based on experience and determination by trial and error are unnecessary, and a plan change at the time of specification change by adding or deleting a work position or a robot can be easily performed. The interference of the work only needs to be performed once between the groups in the interference investigation stage, so that it is not necessary to repeat the interference investigation by the simulator, and the work time can be reduced. Since the best solution can be obtained within a finite time even if the work position increases, a work plan using a plurality of robots can be easily created in an easy and realistic time. Interference between the robots is allowed if there is a shift in the operation time zone, so that the robots can be arranged densely to perform an efficient operation.

Further, according to the present invention, for example, using a simulated annealing method or the like, a best solution search that employs, with a certain probability, a solution for which only an evaluation value that is inferior to an already obtained evaluation value can be obtained. Therefore, it is possible to eliminate the possibility of falling into a local solution and to search for the best solution close to the optimum solution in a short time.

Further, according to the present invention, an initial feasible solution is obtained by using an approximate solution of the traveling salesman problem, for example, a nearest neighbor method, so that a solution from which the best solution is easily obtained is easily determined as an initial feasible solution. be able to.

Further, according to the present invention, an avoidance point is provided in each group, so that handling in the case where interference occurs can be easily performed.

According to the present invention, at the initial possible solution determination stage, based on the work time set for each robot, the selection of a group to be allocated to the robot and the priority of the group to the robot with a small work time are given. Since the selection of the robot to be assigned to is repeated, the initial feasible solution can be easily set.

According to the present invention, in the grouping step,
Since the work that does not cause interference with the work or the tool is divided into groups, the work in the group can be performed without considering the interference.

Further, according to the present invention, the order of the tool direction at the tip of the robot, the tool insertion direction or the work included in the group is determined by using an approximate algorithm for generating a traveling route, and the division is performed when the moving distance between the works is long. For example, the work in the group can be performed efficiently.

Further, according to the present invention, it is possible to reliably determine whether or not a workpiece or a jig having a complicated shape interferes with the movement of the tool.

Further, according to the present invention, the determination of interference is made based on the sign of the cross product of the vectors with respect to the mapping of the object onto each coordinate axis plane, so that it is possible to easily and reliably determine whether or not interference occurs. can do.

[Brief description of the drawings]

FIG. 1 is a schematic plan view of a spot welding line for performing a work plan according to an embodiment of the present invention.

FIG. 2 is a welding instruction diagram showing positions of hit points to be welded to an automobile body which is the work of FIG. 1;

FIG. 3 is a diagram illustrating a process of grouping welding spots in FIG. 2;

FIG. 4 is a diagram showing a process of grouping welding spots in FIG. 2;

FIG. 5 is a view showing a process of grouping the welding points of FIG. 2;

FIG. 6 is a diagram showing a final result of grouping of the welding points of FIG. 2;

FIG. 7 is a flowchart showing an overall flow of a work plan according to the embodiment.

8 is a flowchart showing an operation of performing an interference check with a jig or a vehicle body in the grouping step of FIG.

9 is a flowchart illustrating an operation of performing an inter-group interference determination at the grouping stage in FIG. 7;

FIG. 10 is a simplified perspective view showing the relationship between a robot to be subjected to the inter-group determination in FIG. 9 and a hit point group.

FIG. 11 is a flowchart showing an operation in an initial value generation stage of FIG. 7;

FIG. 12 is a flowchart showing the operation of the solution improvement stage of FIG. 7;

FIG. 13 is a flowchart showing an operation of executing SA in FIG. 12;

FIG. 14 is a graph showing a comparison between a solution improvement process by the SA method and a solution improvement process by the local search method.

FIG. 15 is a Gantt chart showing a comparison between a work plan result according to the present embodiment and a work plan result by a skilled person.

FIG. 16 is a flowchart showing an operation of determining whether or not a movement vector passes through an object in steps b4 and b6 of FIG. 8;

FIG. 17 is a flowchart illustrating a process of determining whether or not a surface mapping and a motion vector mapping interfere with each other.

FIG. 18 is a diagram showing an example of a concave shape.

FIG. 19 is a diagram showing the principle by which the left-right relationship between vectors by cross product calculation of mappings can be grasped.

FIG. 20 is a simplified perspective view corresponding to FIG. 16, showing the principle of determining whether or not a sheet passes through one surface;

FIG. 21 is a diagram showing a process of interference detection by cross product calculation on the xy plane in FIG. 20;

FIG. 22 is a diagram showing a process of interference detection by cross product calculation in relation to the xz plane of FIG. 20;

FIG. 23 is a diagram showing a process of interference detection by cross product calculation in relation to the yz plane of FIG. 20;

FIG. 24 is a simplified perspective view showing that a concave portion exists on a surface f in FIG. 20;

FIG. 25 is a diagram illustrating that the movement vector does not interfere with the plane w corresponding to the concave portion illustrated in FIG. 24, and that the movement vector and the plane f interfere with each other.

FIG. 26 is a perspective view of a structure A to be expressed by B-rep of the structure.

FIG. 27 is a diagram showing a tree structure corresponding to the structure A shown in FIG. 26;

FIG. 28 is a diagram illustrating an example of a surface having a concave shape corresponding to an expanded B-rep expression.

[Explanation of symbols]

 1,2,3 robot 4,5,6 spot welding gun 10 controller 11,12 car body 20 spots 21,22,31,32,33,34 group 41 robot simulator data 42 robot data 43 group data 44 initial value result 45 SA parameter 46 Solution improvement result

 ──────────────────────────────────────────────────続 き Continuing from the front page (72) Inventor Masato Hayashi 1-1, Kawasaki-cho, Akashi-shi, Hyogo Kawasaki Heavy Industries, Ltd. Inside the Akashi Factory (72) Inventor Katsutoshi Hima 1-1, Kawasaki-cho, Akashi-shi, Hyogo Kawasaki Heavy Industries Inside the Akashi Factory (72) Inventor Yoshiaki Nakachi 1-1, Kawasaki-cho, Akashi-shi, Hyogo Kawasaki Heavy Industries Inside Akashi Factory (72) Inventor Hirofumi Tanaka 1-1-1, Kawasaki-cho, Akashi-shi, Hyogo Kawasaki Heavy Industries Stock (72) Inventor Koji Kato 1-1, Kawasaki-cho, Akashi-shi, Hyogo Kawasaki Heavy Industries, Ltd.

Claims (9)

[Claims] In a work planning method for a plurality of robots arranged so that at least a part of a work area overlaps, a plurality of works to be performed by the plurality of robots are described.
A grouping step of dividing the robot into groups of a number equal to or greater than the number of robots based on predetermined constraints, and checking whether a robot combination interferes with a possible combination of the group and the robot with another combination. An interference investigation step of conducting an investigation to determine whether or not the robot is in accordance with a predetermined criterion, the allocation of groups to each robot, the order of work of the group allocated to each robot, the direction in which the work in each group is performed, and An initial feasible solution determining step of determining an initial feasible solution according to a predetermined method as a solution indicating a priority of performing work preferentially when interference occurs in, a solution, a group allocation to each robot, a group A solution change stage that changes the work sequence between the groups, the direction within each group, and the priority of the robot to change the contents of the solution; For the solution determined at the floor or the solution changed at the solution change stage, according to the findings of the interference investigation stage, including the work required to avoid when interference occurs,
An evaluation value calculation step for calculating an evaluation value according to a predetermined standard for the robot operation, and an evaluation value is calculated for the initial feasible solution determined in the initial feasible solution determination step in the evaluation value calculation step, and the evaluation is performed in accordance with a predetermined optimization method. A work solution planning method for a plurality of robots, comprising: repeating a solution change at a change stage and a solution evaluation at an evaluation value calculation stage to search for a solution having the best evaluation value. . 2. The method according to claim 1, wherein in the search for the best solution, a solution having a lower evaluation value than the evaluation value already obtained in the evaluation value determination stage is determined with a certain probability. 2. The method according to claim 1, wherein a method is used.
Work planning method for multiple robots described. 3. The work planning method for a plurality of robots according to claim 1, wherein in the initial possible solution determination step, a predetermined approximate solution of the traveling salesman problem is used. 4. For each group divided in the grouping step, it is determined whether or not it is necessary to add a work position for avoiding interference. If necessary, a new work position is added to both ends of the group. 2. The work position according to claim 1, wherein, in addition to the avoidance point, even if the avoidance is required, if the avoidance at the work points at both ends of the existing group is possible, the work positions at both ends are set as the avoidance points. Work planning method for multiple robots. 5. In the initial possibility solution determination step, a work time with an initial value of 0 is set for each robot, and the movement time from the initial position of each robot to the avoidance point of the group is determined by the motion performance of the robot. Calculate from the data, allocate the group with the shortest moving time to each robot, select the group that adds the working time in the group and the calculated moving time to the working time of the robot, 5. The method according to claim 4, wherein all the groups are distributed to the robots by repeating the selection of the robot for sequentially selecting the groups. 6. In the grouping step, a work dividing step of dividing work into groups according to the movable range of each robot and the type of work tool, and information for inputting spatial information on the work and the jig and tool to be used. In the information input step, whether or not the tool or tool interferes with the work or tool while moving between the work positions in a predetermined order in each group divided in the input step and the work division step is input. 5. The multi-unit robot according to claim 1, further comprising: a group dividing step of dividing the group into works before and after passing when it is determined according to the space information that it interferes with a workpiece or a tool. Work planning method. 7. The method according to claim 7, wherein the group divided by the operation dividing step includes: grouping based on an angle difference between tool direction vectors at the robot tip; grouping based on an angle difference between tool insertion direction vectors; 7. The work planning method for a plurality of robots according to claim 6, wherein for the included work, the order determination using an approximation algorithm of the traveling route generation and the grouping based on the moving distance between the work positions are performed as processing. 8. The method according to claim 6, wherein in the information inputting step, spatial information of a work and a tool in a B-rep expression is input. 9. The determination as to whether or not interference occurs is based on the cross product of the vector from the tool movement start point to each point on the map and the tool movement vector for the mapping of the object onto each coordinate axis plane. 2. It is determined that interference occurs when there are vectors having different signs of outer products.
An operation planning method for a plurality of robots according to any one of claims 1 to 8.