2.1. Assembly process

The assembly machine of this study uses a dual arm robot, that is, each arm chucks a unit necessary for an assembly work, carries it to the assembly workbench and assembles parts. In this research, we define three positions existing on the movement path of the robot arm, approach 1, approach 2 and chuck position. Each definitions is as follows.

• Chuck position: position to put or grasp the unit

• Approach 1: position upward away from the chuck position

• Approach 2: position further upward than Approach 1

The arm passes from approach 2 through approach 1 and arrives at the chuck position. When the arm leaves the unit, it performs the reverse operation (see Fig. 2).With this definition, the assembly time calculations can be formulated.

Fig. 2.

Movement of arm

3.1. Condition creation module

The conditions module is as follows.

• Step 1: Read work data of parts assembly, placement possible area, parts arrangement data and create their database

• Step 2: Divide placement possible area into a lattice shape to create placement possible place

• Step 3: Carry out genes coding

• Step 4: Define the fitness function

• Step 5: Determine various parameters

3.2. GA module

The process flowchart of the GA module is shown in Fig. 4.

Fig. 4.

Flowchart of GA module

This detailed process is described below.

• Step 1: Generate an initial population

• Step 2: Calculate the arrangement coordinates of each unit

• Step 3: Determine part placement inside a parts tray by full search method

• Step 4: Calculate the time taken for each work

• Step 5: Calculate the cycle time of each individual in order not to collide with both arms

• Step 6: Calculate fitness

• Step 7: Give selection, crossover and mutation

• Step 8: Judge whether the termination condition is satisfied or not. If it is satisfied, go to Step 10

• Step 9: Give Step 4 to new individuals

• Step 10: The unit arrangement of individuals with the smallest cycle time is adopted as the optimal arrangement and output as a solution

4.1. System comparison

We compared DELUGA with the following two systems.

• ∙

  System that determines unit arrangement only by reinforcement learning

• ∙

  System that determines unit arrangement only by GA

The above two systems cannot find the parts layout in the tray. On the contrary, DELUGA can determines the arrangement of parts in the tray.

Fig. 6 is the left and right parts tray. Each number means each part. DELUGA decides the part arrangement in the tray by full search as follows.

Fig. 6.

Parts trays

As shown in Fig. 7, we divide the parts in left and right trays into two groups and three groups. Left tray has Group A and Group B, and right tray has Group C, Group D and Group E. Group A has 6 arrangement patterns. Group B to E also have arrangement patterns. Also, we consider arrangements in which Group A and Group B are rearranged, and Group C, Group D and Group E are rearranged. The number of each pattern is shown in Table 3.

Fig. 7.

Arrangement pattern of parts

Fig. 8.

Arrangement of group A

Table 1 shows 6 × 6 × 2 = 72 patterns in the left tray and 5 × 6 × 6 × 6 = 1080 patterns in the right tray.

That means 72 × 1,080 = 77,760 patterns exist.

4.2. Arrangement determination method

DELUGA calculated 77,760 pattern cycle times of parts arrangement in the tray for each individual during GA operations and the parts arrangement in the tray with the smallest cycle time among them is adopted.

4.3. Details of placement possible area

Table 2 shows the detailed data for the possible placement areas of each unit.

Table 3 shows the coordinates of the dual arm robot. All units of the label values are mm.