d i nt a s t e

1. Linear index i

The robot runs inside a loop:

FOR i = 0 TO N-1

where N is the total number of objects to place.

The variable i represents the object number. The main question is:
how do we convert i into a position (x, y, z)?

2. 2D pallet – rows and columns

We assume a pallet with:

• c = number of columns
• r = number of rows
• dx = spacing between objects on X axis
• dy = spacing between objects on Y axis

We need two mathematical operations to get column and row from index i:

🔍 MOD (i / α) returns the remainder of the division
🔍 INT (i / α) returns the quotient of the division

i: 0 1 2 3 4 5 6 7 8

i MOD 3: 0 1 2 0 1 2 0 1 2

INT(i/3): 0 0 0 1 1 1 2 2 2

3. 3D pallet – rows, columns and layers

For 3D palletizing we add:

• h = object height (spacing between objects on Z axis)
• n = objects per layer

layer number = INT( i / n )

The Z position is then calculated as:

z = h × layer

This means:every n boxes, the robot moves up one layer.

Conclusion

Everything shown in the sketch reduces to:

• a linear index i
• simple operations: MOD (i / α) and INT (i / α)