| Task: Allocate spot welding robots for a car body spot welding line.
Spot welding robots are typically 6 or 7 degrees-of-freedom
and work on 3D objects. To keep computational load and complexity
for the computation of the kinematic inverse low, we use
2D objects and 2 degrees-of-freedom SCARA-type robots.
This example demonstrates the principles and top down
construction of the program that solves a fragment of the allocation task.
- The task is to design a welding line.
- A welding line is part of a car body manufacturing line.
- The welding line consists of several welding stations.
- A welding station consists of several welding robots working
concurrently on the same car.
- All robots have the same size.
- Robots can be positioned anywhere at predefined fixed positions.
Input data:
spots to be welded for each car
(e.g. 400 spots for door openings and wheel houses)
physical size of the robots
(e.g. length upper arm, length lower arm,
and arm volume needed for collision avoidance)
performance of robots
time for welding operation (e.g. 0.5sec)
moving time from spot to neighboring spot
(e.g. 1 sec)
moving time from spot to other spot
(e.g. 2 sec)
moving time from spot to rest position
(e.g. 4 sec)
number of cars per day
(e.g. 1000 cars/day 3 shifts/day, 6 hours/shift
= 64.8 seconds per car,
could be 10.8 seconds moving cars along the line
and 54 seconds working on the standing cars)
Task is to compute:
number of welding stations needed
positions of robots within each welding station
path (=sequence of spots to be welded) of each robot
so that:
smallest number of welding stations
smallest number of robots for each welding station
all spots are welded
no robots collide during operation
A few assumptions:
Welding stations do not interfere with each other
(i.e. robots of seperate welding stations never collide)
Spots are given as a set of sequences of neighboring spots.
All spots are within reach of a correctly positioned robot.
Limitations:
Collision detection only for points,
not for the path between points.
Partial Implementation:
LINES PROGRAM
29 weldingline.min describe welding line
88 alloc_robots.min plan robots for spots
51 scara2D.min formula for 2D SCARA robot
18 sleep.min for slow motion animation
23 time.min to measure problem solving time
183 draw.min to visualize data and solution
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