# Mathematical Modelling for Load Balancing and Minimization of Coordination Losses in Multirobot Stations Licentiate thesis, 2020

The automotive industry is moving from mass production towards an individualized production, in order to improve product quality and reduce costs and material waste. This thesis concerns aspects of load balancing of industrial robots in the automotive manufacturing industry, considering efficient algorithms required by an individualized production. The goal of the load balancing problem is to improve the equipment utilization. Several approaches for solving the load balancing problem are presented along with details on mathematical tools and subroutines employed.

Our contributions to the solution of the load balancing problem are manifold. First, to circumvent robot coordination we have constructed disjoint robot programs, which require no coordination schemes, are more flexible, admit competitive cycle times for some industrial instances, and may be preferred in an individualized production. Second, since solving the task assignment problem for generating the disjoint robot programs was found to be unreasonably time-consuming, we modelled it as a generalized unrelated parallel machine problem with set packing constraints and suggested a tighter model formulation, which was proven to be much more tractable for a branch--and--cut solver. Third, within continuous collision detection it needs to be determined whether the sweeps of multiple moving robots are disjoint. Our solution uses the maximum velocity of each robot along with distance computations at certain robot configurations to derive a function that provides lower bounds on the minimum distance between the sweeps. The lower bounding function is iteratively minimized and updated with new distance information; our method is substantially faster than previously developed methods.

Voronoi diagram

vehicle routing

Smart Assembly 4.0

motion planning

mathematical modelling

decomposition

continuous collision detection

set packing

automotive manufacturing

makespan minimization

Pascal, Hörsalsvägen 1.
Opponent: Senior Lecturer Nils-Hassan Quttineh, Department of Mathematics, Linköping University, Sweden.

## Author

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Intersection-Free Geometrical Partitioning of Multirobot Stations for Cycle Time Optimization

IEEE Transactions on Automation Science and Engineering,; Vol. 15(2018)p. 842-851

Journal article

### Smart Assembly 4.0

Swedish Foundation for Strategic Research (SSF), 2016-05-01 -- 2021-06-30.

### Driving Forces

Sustainable development

Production

### Subject Categories

Computational Mathematics

Robotics

### Publisher

Chalmers University of Technology

Pascal, Hörsalsvägen 1.

Opponent: Senior Lecturer Nils-Hassan Quttineh, Department of Mathematics, Linköping University, Sweden.