# Mathematical Modelling for Load Balancing and Minimization of Coordination Losses in Multirobot Stations Licentiatavhandling, 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.

decomposition

mathematical modelling

Voronoi diagram

set packing

automotive manufacturing

Smart Assembly 4.0

continuous collision detection

motion planning

vehicle routing

makespan minimization

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

## Författare

Stiftelsen Fraunhofer-Chalmers Centrum för Industrimatematik

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

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

IEEE Transactions on Automation Science and Engineering,; (2018)

Artikel i vetenskaplig tidskrift

### Smart Assembly 4.0

Stiftelsen för Strategisk forskning (SSF) (RIT15-0025), 2016-05-01 -- 2021-06-30.

### Interlinked combinatorial and geometrical optimization problems in an autonomous automotive manufacturing industry

Stiftelsen Fraunhofer-Chalmers Centrum för Industrimatematik, 2017-08-15 -- 2022-09-05.

Stiftelsen för Strategisk forskning (SSF) (RIT15-0025), 2017-08-15 -- 2022-09-05.

### Drivkrafter

Hållbar utveckling

Produktion

### Ämneskategorier

Beräkningsmatematik

Robotteknik och automation

### Utgivare

Chalmers

Pascal, Hörsalsvägen 1.

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

2021-12-15