Online and Offline Calibration of Digital Twins in the Smart Assembly 4.0 Framework

A. Sjöberg, M. Önnheim, O. Frost, C. Cronrath, E. Gustavsson, B. Lennartsson, and M. Jirstrand. In Proceedings of Kaiserslautern Applied and Industrial Mathematics Days (KLAIM2021), Abstract No. A39, p.54-55. 11-13 October, 2021.


The overarching objective of the project Smart Assembly 4.0 has been to address research challenges related to the realization of the autonomous, selfoptimizing robotized assembly factory, which maximizes quality and throughput, maintaining flexibility and reducing cost, by a sensing, thinking and acting strategy [1].

A specific goal has been to develop a digital twin of a sheet metal welding production cell in an assembly line, including the modeling of the geometric path planning of the robotics, individual part variation as measured by sensors before welding, physical models for the deformation of assemblies during welding, feedback control, and data driven process improvement. Detailed modeling of the end-to-end assembly process has shown promising results [2, 3].

However, an end-to-end digital twin necessarily consists of many interacting parts. Thus, calibration of the digital twin to reality becomes increasingly important, as miscalibration of interacting components may nullify any gains.

We view the family of possible digital twins as a family of functions {Q(x, u; θ}, where x denotes an individual assembly to be manufactured, u the controllable parameters, θ parameters to be calibrated, and Q a mapping from inputs and parameters to final assembly quality, as provided by the digital twin.

We view the calibration as a system identification task, and evaluate two approaches. The offline or batch mode approach, where a significant number of assemblies are processed and identification is performed by global optimization of the discrepancy between Q and observed assemblies. We show that this simple approach can handle significant errors in initial calibration. The online approach considers θ as the state of an unscented Kalman filter [4], for which Q becomes the (non-linear) measurement function, and we show that this approach can track a time-varying ground truth θt .

We further note that the controllability of the parameters u present an exploration/exploitation trade-off, in the sense that u can be optimized for nextassembly quality or for ease of identification. We propose and evaluate an surrogate model approach for balancing this exploration/exploitation trade-off, and show that, in the evaluated scenarios, an approach favouring exploration significantly outperforms exploitation-focused approaches, as well as naive baselines, in terms of average final quality over many assemblies. However, this comes at the cost of significant computational burden.


This work has been funded by the Swedish Foundation for Strategic Research (Grant no RIT15-0025) and also been carried out in the Fraunhofer Cluster of Excellence Cognitive Internet Technologies.

Photo credits: Nic McPhee