Modeling and Simulation with Interval Uncertainties in Julia
(2025)Department of Automatic Control
- Abstract
- In robotic systems, uncertainty in model parameters, such as joint stiffness, link lengths, or mass distributions, can significantly affect performance and precision. This thesis investigates the quantification and propagation of such uncertainties using the programming language Julia, with a focus on developing a systematic framework for uncertainty-aware modeling and simulation. It leverages the ModelingToolkit.jl package to build symbolic, component-based, acausal models and integrates several uncertainty quantification methods, including a Scanning method, Monte Carlo simulations, Polynomial Chaos Expansion, and Taylor Models, to analyze how uncertain parameters and initial conditions impact robotic accuracy.
A novel package,... (More) - In robotic systems, uncertainty in model parameters, such as joint stiffness, link lengths, or mass distributions, can significantly affect performance and precision. This thesis investigates the quantification and propagation of such uncertainties using the programming language Julia, with a focus on developing a systematic framework for uncertainty-aware modeling and simulation. It leverages the ModelingToolkit.jl package to build symbolic, component-based, acausal models and integrates several uncertainty quantification methods, including a Scanning method, Monte Carlo simulations, Polynomial Chaos Expansion, and Taylor Models, to analyze how uncertain parameters and initial conditions impact robotic accuracy.
A novel package, IntervalSimulations.jl, was developed to enable seamless uncertainty propagation within the symbolic modeling framework. It allows uncertain parameters to be defined directly within the models and automatically generates bounded trajectories and plots. The thesis compares the methods in terms of computational efficiency, accuracy, and ease of integration.
Case studies, including a three-degree-of-freedom robot model, a double pendulum, and a pair of scissors, are used to evaluate method performance and demonstrate how uncertainty affects robotic behavior. Results show that while Monte Carlo and scanning methods provide reliable estimates, Polynomial Chaos Expansion often offers improved computational efficiency. Taylor Models, while theoretically rigorous, showed limited robustness in practice.
The results also highlight how uncertainty analysis can enhance robust robot design by pinpointing the parameters that most significantly influence performance. This insight is valuable both during the design phase and when programming robots for tasks requiring high precision. By quantifying how accurately a robot can follow a desired trajectory under uncertainty, the developed tools in this thesis support more informed decisions in robotic planning and control. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9207888
- author
- Kovács, Rasmus
- supervisor
- organization
- alternative title
- Framework Development and Robotic Applications
- year
- 2025
- type
- H3 - Professional qualifications (4 Years - )
- subject
- report number
- TFRT-6282
- other publication id
- 0280-5316
- language
- English
- id
- 9207888
- date added to LUP
- 2025-08-08 15:09:22
- date last changed
- 2025-08-08 15:09:22
@misc{9207888,
abstract = {{In robotic systems, uncertainty in model parameters, such as joint stiffness, link lengths, or mass distributions, can significantly affect performance and precision. This thesis investigates the quantification and propagation of such uncertainties using the programming language Julia, with a focus on developing a systematic framework for uncertainty-aware modeling and simulation. It leverages the ModelingToolkit.jl package to build symbolic, component-based, acausal models and integrates several uncertainty quantification methods, including a Scanning method, Monte Carlo simulations, Polynomial Chaos Expansion, and Taylor Models, to analyze how uncertain parameters and initial conditions impact robotic accuracy.
A novel package, IntervalSimulations.jl, was developed to enable seamless uncertainty propagation within the symbolic modeling framework. It allows uncertain parameters to be defined directly within the models and automatically generates bounded trajectories and plots. The thesis compares the methods in terms of computational efficiency, accuracy, and ease of integration.
Case studies, including a three-degree-of-freedom robot model, a double pendulum, and a pair of scissors, are used to evaluate method performance and demonstrate how uncertainty affects robotic behavior. Results show that while Monte Carlo and scanning methods provide reliable estimates, Polynomial Chaos Expansion often offers improved computational efficiency. Taylor Models, while theoretically rigorous, showed limited robustness in practice.
The results also highlight how uncertainty analysis can enhance robust robot design by pinpointing the parameters that most significantly influence performance. This insight is valuable both during the design phase and when programming robots for tasks requiring high precision. By quantifying how accurately a robot can follow a desired trajectory under uncertainty, the developed tools in this thesis support more informed decisions in robotic planning and control.}},
author = {{Kovács, Rasmus}},
language = {{eng}},
note = {{Student Paper}},
title = {{Modeling and Simulation with Interval Uncertainties in Julia}},
year = {{2025}},
}