Radau to the rescue: efficient and accurate discretization for optimal control simulations of running
Weiß A, Lluch È, Koelewijn A (2026)
Publication Language: English
Publication Type: Journal article
Publication year: 2026
Journal
DOI: 10.1080/10255842.2026.2640432
Open Access Link: https://www.tandfonline.com/doi/full/10.1080/10255842.2026.2640432#abstract
Abstract
Biomechanical simulations based on optimal control provide valuable insights into muscle-driven locomotion when incorporating muscle-tendon dynamics. However, the influence of discretization methods in direct collocation for musculoskeletal simulations remains unexplored. We systematically evaluated six implicit Runge-Kutta schemes across gait tasks, dimensionalities, discretizations, and collocation densities. Radau IIa consistently minimized dynamic errors and outperformed Lobatto IIIc and Euler due to its numerical stability. Repeated-measures ANOVA showed significant method–node interactions. Backward Euler was fastest but least dynamically consistent, while two-stage Radau IIa offered a practical trade-off between dynamic consistency and computational effort. This paper provides guidelines for efficient optimal control in musculoskeletal modeling with implicit muscle dynamics.
Authors with CRIS profile
Alexander Weiß
Professur für Computational Movement Science
Anne Koelewijn
Professur für Computational Movement Science
Involved external institutions
Germany (DE)How to cite
APA:
Weiß, A., Lluch, È., & Koelewijn, A. (2026). Radau to the rescue: efficient and accurate discretization for optimal control simulations of running. Computer Methods in Biomechanics and Biomedical Engineering. https://doi.org/10.1080/10255842.2026.2640432
MLA:
Weiß, Alexander, Èric Lluch, and Anne Koelewijn. "Radau to the rescue: efficient and accurate discretization for optimal control simulations of running." Computer Methods in Biomechanics and Biomedical Engineering (2026).
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