Adaptive Velocity Estimation for Lagrangian Systems using Modulating Functions

Matti Noack*, Johann Reger, Jerome Jouffroy

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


Information about the internal position and velocity of a robotic system is crucial for its control. Especially, under uncertain models, changing dynamic parameters and noisy position measurement signals, an adaptive differentiation is needed combining structural knowledge of the model with adequate filtering of the sensor data. To this end, the Modulating Function Method is applied to the Lagrange formulation of the robotic system to preserve the structure while enabling to incorporate nonlinear terms into the integral transform methodology. Different types of Modulating Functions and the function projection approach are used to develop a simultaneous parameter and state estimation procedure for the general structure of open kinematic chains. The developed algorithm for an adaptive velocity estimation is capable of robustly reconstructing the generalized state and consists of an efficient Finite Impulse Response (FIR) filter type implementation. The resulting architecture is demonstrated on a two-link robot setup.

Original languageEnglish
Title of host publication2023 IEEE International Conference on Mechatronics (ICM)
Number of pages8
Publication date2023
ISBN (Electronic)9781665466615
Publication statusPublished - 2023
Event2023 IEEE International Conference on Mechatronics, ICM 2023 - Leicestershire, United Kingdom
Duration: 15. Mar 202317. Mar 2023


Conference2023 IEEE International Conference on Mechatronics, ICM 2023
Country/TerritoryUnited Kingdom
SponsorIEEE Industrial Electronics Society, Loughborough University, The Institute of Electrical and Electronics Engineers (IEEE)


  • Lagrange formalism
  • modulating functions
  • robotic equation
  • simultaneous parameter and state estimation


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