Invariant-Based Inverse Engineering for Balanced Displacement of a Cartpole System

Ion Lizuain (), Ander Tobalina and Alvaro Rodriguez-Prieto
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Ion Lizuain: Department of Applied Mathematics, University of the Basque Country UPV/EHU, 48940 Leioa, Spain
Ander Tobalina: Department of Applied Mathematics, University of the Basque Country UPV/EHU, 48940 Leioa, Spain
Alvaro Rodriguez-Prieto: Department of Applied Mathematics, University of the Basque Country UPV/EHU, 48940 Leioa, Spain

Mathematics, 2025, vol. 13, issue 8, 1-11

Abstract: Adiabaticity is a key concept in physics, but its applications in mechanical and control engineering remain underexplored. Adiabatic invariants ensure robust dynamics under slow changes, but they impose impractical time limitations. Shortcuts to Adiabaticity (STA) overcome these limitations by enabling fast operations with minimal final excitations. In this work, we set a STA strategy based on dynamical invariants and inverse engineering to design the trajectory of a cartpole, a system characterized by its instability and repulsive potential. The trajectories found guarantee a balanced transport of the cartpole within the small oscillations regime. The results are compared to numerical simulations with the exact non-linear model to set the working domain of the designed protocol.

Keywords: shortcuts to adiabaticity; invariant-based engineering; mechatronics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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