6e12cef1-a287-4e21-b78d-bdc0b25ee58a20251114124817198wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS AND CONTROL2224-28561991-876310.37394/23203http://wseas.org/wseas/cms.action?id=40731720251720252010.37394/23203.2025.20https://wseas.com/journals/sac/2025.phpJuan Andrés RotetaLannesUniversidad Tecnológica Nacional - Comisión de Investigaciones Científicas, Facultad Regional Bahía Blanca, Grupo de Investigación en Multifísica Aplicada, 11 de abril 461, Bahía Blanca,Buenos Aires, ARGENTINAAndres GabrielGarciaUniversidad Tecnológica Nacional, Facultad Regional Bahía Blanca, Grupo de Estudio Sobre Energía - Departamento de Ingenieria Electrica, 11 de abril 461, Bahía Blanca, Buenos Aires, ARGENTINAOsvaldo EnriqueAgamennoniCONICET - Universidad Nacional del Sur, Instituto de Investigaciones en Ingeniería Eléctrica “Alfredo Desages”, San Andrés 800, Bahía Blanca, Buenos Aires, ARGENTINAThis study introduces a novel non-linear real-time filter based on the concept of Free Energy, which is applied to estimate the state of mobile robots in dynamic environments. By leveraging the principles of Bayesian inference, the proposed Free Energy Filter aims to minimize prediction errors between the observed and estimated trajectories. The approach extends existing non-linear filtering techniques, incorporating elements such as the Fokker-Planck equation. The simulation results demonstrate the effectiveness of this method in improving the control accuracy of unicycle robots equipped with the Bessel controller. The study also discusses comparisons with traditional Kalman filtering, highlighting the advantages of the proposed approach in adapting to noisy and uncertain conditions.111420251114202545947046https://wseas.com/journals/sac/2025/a925103-037(2025).pdf10.37394/23203.2025.20.46https://wseas.com/journals/sac/2025/a925103-037(2025).pdf10.1098/rstb.2005.1622Karl Friston, A theory of cortical responses, Philosophical Transactions of the Royal Society B: Biological Sciences, Volume 360, 2005, Pages 815-816, https://doi.org/10.1098/rstb.2005.1622. 10.1038/nrn2787Karl Friston, The free-energy principle: A unified brain theory?, Nature Reviews Neuroscience, Volume 11, 2010, Pages 127-138, ISSN 1471-003X, https://doi.org/10.1038/nrn2787. 10.1016/j.jphysparis.2006.10.001Karl Friston and James Kilner and Lee Harrison, A free energy principle for the brain, Journal of Physiology Paris, Volume 100, 2006, Pages 70-87, ISSN 0928-4257, https://doi.org/10.1016/j.jphysparis.2006.10.001. 10.3390/e14112100Karl Friston, A free energy principle for biological systems, Entropy, Volume 14, 2012, Pages 2100-2121, ISSN 1099-4300, https://doi.org/10.3390/e14112100. 10.1016/j.jmp.2015.11.003Rafal Bogacz, A tutorial on the free-energy framework for modeling perception and learning, Journal of Mathematical Psychology, Volume 76, Part B, 2017, Pages 198-211, ISSN 0022-2496, https://doi.org/10.1016/j.jmp.2015.11.003. 10.1016/j.jmp.2017.09.004Christopher L Buckley and Chang Sub Kim and Simon McGregor and Anil K Seth, The free energy principle for action and perception: A mathematical review, Journal of Mathematical Psychology, Volume 81, 2017, Pages 55-79, ISSN 0022-2496, https://doi.org/10.1016/j.jmp.2017.09.004. 10.3844/jmrsp.2020.1.7García, Andrés Gabriel, Asymptotic Stability of Unicycle-Like Robots: The Bessel’s Controller, Journal of Mechatronics and Robotics, Volume 4, 2020, Pages 1-7, https://doi.org/10.3844/jmrsp.2020.1.7. Huibert Kwakernaak and Raphael Sivan, Linear Optimal Control Systems, , 1972. 10.37394/23203.2024.19.40Nicholas Assimakis, Maria Adam, ”I/O SNR and Noise Covariances Norm Ratio Relation in Kalman Filter,” WSEAS Transactions on Systems and Control, vol. 19, pp. 373-378, 2024, https://doi.org/10.37394/23203.2024.19.40. Y. Sun and M. Kumar, Nonlinear Bayesian filtering based on Fokker-Planck equation and tensor decomposition, 18th International Conference on Information Fusion (Fusion), Washington, DC, USA, 2015, Pages 1483-1488, https://ieeexplore.ieee.org/document/7266732.