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In this paper, we explain how active inference\u2014a well-known description of sentient behaviour from neuroscience\u2014can be exploited in robotics. In short, active inference leverages the processes thought to underwrite human behaviour to build effective autonomous systems. These systems show state-of-the-art performance in several robotics settings; we highlight these and explain how this framework may be used to advance robotics.<\/jats:p>","DOI":"10.3390\/e24030361","type":"journal-article","created":{"date-parts":[[2022,3,2]],"date-time":"2022-03-02T08:37:16Z","timestamp":1646210236000},"page":"361","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["How Active Inference Could Help Revolutionise Robotics"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0126-4588","authenticated-orcid":false,"given":"Lancelot","family":"Da Costa","sequence":"first","affiliation":[{"name":"Department of Mathematics, Imperial College London, London SW7 2AZ, UK"},{"name":"Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9154-0798","authenticated-orcid":false,"given":"Pablo","family":"Lanillos","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence, Donders Institute for Brain, Cognition and Behavior, Radboud University, 6525 XZ Nijmegen, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Noor","family":"Sajid","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7984-8909","authenticated-orcid":false,"given":"Karl","family":"Friston","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shujhat","family":"Khan","sequence":"additional","affiliation":[{"name":"Milton Keynes Hospital, Oxford Deanery, Milton Keynes MK6 5LD, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"102447","DOI":"10.1016\/j.jmp.2020.102447","article-title":"Active inference on discrete state-spaces: A synthesis","volume":"99","author":"Parr","year":"2020","journal-title":"J. Math. Psychol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Barp, A., Da Costa, L., Fran\u00e7a, G., Friston, K., Girolami, M., Jordan, M.I., and Pavliotis, G.A. (2022). Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents. Geometry and Statistics, Academic Press.","DOI":"10.1016\/bs.host.2022.03.005"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s00422-010-0364-z","article-title":"Action and behavior: A free-energy formulation","volume":"102","author":"Friston","year":"2010","journal-title":"Biol. Cybern."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.jmp.2017.09.004","article-title":"The free energy principle for action and perception: A mathematical review","volume":"81","author":"Buckley","year":"2017","journal-title":"J. Math. Psychol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1038\/nrn2787","article-title":"The free-energy principle: A unified brain theory?","volume":"11","author":"Friston","year":"2010","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_6","first-page":"70","article-title":"A free energy principle for the brain","volume":"100","author":"Friston","year":"2006","journal-title":"J. Physiol."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Friston, K., Da Costa, L., Sajid, N., Heins, C., Ueltzh\u00f6ffer, K., Pavliotis, G.A., and Parr, T. (2022). The free energy principle made simpler but not too simple. arXiv.","DOI":"10.1016\/j.physrep.2023.07.001"},{"key":"ref_8","unstructured":"Parr, T. (2019). The Computational Neurology of Active Vision. [Ph.D. Thesis, University College London]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"102348","DOI":"10.1016\/j.jmp.2020.102348","article-title":"Deep active inference as variational policy gradients","volume":"96","author":"Millidge","year":"2020","journal-title":"J. Math. Psychol."},{"key":"ref_10","unstructured":"Fountas, Z., Sajid, N., Mediano, P.A.M., and Friston, K. (2020). Deep active inference agents using Monte-Carlo methods. arXiv."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Tschantz, A., Millidge, B., Seth, A.K., and Buckley, C.L. (2020). Reinforcement Learning through Active Inference. arXiv.","DOI":"10.1109\/IJCNN48605.2020.9207382"},{"key":"ref_12","unstructured":"Sajid, N., Tigas, P., Zakharov, A., Fountas, Z., and Friston, K. (2021). Exploration and preference satisfaction trade-off in reward-free learning. arXiv."},{"key":"ref_13","unstructured":"Mazzaglia, P., Verbelen, T., and Dhoedt, B. (2022, February 18). Contrastive Active Inference. Available online: https:\/\/openreview.net\/forum?id=5t5FPwzE6mq."},{"key":"ref_14","unstructured":"Lanillos, P., Meo, C., Pezzato, C., Meera, A.A., Baioumy, M., Ohata, W., Tschantz, A., Millidge, B., Wisse, M., and Buckley, C.L. (2021). Active Inference in Robotics and Artificial Agents: Survey and Challenges. arXiv."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational Inference: A Review for Statisticians","volume":"112","author":"Blei","year":"2017","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Meo, C., and Lanillos, P. (October, January 27). Multimodal VAE Active Inference Controller. Proceedings of the 2021 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Prague, Czech.","DOI":"10.1109\/IROS51168.2021.9636394"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1038\/nature16961","article-title":"Mastering the game of Go with deep neural networks and tree search","volume":"529","author":"Silver","year":"2016","journal-title":"Nature"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1038\/s41586-019-1724-z","article-title":"Grandmaster level in StarCraft II using multi-agent reinforcement learning","volume":"575","author":"Vinyals","year":"2019","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Verbelen, T., Lanillos, P., Buckley, C.L., and De Boom, C. (2020). Deep Active Inference for Partially Observable MDPs. Active Inference, IWAI 2020, Communications in Computer and Information Science, Springer.","DOI":"10.1007\/978-3-030-64919-7"},{"key":"ref_20","first-page":"809","article-title":"Active Inference in OpenAI Gym: A Paradigm for Computational Investigations Into Psychiatric Illness","volume":"3","author":"Cullen","year":"2018","journal-title":"Biol. Psychiatry Cogn. Neurosci. Neuroimaging"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1162\/neco_a_01357","article-title":"Active Inference: Demystified and Compared","volume":"33","author":"Sajid","year":"2021","journal-title":"Neural Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.neunet.2021.08.018","article-title":"An empirical evaluation of active inference in multi-armed bandits","volume":"144","author":"Kiebel","year":"2021","journal-title":"Neural Netw."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Paul, A., Sajid, N., Gopalkrishnan, M., and Razi, A. (2021). Active Inference for Stochastic Control. arXiv.","DOI":"10.1007\/978-3-030-93736-2_47"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1162\/neco_a_01351","article-title":"Sophisticated Inference","volume":"33","author":"Friston","year":"2021","journal-title":"Neural Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"102632","DOI":"10.1016\/j.jmp.2021.102632","article-title":"A step-by-step tutorial on active inference and its application to empirical data","volume":"107","author":"Smith","year":"2022","journal-title":"J. Math. Psychol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/j.neuroimage.2008.02.054","article-title":"DEM: A variational treatment of dynamic systems","volume":"41","author":"Friston","year":"2008","journal-title":"NeuroImage"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Meera, A.A., and Wisse, M. (2020, January 1\u20133). Free Energy Principle Based State and Input Observer Design for Linear Systems with Colored Noise. Proceedings of the 2020 American Control Conference (ACC), Denver, CO, USA.","DOI":"10.23919\/ACC45564.2020.9147581"},{"key":"ref_28","unstructured":"Baltieri, M., and Isomura, T. (2021). Kalman filters as the steady-state solution of gradient descent on variational free energy. arXiv."},{"key":"ref_29","unstructured":"da Costa, L., Sajid, N., Parr, T., Friston, K., and Smith, R. (2020). The relationship between dynamic programming and active inference: The discrete, finite-horizon case. arXiv."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Imohiosen, A., Watson, J., and Peters, J. (2020). Active Inference or Control as Inference? A Unifying View. arXiv.","DOI":"10.1007\/978-3-030-64919-7_2"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Millidge, B., Tschantz, A., Seth, A.K., and Buckley, C.L. (2020). On the Relationship Between Active Inference and Control as Inference. International Workshop on Active Inference, Springer.","DOI":"10.1109\/IJCNN48605.2020.9207382"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Sajid, N., da Costa, L., Parr, T., and Friston, K. (2021). Active inference, Bayesian optimal design, and expected utility. arXiv.","DOI":"10.1017\/9781009026949.007"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"41","DOI":"10.3389\/fncom.2020.00041","article-title":"An Active Inference Approach to Modeling Structure Learning: Concept Learning as an Example Case","volume":"14","author":"Smith","year":"2020","journal-title":"Front. Comput. Neurosci."},{"key":"ref_34","first-page":"103","article-title":"Learning Generative State Space Models for Active Inference","volume":"14","author":"Wauthier","year":"2020","journal-title":"Front. Comput. Neurosci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2633","DOI":"10.1162\/neco_a_00999","article-title":"Active Inference, Curiosity and Insight","volume":"29","author":"Friston","year":"2017","journal-title":"Neural Comput."},{"key":"ref_36","first-page":"1","article-title":"An empirical study of active inference on a humanoid robot","volume":"4","author":"Oliver","year":"2021","journal-title":"IEEE Trans. Cogn. Dev. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Meera, A.A., and Wisse, M. (2021). Dynamic Expectation Maximization Algorithm for Estimation of Linear Systems with Colored Noise. Entropy, 23.","DOI":"10.3390\/e23101306"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Baltieri, M., and Buckley, C.L. (2019). PID Control as a Process of Active Inference with Linear Generative Models. Entropy, 21.","DOI":"10.20944\/preprints201902.0246.v1"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Lanillos, P., and Cheng, G. (2018, January 1\u20135). Adaptive Robot Body Learning and Estimation Through Predictive Coding. Proceedings of the 2018 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain.","DOI":"10.1109\/IROS.2018.8593684"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2973","DOI":"10.1109\/LRA.2020.2974451","article-title":"A Novel Adaptive Controller for Robot Manipulators Based on Active Inference","volume":"5","author":"Pezzato","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Chame, H.F., and Tani, J. (August, January 31). Cognitive and motor compliance in intentional human-robot interaction. Proceedings of the 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France.","DOI":"10.1109\/ICRA40945.2020.9196896"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/j.neunet.2021.09.011","article-title":"World model learning and inference","volume":"144","author":"Friston","year":"2021","journal-title":"Neural Netw."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1109\/TCDS.2018.2867772","article-title":"Symbol Emergence in Cognitive Developmental Systems: A Survey","volume":"11","author":"Taniguchi","year":"2018","journal-title":"IEEE Trans. Cogn. Dev. Syst."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Smets, P. (1998). Graphical Models for Probabilistic and Causal Reasoning. Quantified Representation of Uncertainty and Imprecision, Springer.","DOI":"10.1007\/978-94-017-1735-9"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1162\/NETN_a_00018","article-title":"The graphical brain: Belief propagation and active inference","volume":"1","author":"Friston","year":"2017","journal-title":"Netw. Neurosci."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Verbelen, T., Lanillos, P., Buckley, C., and Boom, C.D. (2020, January 14). Active Inference. Proceedings of the First International Workshop, IWAI 2020, Co-Located with ECML\/PKDD 2020, Ghent, Belgium.","DOI":"10.1007\/978-3-030-64919-7"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"6024","DOI":"10.1109\/LRA.2021.3090015","article-title":"Leading or Following? Dyadic Robot Imitative Interaction Using the Active Inference Framework","volume":"6","author":"Wirkuttis","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"684401","DOI":"10.3389\/frobt.2021.684401","article-title":"Active Inference Through Energy Minimization in Multimodal Affective Human\u2013Robot Interaction","volume":"8","author":"Horii","year":"2021","journal-title":"Front. Robot. AI"},{"key":"ref_49","unstructured":"Lanillos, P., Pages, J., and Cheng, G. (September, January 29). Robot Self\/Other Distinction: Active Inference Meets Neural Networks Learning in a Mirror. Proceedings of the ECAI 2020-24th European Conference on Artificial Intelligence, Compostela, Spain."},{"key":"ref_50","first-page":"42","article-title":"Prior preference learning from experts: Designing a reward with active inference","volume":"12","author":"Shin","year":"2021","journal-title":"Neurocomputing"},{"key":"ref_51","unstructured":"Friston, K. (2022, February 18). Complexity and Computation in the Brain: The Knowns and the Known Unknowns. Available online: https:\/\/direct.mit.edu\/books\/book\/4588\/chapter\/204732\/Complexity-and-Computation-in-the-Brain-The-Knowns."},{"key":"ref_52","unstructured":"Lanillos, P., and van Gerven, M. (2021). Neuroscience-inspired perception-action in robotics: Applying active inference for state estimation, control and self-perception. arXiv."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1007\/s10514-017-9677-2","article-title":"Progress and prospects of the human\u2013robot collaboration","volume":"42","author":"Ajoudani","year":"2018","journal-title":"Auton. Robot."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.neunet.2021.05.010","article-title":"Robot navigation as hierarchical active inference","volume":"142","author":"Verbelen","year":"2021","journal-title":"Neural Netw."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"108266","DOI":"10.1016\/j.biopsycho.2022.108266","article-title":"Simulating homeostatic, allostatic and goal-directed forms of interoceptive control using active inference","volume":"169","author":"Tschantz","year":"2022","journal-title":"Biol. Psychol."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/NECO_a_00912","article-title":"Active Inference: A Process Theory","volume":"29","author":"Friston","year":"2017","journal-title":"Neural Comput."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"eabd1911","DOI":"10.1126\/scirobotics.abd1911","article-title":"Neuroengineering challenges of fusing robotics and neuroscience","volume":"5","author":"Cheng","year":"2020","journal-title":"Sci. Robot."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"fcaa164","DOI":"10.1093\/braincomms\/fcaa164","article-title":"Paradoxical lesions, plasticity and active inference","volume":"2","author":"Sajid","year":"2020","journal-title":"Brain Commun."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Tschantz, A., Baltieri, M., Seth, A.K., and Buckley, C.L. (2019). Scaling active inference. arXiv.","DOI":"10.1109\/IJCNN48605.2020.9207382"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/3\/361\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:30:59Z","timestamp":1760135459000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/3\/361"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,2]]},"references-count":59,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["e24030361"],"URL":"https:\/\/doi.org\/10.3390\/e24030361","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,2]]}}}