{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T10:24:13Z","timestamp":1771064653017,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1012599","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T00:00:00Z","timestamp":1736467200000}}],"reference-count":58,"publisher":"Public Library of Science (PLoS)","issue":"11","license":[{"start":{"date-parts":[[2024,11,18]],"date-time":"2024-11-18T00:00:00Z","timestamp":1731888000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R37-HD087089, R01-CRCNS-NS120579"],"award-info":[{"award-number":["R37-HD087089, R01-CRCNS-NS120579"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Eric P. and Evelyn E. Newman Fund"},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["Graduate Research Fellowship: 1745302, 2141064"],"award-info":[{"award-number":["Graduate Research Fellowship: 1745302, 2141064"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Humans are skillful at manipulating objects that possess nonlinear underactuated dynamics, such as clothes or containers filled with liquids. Several studies suggested that humans implement a predictive model-based strategy to control such objects. However, these studies only considered unconstrained reaching without any object involved or, at most, linear mass-spring systems with relatively simple dynamics. It is not clear what internal model humans develop of more complex objects, and what level of granularity is represented. To answer these questions, this study examined a task where participants physically interacted with a nonlinear underactuated system mimicking a cup of sloshing coffee: a cup with a ball rolling inside. The cup and ball were simulated in a virtual environment and subjects interacted with the system via a haptic robotic interface. Participants were instructed to move the system and arrive at a target region with both cup and ball at rest, \u2018zeroing out\u2019 residual oscillations of the ball. This challenging task affords a solution known as \u2018input shaping\u2019, whereby a series of pulses moves the dynamic object to the target leaving no residual oscillations. Since the timing and amplitude of these pulses depend on the controller\u2019s internal model of the object, input shaping served as a tool to identify the subjects\u2019 internal representation of the cup-and-ball. Five simulations with different internal models were compared against the human data. Results showed that the features in the data were correctly predicted by a simple internal model that represented the cup-and-ball as a single rigid mass coupled to the hand impedance. These findings provide evidence that humans use simplified internal models along with mechanical impedance to manipulate complex objects.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012599","type":"journal-article","created":{"date-parts":[[2024,11,18]],"date-time":"2024-11-18T18:38:43Z","timestamp":1731955123000},"page":"e1012599","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":5,"title":["Simplified internal models in human control of complex objects"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8631-0426","authenticated-orcid":true,"given":"Salah","family":"Bazzi","sequence":"first","affiliation":[]},{"given":"Stephan","family":"Stansfield","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5366-2145","authenticated-orcid":true,"given":"Neville","family":"Hogan","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9318-2920","authenticated-orcid":true,"given":"Dagmar","family":"Sternad","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2024,11,18]]},"reference":[{"issue":"4","key":"pcbi.1012599.ref001","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1523\/JNEUROSCI.17-04-01519.1997","article-title":"The role of internal models in motion planning and control: evidence from grip force adjustments during movements of hand-held loads","volume":"17","author":"JR Flanagan","year":"1997","journal-title":"Journal of Neuroscience"},{"issue":"7","key":"pcbi.1012599.ref002","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1152\/jn.00754.2013","article-title":"Coordination between digit forces and positions: interactions between anticipatory and feedback control","volume":"111","author":"Q Fu","year":"2014","journal-title":"Journal of Neurophysiology"},{"issue":"1","key":"pcbi.1012599.ref003","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s00221-005-2282-1","article-title":"Internal forces during object manipulation","volume":"165","author":"F Gao","year":"2005","journal-title":"Experimental Brain Research"},{"issue":"3","key":"pcbi.1012599.ref004","doi-asserted-by":"crossref","first-page":"1158","DOI":"10.1152\/jn.00704.2003","article-title":"Experimentally confirmed mathematical model for human control of a non-rigid object","volume":"91","author":"JB Dingwell","year":"2004","journal-title":"Journal of Neurophysiology"},{"issue":"6","key":"pcbi.1012599.ref005","doi-asserted-by":"crossref","first-page":"1646","DOI":"10.1152\/jn.00224.2012","article-title":"Minimum acceleration with constraints of center of mass: a unified model for arm movements and object manipulation","volume":"108","author":"R Leib","year":"2012","journal-title":"Journal of Neurophysiology"},{"key":"pcbi.1012599.ref006","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.humov.2018.12.004","article-title":"Motion planning strategies in human control of non-rigid objects with internal degrees of freedom","volume":"63","author":"M Svinin","year":"2019","journal-title":"Human Movement Science"},{"issue":"6","key":"pcbi.1012599.ref007","doi-asserted-by":"crossref","first-page":"e1000419","DOI":"10.1371\/journal.pcbi.1000419","article-title":"Optimal control predicts human performance on objects with internal degrees of freedom","volume":"5","author":"AJ Nagengast","year":"2009","journal-title":"PLoS Computational Biology"},{"issue":"5","key":"pcbi.1012599.ref008","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1162\/neco_a_01576","article-title":"Body mechanics, optimality, and sensory feedback in the human control of complex objects","volume":"35","author":"RS Razavian","year":"2023","journal-title":"Neural Computation"},{"issue":"1","key":"pcbi.1012599.ref009","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1152\/jn.2002.88.1.222","article-title":"Manipulating objects with internal degrees of freedom: Evidence for Model-Based Control","volume":"88","author":"JB Dingwell","year":"2002","journal-title":"Journal of Neurophysiology"},{"issue":"10","key":"pcbi.1012599.ref010","doi-asserted-by":"crossref","first-page":"e1003900","DOI":"10.1371\/journal.pcbi.1003900","article-title":"Rhythmic manipulation of objects with complex dynamics: predictability over chaos","volume":"10","author":"B Nasseroleslami","year":"2014","journal-title":"PLoS Computational Biology"},{"issue":"2","key":"pcbi.1012599.ref011","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1080\/00222890109603150","article-title":"Stability in force-production tasks","volume":"33","author":"D Rancourt","year":"2001","journal-title":"Journal of Motor Behavior"},{"key":"pcbi.1012599.ref012","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.conb.2015.04.003","article-title":"On simplicity and complexity in the brave new world of large-scale neuroscience","volume":"32","author":"P Gao","year":"2015","journal-title":"Current Opinion in Neurobiology"},{"key":"pcbi.1012599.ref013","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.plrev.2023.07.006","article-title":"Beyond simple laboratory studies: Developing sophisticated models to study rich behavior","volume":"46","author":"A Maselli","year":"2023","journal-title":"Physics of Life Reviews"},{"issue":"2","key":"pcbi.1012599.ref014","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1152\/jn.00918.2017","article-title":"Predictability, force, and (anti)resonance in complex object control,\u201d","volume":"120","author":"P Maurice","year":"2018","journal-title":"Journal of Neurophysiology"},{"issue":"10","key":"pcbi.1012599.ref015","doi-asserted-by":"crossref","first-page":"103103","DOI":"10.1063\/1.5042090","article-title":"Stability and predictability in human control of complex objects","volume":"28","author":"S Bazzi","year":"2018","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"issue":"12","key":"pcbi.1012599.ref016","doi-asserted-by":"crossref","first-page":"e1009597","DOI":"10.1371\/journal.pcbi.1009597","article-title":"Preparing to move: Setting initial conditions to simplify interactions with complex objects","volume":"17","author":"Dec.","year":"2021","journal-title":"PLoS Computational Biology"},{"key":"pcbi.1012599.ref017","doi-asserted-by":"crossref","unstructured":"Singh T, Singhose W, \u201cInput shaping\/time delay control of maneuvering flexible structures,\u201d in IEEE Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), Anchorage, AK, USA: IEEE, 2002, pp. 1717\u20131731 vol.3. doi: 10.1109\/ACC.2002.1023813","DOI":"10.1109\/ACC.2002.1023813"},{"issue":"6","key":"pcbi.1012599.ref018","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1108\/01439910310506783","article-title":"HapticMaster\u2013a generic force controlled robot for human interaction","volume":"30","author":"Dec.","year":"2003","journal-title":"Industrial Robot: An International Journal"},{"issue":"7","key":"pcbi.1012599.ref019","doi-asserted-by":"crossref","first-page":"1688","DOI":"10.1523\/JNEUROSCI.05-07-01688.1985","article-title":"The coordination of arm movements: An experimentally confirmed mathematical model","volume":"5","author":"T Flash","year":"1985","journal-title":"Journal of Neuroscience"},{"key":"pcbi.1012599.ref020","doi-asserted-by":"crossref","unstructured":"Smith JY, Kozak K, Singhose WE, \u201cInput shaping for a simple nonlinear system,\u201d in IEEE Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), Anchorage, AK, USA: American Automatic Control Council, 2002, pp. 821\u2013826. doi: 10.1109\/ACC.2002.1024916","DOI":"10.1109\/ACC.2002.1024916"},{"key":"pcbi.1012599.ref021","doi-asserted-by":"crossref","unstructured":"Guang H, Bazzi S, Sternad D, Hogan N, \u201cDynamic primitives in human manipulation of non-rigid objects,\u201d in 2019 International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada: IEEE, May 2019, pp. 3783\u20133789. doi: 10.1109\/ICRA.2019.8793687","DOI":"10.1109\/ICRA.2019.8793687"},{"issue":"17","key":"pcbi.1012599.ref022","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1080\/01691864.2020.1777198","article-title":"Human control of complex objects: Towards more dexterous robots","volume":"34","author":"S Bazzi","year":"2020","journal-title":"Advanced Robotics"},{"key":"pcbi.1012599.ref023","doi-asserted-by":"crossref","DOI":"10.1201\/9780203718841","volume-title":"Theory of Vibration with Applications","author":"WT Thomson","year":"2018","edition":"4"},{"key":"pcbi.1012599.ref024","volume-title":"Command generation for dynamic systems","author":"W Singhose","year":"2011"},{"key":"pcbi.1012599.ref025","article-title":"The NLopt nonlinear-optimization package","author":"SG Johnson","year":"2007"},{"issue":"2","key":"pcbi.1012599.ref026","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s10957-006-9101-0","article-title":"Some variants of the controlled random search algorithm for global optimization","volume":"130","author":"Dec.","year":"2006","journal-title":"Journal of Optimization Theory and Applications"},{"key":"pcbi.1012599.ref027","volume-title":"Lecture Notes in Control and Information Sciences","author":"R T\u00f3th","year":"2010"},{"issue":"5","key":"pcbi.1012599.ref028","doi-asserted-by":"crossref","first-page":"1750","DOI":"10.1523\/JNEUROSCI.12-05-01750.1992","article-title":"Internal models of limb geometry in the control of hand compliance","volume":"12","author":"F Lacquaniti","year":"1992","journal-title":"Journal of Neuroscience"},{"issue":"4","key":"pcbi.1012599.ref029","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s004220000159","article-title":"Spinal motor control system incorporates an internal model of limb dynamics","volume":"83","author":"YP Shimansky","year":"2000","journal-title":"Biological Cybernetics"},{"issue":"3","key":"pcbi.1012599.ref030","doi-asserted-by":"crossref","first-page":"S266","DOI":"10.1088\/1741-2560\/2\/3\/S09","article-title":"Internal models of limb dynamics and the encoding of limb state","volume":"2","author":"EJ Hwang","year":"2005","journal-title":"Journal of Neural Engineering"},{"issue":"6","key":"pcbi.1012599.ref031","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.cub.2008.02.053","article-title":"Long-latency reflexes of the human arm reflect an internal model of limb dynamics","volume":"18","author":"IL Kurtzer","year":"2008","journal-title":"Current Biology"},{"key":"pcbi.1012599.ref032","first-page":"111","article-title":"Learning to never forget\u2014time scales and specificity of long-term memory of a motor skill","volume":"7","author":"S-W Park","year":"2013","journal-title":"Frontiers in Computational Neuroscience"},{"issue":"1","key":"pcbi.1012599.ref033","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1080\/00222895.1992.9941600","article-title":"Skill acquisition and development: The roles of state-, parameter-, and graph-dynamics","volume":"24","author":"EL Saltzman","year":"1992","journal-title":"Journal of Motor Behavior"},{"issue":"5","key":"pcbi.1012599.ref034","doi-asserted-by":"crossref","first-page":"3208","DOI":"10.1523\/JNEUROSCI.14-05-03208.1994","article-title":"Adaptive representation of dynamics during learning of a motor task","volume":"14","author":"R Shadmehr","year":"1994","journal-title":"Journal of Neuroscience"},{"issue":"5232","key":"pcbi.1012599.ref035","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.1126\/science.7569931","article-title":"An internal model for sensorimotor integration","volume":"269","author":"DM Wolpert","year":"1995","journal-title":"Science"},{"issue":"8","key":"pcbi.1012599.ref036","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1016\/S0893-6080(96)00035-4","article-title":"Forward models for physiological motor control","volume":"9","author":"RC Miall","year":"1996","journal-title":"Neural Networks"},{"issue":"19","key":"pcbi.1012599.ref037","doi-asserted-by":"crossref","first-page":"8573","DOI":"10.1523\/JNEUROSCI.19-19-08573.1999","article-title":"Electromyographic correlates of learning an internal model of reaching movements","volume":"19","author":"KA Thoroughman","year":"1999","journal-title":"Journal of Neuroscience"},{"issue":"7","key":"pcbi.1012599.ref038","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1038\/89477","article-title":"Does the brain model Newton\u2019s laws","volume":"4","author":"J McIntyre","year":"2001","journal-title":"Nature Neuroscience"},{"issue":"2","key":"pcbi.1012599.ref039","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1152\/jn.2002.88.2.942","article-title":"Forward models in visuomotor control","volume":"88","author":"B Mehta","year":"2002","journal-title":"Journal of Neurophysiology"},{"issue":"12","key":"pcbi.1012599.ref040","doi-asserted-by":"crossref","first-page":"4821","DOI":"10.1523\/JNEUROSCI.23-12-04821.2003","article-title":"Generalization of object manipulation skills learned without limb motion","volume":"23","author":"CD Mah","year":"2003","journal-title":"Journal of Neuroscience"},{"issue":"1","key":"pcbi.1012599.ref041","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1007\/s00422-002-0347-9","article-title":"Evidence for a specific internal representation of motion-force relationships during object manipulation","volume":"88","author":"CD Mah","year":"2003","journal-title":"Biological Cybernetics"},{"issue":"1","key":"pcbi.1012599.ref042","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s00422-020-00815-z","article-title":"Establishing metrics and control laws for the learning process: ball and beam balancing","volume":"114","author":"G Buza","year":"2020","journal-title":"Biological Cybernetics"},{"issue":"1","key":"pcbi.1012599.ref043","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1006\/jmps.1999.1280","article-title":"Model selection based on minimum description length","volume":"44","author":"P Gr\u00fcnwald","year":"2000","journal-title":"Journal of Mathematical Psychology"},{"key":"pcbi.1012599.ref044","doi-asserted-by":"crossref","first-page":"e1","DOI":"10.1017\/S0140525X1900061X","article-title":"Resource-rational analysis: Understanding human cognition as the optimal use of limited computational resources","volume":"43","author":"F Lieder","year":"2020","journal-title":"Behavioral and Brain Sciences"},{"issue":"7912","key":"pcbi.1012599.ref045","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1038\/s41586-022-04743-9","article-title":"People construct simplified mental representations to plan","volume":"606","author":"MK Ho","year":"2022","journal-title":"Nature"},{"issue":"4","key":"pcbi.1012599.ref046","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1109\/TRO.2020.2988642","article-title":"TossingBot: Learning to throw arbitrary objects with residual physics","volume":"36","author":"A Zeng","year":"2020","journal-title":"IEEE Transactions on Robotics"},{"key":"pcbi.1012599.ref047","article-title":"Iterative residual policy: For goal-conditioned dynamic manipulation of deformable objects","author":"C Chi","year":"2022","journal-title":"Proceedings of Robotics: Science and Systems (RSS)"},{"issue":"2","key":"pcbi.1012599.ref048","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.arcontrol.2005.08.002","article-title":"An overview of approximation methods for large-scale dynamical systems","volume":"29","author":"AC Antoulas","year":"2005","journal-title":"Annual Reviews in Control"},{"issue":"4","key":"pcbi.1012599.ref049","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1137\/130932715","article-title":"A survey of projection-based model reduction methods for parametric dynamical systems","volume":"57","author":"P Benner","year":"2015","journal-title":"SIAM Review"},{"issue":"11","key":"pcbi.1012599.ref050","doi-asserted-by":"crossref","first-page":"2883","DOI":"10.1523\/JNEUROSCI.5359-07.2008","article-title":"Motor adaptation as a process of reoptimization","volume":"28","author":"J Izawa","year":"2008","journal-title":"Journal of Neuroscience"},{"issue":"2","key":"pcbi.1012599.ref051","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1080\/00140135908930419","article-title":"A theory of the acquisition of speed-skill*","volume":"2","author":"ERFW Crossman","year":"1959","journal-title":"Ergonomics"},{"issue":"11","key":"pcbi.1012599.ref052","doi-asserted-by":"crossref","first-page":"2745","DOI":"10.1523\/JNEUROSCI.04-11-02745.1984","article-title":"An organizing principle for a class of voluntary movements","volume":"4","author":"N Hogan","year":"1984","journal-title":"Journal of Neuroscience"},{"issue":"1","key":"pcbi.1012599.ref053","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1146\/annurev-control-042920-010933","article-title":"Contact and physical interaction","volume":"5","author":"N Hogan","year":"2022","journal-title":"Annual Review of Control, Robotics, and Autonomous"},{"issue":"6862","key":"pcbi.1012599.ref054","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1038\/35106566","article-title":"The central nervous system stabilizes unstable dynamics by learning optimal impedance","volume":"414","author":"E Burdet","year":"2001","journal-title":"Nature"},{"issue":"2","key":"pcbi.1012599.ref055","doi-asserted-by":"crossref","first-page":"e1007414","DOI":"10.1371\/journal.pcbi.1007414","article-title":"Stochastic optimal open-loop control as a theory of force and impedance planning via muscle co-contraction","volume":"16","author":"B Berret","year":"2020","journal-title":"PLoS Computational Biology"},{"issue":"2","key":"pcbi.1012599.ref056","first-page":"65","article-title":"A simple sequentially rejective multiple test procedure","volume":"6","author":"S Holm","year":"1979","journal-title":"Scandinavian Journal of Statistics"},{"key":"pcbi.1012599.ref057","article-title":"R. Core Team. 2021. nlme: linear and nonlinear mixed effects models. R package version 3.1\u2013152","author":"J Pinheiro","year":"2021","journal-title":"Journal of Apicultural Research"},{"issue":"8","key":"pcbi.1012599.ref058","article-title":"emmeans: estimated marginal means, aka least-squares means","volume":"1","author":"RV Lenth","year":"2020","journal-title":"R package version"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1012599","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T00:00:00Z","timestamp":1736467200000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012599","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T20:31:16Z","timestamp":1736541076000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012599"}},"subtitle":[],"editor":[{"given":"Alex Leonidas","family":"Doumas","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2024,11,18]]},"references-count":58,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11,18]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1012599","relation":{"new_version":[{"id-type":"doi","id":"10.1371\/journal.pcbi.1012599","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,18]]}}}