{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T03:37:48Z","timestamp":1777347468816,"version":"3.51.4"},"reference-count":85,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T00:00:00Z","timestamp":1612137600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,2,15]],"date-time":"2021-02-15T00:00:00Z","timestamp":1613347200000},"content-version":"vor","delay-in-days":14,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK 2198\/1"],"award-info":[{"award-number":["GRK 2198\/1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC 2075 - 390740016"],"award-info":[{"award-number":["EXC 2075 - 390740016"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SCHM2392\/5-2"],"award-info":[{"award-number":["SCHM2392\/5-2"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003542","name":"Ministerium f\u00fcr Wissenschaft, Forschung und Kunst Baden-W\u00fcrttemberg","doi-asserted-by":"publisher","award":["Az: 33-7533.-30-20\/7\/2"],"award-info":[{"award-number":["Az: 33-7533.-30-20\/7\/2"]}],"id":[{"id":"10.13039\/501100003542","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Biol Cybern"],"published-print":{"date-parts":[[2021,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A key problem for biological motor control is to establish a link between an idea of a movement and the generation of a set of muscle-stimulating signals that lead to the movement execution. The number of signals to generate is thereby larger than the body\u2019s mechanical degrees of freedom in which the idea of the movement may be easily expressed, as the movement is actually executed in this space. A mathematical formulation that provides a solving link is presented in this paper in the form of a layered, hierarchical control architecture. It is meant to synthesise a wide range of complex three-dimensional muscle-driven movements. The control architecture consists of a \u2018conceptional layer\u2019, where the movement is planned, a \u2018structural layer\u2019, where the muscles are stimulated, and between both an additional \u2018transformational layer\u2019, where the muscle-joint redundancy is resolved. We demonstrate the operativeness by simulating human stance and squatting in a three-dimensional digital human model (DHM). The DHM considers 20 angular DoFs and 36 Hill-type muscle\u2013tendon units (MTUs) and is exposed to gravity, while its feet contact the ground via reversible stick\u2013slip interactions. The control architecture continuously stimulates all MTUs (\u2018structural layer\u2019) based on a high-level, torque-based task formulation within its \u2018conceptional layer\u2019. Desired states of joint angles (postural plan) are fed to two mid-level joint controllers in the \u2018transformational layer\u2019. The \u2018transformational layer\u2019 communicates with the biophysical structures in the \u2018structural layer\u2019 by providing direct MTU stimulation contributions and further input signals for low-level MTU controllers. Thereby, the redundancy of the MTU stimulations with respect to the joint angles is resolved, i.e. a link between plan and execution is established, by exploiting some properties of the biophysical structures modelled. The resulting joint torques generated by the MTUs via their moment arms are fed back to the conceptional layer, closing the high-level control loop. Within our mathematical formulations of the Jacobian matrix-based layer transformations, we identify the crucial information for the redundancy solution to be the muscle moment arms, the stiffness relations of muscle and tendon tissue within the muscle model, and the length\u2013stimulation relation of the muscle activation dynamics. The present control architecture allows the straightforward feeding of conceptional movement task formulations to MTUs. With this approach, the problem of movement planning is eased, as solely the mechanical system has to be considered in the conceptional plan.\n<\/jats:p>","DOI":"10.1007\/s00422-020-00856-4","type":"journal-article","created":{"date-parts":[[2021,2,18]],"date-time":"2021-02-18T21:14:20Z","timestamp":1613682860000},"page":"7-37","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A geometry- and muscle-based control architecture for synthesising biological movement"],"prefix":"10.1007","volume":"115","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3705-2536","authenticated-orcid":false,"given":"Johannes R.","family":"Walter","sequence":"first","affiliation":[]},{"given":"Michael","family":"G\u00fcnther","sequence":"additional","affiliation":[]},{"given":"Daniel F. B.","family":"Haeufle","sequence":"additional","affiliation":[]},{"given":"Syn","family":"Schmitt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,15]]},"reference":[{"issue":"6","key":"856_CR1","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/PL00007986","volume":"84","author":"AV Alexandrov","year":"2001","unstructured":"Alexandrov AV, Frolov AA, Massion J (2001) Biomechanical analysis of movement strategies in human forward trunk bending I. Modeling. Biol Cybern 84(6):425\u2013434","journal-title":"Biol Cybern"},{"issue":"1","key":"856_CR2","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/S0022-5193(85)80120-X","volume":"112","author":"MA Arbib","year":"1985","unstructured":"Arbib MA, Amari S-I (1985) Sensori-motor transformations in the brain (with a critique of the tensor theory of cerebellum). J Theor Biol 112(1):123\u2013155","journal-title":"J Theor Biol"},{"issue":"8","key":"856_CR3","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1080\/10255842.2017.1293663","volume":"20","author":"A Bayer","year":"2017","unstructured":"Bayer A, Schmitt S, G\u00fcnther M, Haeufle DF (2017) The influence of biophysical muscle properties on simulating fast human arm movements. Comput Methods Biomech Biomed Eng 20(8):803\u2013821","journal-title":"Comput Methods Biomech Biomed Eng"},{"key":"856_CR4","volume-title":"The co-ordination and regulation of movements","author":"NA Bernstein","year":"1967","unstructured":"Bernstein NA (1967) The co-ordination and regulation of movements. Pergamon Press, Oxford"},{"issue":"4","key":"856_CR5","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1017\/S0140525X00072538","volume":"15","author":"E Bizzi","year":"1992","unstructured":"Bizzi E, Hogan N, Mussa-Ivaldo F, Giszter S (1992) Does the nervous system use equilibrium-point control to guide single and multiple joint movements? Behav Brain Sci 15(4):603\u2013613","journal-title":"Behav Brain Sci"},{"issue":"5","key":"856_CR6","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1162\/089892999563607","volume":"11","author":"S-J Blakemore","year":"1999","unstructured":"Blakemore S-J, Frith CD, Wolpert DM (1999) Spatio-temporal prediction modulates the perception of self-produced stimuli. J Cogn Neurosci 11(5):551\u2013559","journal-title":"J Cogn Neurosci"},{"issue":"4","key":"856_CR7","doi-asserted-by":"publisher","first-page":"1139","DOI":"10.1007\/s00285-019-01455-z","volume":"80","author":"S Br\u00e4ndle","year":"2020","unstructured":"Br\u00e4ndle S, Schmitt S, M\u00fcller MA (2020) A systems-theoretic analysis of low-level human motor control: application to a single-joint arm model. J Math Biol 80(4):1139\u20131158","journal-title":"J Math Biol"},{"issue":"1","key":"856_CR8","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1152\/jn.00961.2010","volume":"107","author":"CJ de Luca","year":"2012","unstructured":"de Luca CJ, Contessa P (2012) Hierarchical control of motor units in voluntary contractions. J Neurophysiol 107(1):178\u2013195","journal-title":"J Neurophysiol"},{"issue":"2","key":"856_CR9","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/BF00228972","volume":"86","author":"S De Serres","year":"1991","unstructured":"De Serres S, Milner T (1991) Wrist muscle activation patterns and stiffness associated with stable and unstable mechanical loads. Exp Brain Res 86(2):451\u2013458","journal-title":"Exp Brain Res"},{"issue":"6","key":"856_CR10","doi-asserted-by":"publisher","first-page":"065009","DOI":"10.1088\/1741-2560\/8\/6\/065009","volume":"8","author":"T DeWolf","year":"2011","unstructured":"DeWolf T, Eliasmith C (2011) The neural optimal control hierarchy for motor control. J Neural Eng 8(6):065009","journal-title":"J Neural Eng"},{"issue":"6","key":"856_CR11","doi-asserted-by":"publisher","first-page":"732","DOI":"10.1016\/S0959-4388(00)00153-7","volume":"10","author":"K Doya","year":"2000","unstructured":"Doya K (2000) Complementary roles of basal ganglia and cerebellum in learning and motor control. Curr Opin Neurobiol 10(6):732\u2013739","journal-title":"Curr Opin Neurobiol"},{"issue":"3","key":"856_CR12","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1016\/j.gaitpost.2006.05.009","volume":"25","author":"WT Edwards","year":"2007","unstructured":"Edwards WT (2007) Effect of joint stiffness on standing stability. Gait Posture 25(3):432\u2013439","journal-title":"Gait Posture"},{"issue":"2","key":"856_CR13","first-page":"766","volume":"19","author":"A Feldman","year":"1974","unstructured":"Feldman A (1974) Control of the length of a muscle. Biophysics 19(2):766\u2013771","journal-title":"Biophysics"},{"issue":"2","key":"856_CR14","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1113\/jphysiol.1977.sp011911","volume":"269","author":"L Ford","year":"1977","unstructured":"Ford L, Huxley A, Simmons R (1977) Tension responses to sudden length change in stimulated frog muscle fibres near slack length. J Physiol 269(2):441\u2013515","journal-title":"J Physiol"},{"issue":"Pt 23","key":"856_CR15","doi-asserted-by":"publisher","first-page":"3325","DOI":"10.1242\/jeb.202.23.3325","volume":"202","author":"R Full","year":"1999","unstructured":"Full R, Koditschek D (1999) Templates and anchors: neuromechanical hypotheses of legged locomotion on land. J Exp Biol 202(Pt 23):3325\u20133332","journal-title":"J Exp Biol"},{"issue":"5","key":"856_CR16","doi-asserted-by":"publisher","first-page":"eaaq0183","DOI":"10.1126\/sciadv.aaq0183","volume":"4","author":"G Ganesh","year":"2018","unstructured":"Ganesh G, Nakamura K, Saetia S, Tobar AM, Yoshida E, Ando H, Yoshimura N, Koike Y (2018) Utilizing sensory prediction errors for movement intention decoding: a new methodology. Sci Adv 4(5):eaaq0183","journal-title":"Sci Adv"},{"issue":"5261","key":"856_CR17","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1126\/science.272.5261.545","volume":"272","author":"J-H Gao","year":"1996","unstructured":"Gao J-H, Parsons LM, Bower JM, Xiong J, Li J, Fox PT (1996) Cerebellum implicated in sensory acquisition and discrimination rather than motor control. Science 272(5261):545\u2013547","journal-title":"Science"},{"issue":"2","key":"856_CR18","doi-asserted-by":"publisher","first-page":"774","DOI":"10.1152\/jn.00257.2010","volume":"104","author":"R Gentili","year":"2010","unstructured":"Gentili R, Han CE, Schweighofer N, Papaxanthis C (2010) Motor learning without doing: trial-by-trial improvement in motor performance during mental training. J Neurophysiol 104(2):774\u2013783","journal-title":"J Neurophysiol"},{"key":"856_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-20621-5","volume-title":"Morphological Intelligence","author":"K Ghazi-Zahedi","year":"2019","unstructured":"Ghazi-Zahedi K (2019) Morphological Intelligence. Springer, Berlin"},{"issue":"5","key":"856_CR20","doi-asserted-by":"publisher","first-page":"2396","DOI":"10.1152\/jn.01020.2002","volume":"89","author":"P Gribble","year":"2003","unstructured":"Gribble P, Mullin L, Cothros N, Mattar A (2003) Role of cocontraction in arm movement accuracy. J Neurophysiol 89(5):2396\u20132405","journal-title":"J Neurophysiol"},{"issue":"3","key":"856_CR21","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.1152\/jn.1998.79.3.1409","volume":"79","author":"P Gribble","year":"1998","unstructured":"Gribble P, Ostry D, Sanguineti V, Laboissi\u00e8re R (1998) Are complex control signals required for human arm movement? J Neurophysiol 79(3):1409\u20131424","journal-title":"J Neurophysiol"},{"key":"856_CR22","unstructured":"Guennebaud G, Jacob B et al (2010) Eigen v3. http:\/\/eigen.tuxfamily.org"},{"key":"856_CR23","unstructured":"G\u00fcnther M (1997) Computersimulationen zur Synthetisierung des muskul\u00e4r erzeugten menschlichen Gehens unter Verwendung eines biomechanischen Mehrk\u00f6rpermodells. Ph.D. thesis, Eberhard-Karls-Universit\u00e4t, T\u00fcbingen, Germany"},{"key":"856_CR24","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/j.jtbi.2018.07.023","volume":"456","author":"M G\u00fcnther","year":"2018","unstructured":"G\u00fcnther M, Haeufle DFB, Schmitt S (2018) The basic mechanical structure of the skeletal muscle machinery: one model for linking microscopic and macroscopic scales. J Theor Biol 456:137\u2013167 [with Corrigendum]","journal-title":"J Theor Biol"},{"issue":"3","key":"856_CR25","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s00419-010-0414-y","volume":"81","author":"M G\u00fcnther","year":"2011","unstructured":"G\u00fcnther M, M\u00fcller O, Blickhan R (2011) Watching quiet human stance to shake off its straitjacket. Arch Appl Mech 81(3):283\u2013302","journal-title":"Arch Appl Mech"},{"issue":"3","key":"856_CR26","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s00419-011-0559-3","volume":"82","author":"M G\u00fcnther","year":"2012","unstructured":"G\u00fcnther M, M\u00fcller O, Blickhan R (2012) What does head movement tell about the minimum number of mechanical degrees of freedom in quiet human stance? Arch Appl Mech 82(3):333\u2013344","journal-title":"Arch Appl Mech"},{"issue":"2","key":"856_CR27","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s00422-003-0414-x","volume":"89","author":"M G\u00fcnther","year":"2003","unstructured":"G\u00fcnther M, Ruder H (2003) Synthesis of two-dimensional human walking: a test of the $$\\lambda $$-model. Biol Cybern 89(2):89\u2013106","journal-title":"Biol Cybern"},{"issue":"8","key":"856_CR28","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1080\/10255842.2015.1067306","volume":"19","author":"M G\u00fcnther","year":"2016","unstructured":"G\u00fcnther M, Wagner H (2016) Dynamics of quiet human stance: computer simulations of a triple inverted pendulum model. Comput Methods Biomech Biomed Eng 19(8):819\u2013834","journal-title":"Comput Methods Biomech Biomed Eng"},{"issue":"2","key":"856_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12311-019-01095-5","volume":"19","author":"C Habas","year":"2020","unstructured":"Habas C, Bertholz A, Flash T, Bennequin D (2020) Does the cerebellum implement or select geometries? A speculative note. The Cerebellum 19(2):1\u20137","journal-title":"The Cerebellum"},{"issue":"6","key":"856_CR30","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1016\/j.jbiomech.2014.02.009","volume":"47","author":"DFB Haeufle","year":"2014","unstructured":"Haeufle DFB, G\u00fcnther M, Bayer A, Schmitt S (2014a) Hill-type muscle model with serial damping and eccentric force\u2013velocity relation. J Biomech 47(6):1531\u20131536","journal-title":"J Biomech"},{"issue":"1","key":"856_CR31","doi-asserted-by":"publisher","first-page":"012716","DOI":"10.1103\/PhysRevE.89.012716","volume":"89","author":"DFB Haeufle","year":"2014","unstructured":"Haeufle DFB, G\u00fcnther M, Wunner G, Schmitt S (2014b) Quantifying control effort of biological and technical movements: an information-entropy-based approach. Phys Rev E 89(1):012716","journal-title":"Phys Rev E"},{"key":"856_CR32","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.mbs.2019.02.004","volume":"311","author":"M Hammer","year":"2019","unstructured":"Hammer M, G\u00fcnther M, Haeufle D, Schmitt S (2019) Tailoring anatomical muscle paths: a sheath-like solution for muscle routing in musculo-skeletal computer models. Math Biosci 311:68\u201381","journal-title":"Math Biosci"},{"issue":"2","key":"856_CR33","first-page":"215","volume":"77","author":"RS Hartenberg","year":"1955","unstructured":"Hartenberg RS, Denavit J (1955) A kinematic notation for lower pair mechanisms based on matrices. J Appl Mech 77(2):215\u2013221","journal-title":"J Appl Mech"},{"issue":"2","key":"856_CR34","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/BF00337268","volume":"25","author":"H Hatze","year":"1977","unstructured":"Hatze H (1977) A myocybernetic control model of skeletal muscle. Biol Cybern 25(2):103\u2013119","journal-title":"Biol Cybern"},{"key":"856_CR35","unstructured":"Henze A (2002) Dreidimensionale biomechanische Modellierung und die Entwicklung eines Reglers zur Simulation zweibeinigen Gehens. Ph.D. thesis, Eberhard-Karls-Universit\u00e4t, T\u00fcbingen, Germany"},{"issue":"2","key":"856_CR36","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.tics.2013.10.015","volume":"18","author":"DJ Herzfeld","year":"2014","unstructured":"Herzfeld DJ, Shadmehr R (2014) Cerebellum estimates the sensory state of the body. Trends Cognit Sci 18(2):66\u201367","journal-title":"Trends Cognit Sci"},{"key":"856_CR37","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/978-1-4613-9030-5_9","volume-title":"Multiple muscle systems","author":"N Hogan","year":"1990","unstructured":"Hogan N (1990) Chapter 9: Mechanical impedance of single- and multi-articular systems. In: Winters JM, Woo SL-Y (eds) Multiple muscle systems. Springer, Berlin, pp 149\u2013164"},{"issue":"2","key":"856_CR38","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1137\/S0036144504445133","volume":"48","author":"P Holmes","year":"2006","unstructured":"Holmes P, Full R, Koditschek D, Guckenheimer J (2006) The dynamics of legged locomotion: models, analyses, and challenges. SIAM Rev 48(2):207\u2013304","journal-title":"SIAM Rev"},{"issue":"4","key":"856_CR39","doi-asserted-by":"publisher","first-page":"844","DOI":"10.1016\/j.humov.2011.07.017","volume":"31","author":"W-L Hsu","year":"2012","unstructured":"Hsu W-L, Scholz JP (2012) Motor abundance supports multitasking while standing. Hum Mov Sci 31(4):844\u2013862","journal-title":"Hum Mov Sci"},{"key":"856_CR40","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0079-6123(08)62202-5","volume":"80","author":"M Hulliger","year":"1989","unstructured":"Hulliger M, D\u00fcrm\u00fcller N, Prochazka A, Trend P (1989) Flexible fusimotor control of muscle spindle feedback during a variety of natural movements. Prog Brain Res 80:87\u2013101","journal-title":"Prog Brain Res"},{"issue":"4","key":"856_CR41","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1038\/nrn.2016.9","volume":"17","author":"O Kiehn","year":"2016","unstructured":"Kiehn O (2016) Decoding the organization of spinal circuits that control locomotion. Nat Rev Neurosci 17(4):224\u2013238","journal-title":"Nat Rev Neurosci"},{"issue":"5","key":"856_CR42","doi-asserted-by":"publisher","first-page":"2898","DOI":"10.1152\/jn.00983.2005","volume":"95","author":"DA Kistemaker","year":"2006","unstructured":"Kistemaker DA, van Soest AJ, Bobbert MF (2006) Is equilibrium point control feasible for fast goal-directed single-joint movements? J Neurophysiol 95(5):2898\u20132912","journal-title":"J Neurophysiol"},{"issue":"3","key":"856_CR43","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s00422-006-0120-6","volume":"96","author":"DA Kistemaker","year":"2007","unstructured":"Kistemaker DA, van Soest AJ, Bobbert MF (2007) A model of open-loop control of equilibrium position and stiffness of the human elbow joint. Biol Cybern 96(3):341\u2013350","journal-title":"Biol Cybern"},{"issue":"3","key":"856_CR44","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda TG, Bader BW (2009) Tensor decompositions and applications. SIAM Rev 51(3):455\u2013500","journal-title":"SIAM Rev"},{"issue":"1","key":"856_CR45","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00221-012-3000-4","volume":"217","author":"ML Latash","year":"2012","unstructured":"Latash ML (2012) The bliss (not the problem) of motor abundance (not redundancy). Exp Brain Res 217(1):1\u20135","journal-title":"Exp Brain Res"},{"issue":"1","key":"856_CR46","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1097\/00003677-200201000-00006","volume":"30","author":"ML Latash","year":"2002","unstructured":"Latash ML, Scholz JP, Sch\u00f6ner G (2002) Motor control strategies revealed in the structure of motor variability. Exerc Sport Sci Rev 30(1):26\u201331","journal-title":"Exerc Sport Sci Rev"},{"issue":"5","key":"856_CR47","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1016\/0094-114X(95)00101-4","volume":"31","author":"G Legnani","year":"1996","unstructured":"Legnani G, Casalo F, Righettini P, Zappa B (1996) A homogeneous matrix approach to 3d kinematics and dynamics - II. Applications to chains of rigid bodies and serial manipulators. Mech Mach Theory 31(5):589\u2013605","journal-title":"Mech Mach Theory"},{"issue":"5","key":"856_CR48","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1016\/0094-114X(95)00100-D","volume":"31","author":"G Legnani","year":"1996","unstructured":"Legnani G, Casolo F, Righettini P, Zappa B (1996b) A homogeneous matrix approach to 3d kinematics and dynamics\u2014I. Theory. Mech Mach Theory 31(5):573\u2013587","journal-title":"Mech Mach Theory"},{"issue":"2","key":"856_CR49","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1177\/1073858404270843","volume":"11","author":"JH Martin","year":"2005","unstructured":"Martin JH (2005) The corticospinal system: from development to motor control. Neuroscientist 11(2):161\u2013173","journal-title":"Neuroscientist"},{"issue":"3","key":"856_CR50","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1113\/jphysiol.1959.sp006261","volume":"147","author":"P Matthews","year":"1959","unstructured":"Matthews P (1959) A study of certain factors influencing the stretch reflex of the decerebrate cat. J Physiol 147(3):547","journal-title":"J Physiol"},{"issue":"3","key":"856_CR51","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1080\/00222895.1993.9942049","volume":"25","author":"J McIntyre","year":"1993","unstructured":"McIntyre J, Bizzi E (1993) Servo hypotheses for the biological control of movement. J Mot Behav 25(3):193\u2013202","journal-title":"J Mot Behav"},{"issue":"1","key":"856_CR52","doi-asserted-by":"publisher","first-page":"5489","DOI":"10.1038\/s41467-019-13239-6","volume":"10","author":"J Merel","year":"2019","unstructured":"Merel J, Botvinick M, Wayne G (2019) Hierarchical motor control in mammals and machines. Nat Commun 10(1):5489","journal-title":"Nat Commun"},{"issue":"4","key":"856_CR53","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1007\/s00221-002-1001-4","volume":"143","author":"T Milner","year":"2002","unstructured":"Milner T (2002) Adaptation to destabilizing dynamics by means of muscle cocontraction. Exp Brain Res 143(4):406\u2013416","journal-title":"Exp Brain Res"},{"issue":"2","key":"856_CR54","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/BF00230049","volume":"107","author":"T Milner","year":"1995","unstructured":"Milner T, Cloutier C, Leger A, Franklin D (1995) Inability to activate muscles maximally during cocontraction and the effect on joint stiffness. Exp Brain Res 107(2):293\u2013305","journal-title":"Exp Brain Res"},{"key":"856_CR55","doi-asserted-by":"crossref","unstructured":"M\u00f6rl F, G\u00f6nther M, Riede JM, Hammer M, Schmitt S (2020) Loads distributed in vivo among vertebrae, muscles, spinal ligaments, and intervertebral discs in a passively flexed lumbar spine. Biomech Model Mechanobiol 19(6):2015\u20132047","DOI":"10.1007\/s10237-020-01322-7"},{"key":"856_CR56","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.neures.2015.10.013","volume":"104","author":"E Naito","year":"2016","unstructured":"Naito E, Morita T, Amemiya K (2016) Body representations in the human brain revealed by kinesthetic illusions and their essential contributions to motor control and corporeal awareness. Neurosci Res 104:16\u201330","journal-title":"Neurosci Res"},{"issue":"6","key":"856_CR57","doi-asserted-by":"publisher","first-page":"870","DOI":"10.1109\/70.976014","volume":"17","author":"JH Park","year":"2001","unstructured":"Park JH (2001) Impedance control for biped robot locomotion. IEEE Trans Robot Autom 17(6):870\u2013882","journal-title":"IEEE Trans Robot Autom"},{"issue":"2","key":"856_CR58","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/0306-4522(85)90001-6","volume":"16","author":"A Pellionisz","year":"1985","unstructured":"Pellionisz A, Llin\u00e1s RR (1985) Tensor network theory of the metaorganization of functional geometries in the central nervous system. Neuroscience 16(2):245\u2013273","journal-title":"Neuroscience"},{"issue":"5","key":"856_CR59","doi-asserted-by":"publisher","first-page":"1966","DOI":"10.1016\/S0006-3495(95)80374-7","volume":"68","author":"G Piazzesi","year":"1995","unstructured":"Piazzesi G, Lombardi V (1995) A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle. Biophys J 68(5):1966\u20131979","journal-title":"Biophys J"},{"issue":"8","key":"856_CR60","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1007\/s00422-012-0505-7","volume":"106","author":"IJ Pinter","year":"2012","unstructured":"Pinter IJ, van Soest AJ, Bobbert MF, Smeets JBJ (2012) Conclusions on motor control depend on the type of model used to represent the periphery. Biol Cybern 106(8):441\u2013451","journal-title":"Biol Cybern"},{"key":"856_CR61","doi-asserted-by":"crossref","unstructured":"Pratt J, Dilworth P, Pratt G (1997) Virtual model control of a bipedal walking robot. In: Proceedings of the international conference on robotics and automation, vol 1. IEEE, pp 193\u2013198","DOI":"10.1109\/ROBOT.1997.620037"},{"key":"856_CR62","doi-asserted-by":"crossref","unstructured":"Pratt J, Pratt G (1998) Intuitive control of a planar bipedal walking robot. In: Proceedings of the international conference on robotics and automation, vol\u00a03. IEEE, pp 2014\u20132021","DOI":"10.1109\/ROBOT.1998.680611"},{"issue":"1","key":"856_CR63","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1177\/105971239900700105","volume":"7","author":"TJ Prescott","year":"1999","unstructured":"Prescott TJ, Redgrave P, Gurney K (1999) Layered control architectures in robots and vertebrates. Adapt Behav 7(1):99\u2013127","journal-title":"Adapt Behav"},{"key":"856_CR64","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.jtbi.2017.07.023","volume":"431","author":"R Rockenfeller","year":"2017","unstructured":"Rockenfeller R, G\u00fcnther M (2017) Hill equation and Hatze\u2019s muscle activation dynamics complement each other: enhanced pharmacological and physiological interpretability of modelled activity-pCa curves. J Theor Biol 431:11\u201324","journal-title":"J Theor Biol"},{"key":"856_CR65","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1016\/j.jtbi.2018.06.009","volume":"454","author":"R Rockenfeller","year":"2018","unstructured":"Rockenfeller R, G\u00fcnther M (2018) Inter-filament spacing mediates calcium binding to troponin: a simple geometric-mechanistic model explains the shift of force-length maxima with muscle activation. J Theor Biol 454:240\u2013252","journal-title":"J Theor Biol"},{"key":"856_CR66","doi-asserted-by":"publisher","first-page":"585409","DOI":"10.1155\/2015\/585409","volume":"2015","author":"R Rockenfeller","year":"2015","unstructured":"Rockenfeller R, G\u00fcnther M, Schmitt S, G\u00f6tz T (2015) Comparative sensitivity analysis of muscle activation dynamics. Comput Math Methods Med 2015:585409 [with Corrigendum]","journal-title":"Comput Math Methods Med"},{"key":"856_CR67","unstructured":"Rozendaal LA, van Soest AJ (2005) Joint stiffness requirements in a multi-segment stance model. In: Proceedings of the XXth congress of the ISB, Cleveland, Ohio, p 622"},{"issue":"5","key":"856_CR68","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1007\/s10237-015-0656-2","volume":"14","author":"T Rupp","year":"2015","unstructured":"Rupp T, Ehlers W, Karajan N, G\u00fcnther M, Schmitt S (2015) A forward dynamics simulation of human lumbar spine flexion predicting the load sharing of intervertebral discs, ligaments, and muscles. Biomech Model Mechanobiol 14(5):1081\u20131105","journal-title":"Biomech Model Mechanobiol"},{"issue":"3","key":"856_CR69","doi-asserted-by":"publisher","first-page":"e201900013","DOI":"10.1002\/gamm.201900013","volume":"42","author":"S Schmitt","year":"2019","unstructured":"Schmitt S, G\u00fcnther M, Haeufle DFB (2019) The dynamics of the skeletal muscle: a systems biophysics perspective on muscle modeling with the focus on Hill-type muscle models. GAMM-Mitteilungen 42(3):e201900013","journal-title":"GAMM-Mitteilungen"},{"issue":"3","key":"856_CR70","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/s002210050738","volume":"126","author":"JP Scholz","year":"1999","unstructured":"Scholz JP, Sch\u00f6ner G (1999) The uncontrolled manifold concept: identifying control variables for a functional task. Exp Brain Res 126(3):289\u2013306","journal-title":"Exp Brain Res"},{"key":"856_CR71","volume-title":"Computer solution of ordinary differential equations: the initial value problem","author":"L Shampine","year":"1975","unstructured":"Shampine L, Gordon M (1975) Computer solution of ordinary differential equations: the initial value problem. W.H. Freeman & Co., San Francisco"},{"key":"856_CR72","doi-asserted-by":"crossref","unstructured":"Sherman MA, Seth A, Delp SL (2013) What is a moment arm? Calculating muscle effectiveness in biomechanical models using generalized coordinates. In: 9th international conference on multibody systems, nonlinear dynamics, and control, vol\u00a07B. pp DETC2013\u201313633","DOI":"10.1115\/DETC2013-13633"},{"issue":"4","key":"856_CR73","first-page":"545","volume":"91","author":"JW Smith","year":"1957","unstructured":"Smith JW (1957) The forces operating at the human ankle joint during standing. J Anat 91(4):545\u201364","journal-title":"J Anat"},{"key":"856_CR74","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/j.jbiomech.2019.01.017","volume":"85","author":"D Stanev","year":"2019","unstructured":"Stanev D, Moustakas K (2019) Stiffness modulation of redundant musculoskeletal systems. J Biomech 85:101\u2013107","journal-title":"J Biomech"},{"key":"856_CR75","doi-asserted-by":"publisher","first-page":"308","DOI":"10.3389\/fbioe.2020.00308","volume":"8","author":"K Stollenmaier","year":"2020","unstructured":"Stollenmaier K, Ilg W, Haeufle DFB (2020) Predicting perturbed human arm movements in a neuro-musculoskeletal model to investigate the muscular force response. Front Bioeng Biotechnol 8:308","journal-title":"Front Bioeng Biotechnol"},{"issue":"1","key":"856_CR76","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1049\/iet-cta:20070435","volume":"3","author":"S Tarbouriech","year":"2009","unstructured":"Tarbouriech S, Turner M (2009) Anti-windup design: an overview of some recent advances and open problems. IET Control Theory Appl 3(1):1\u201319","journal-title":"IET Control Theory Appl"},{"issue":"11","key":"856_CR77","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1002\/rob.20093","volume":"22","author":"E Todorov","year":"2005","unstructured":"Todorov E, Li W, Pan X (2005) From task parameters to motor synergies: a hierarchical framework for approximately optimal control of redundant manipulators. J Robot Syst 22(11):691\u2013710","journal-title":"J Robot Syst"},{"issue":"2","key":"856_CR78","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1038\/5721","volume":"2","author":"MC Tresch","year":"1999","unstructured":"Tresch MC, Saltiel P, Bizzi E (1999) The construction of movement by the spinal cord. Nat Neurosci 2(2):162\u2013167","journal-title":"Nat Neurosci"},{"issue":"1","key":"856_CR79","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1152\/jn.00266.2007","volume":"98","author":"Y-W Tseng","year":"2007","unstructured":"Tseng Y-W, Diedrichsen J, Krakauer JW, Shadmehr R, Bastian AJ (2007) Sensory prediction errors drive cerebellum-dependent adaptation of reaching. J Neurophysiol 98(1):54\u201362","journal-title":"J Neurophysiol"},{"issue":"3","key":"856_CR80","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/BF00198959","volume":"69","author":"AJ van Soest","year":"1993","unstructured":"van Soest AJ, Bobbert MF (1993) The contribution of muscle properties in the control of explosive movements. Biol Cybern 69(3):195\u2013204","journal-title":"Biol Cybern"},{"key":"856_CR81","volume-title":"Cybernetics, or control and communication in the animal and the machine","author":"N Wiener","year":"1948","unstructured":"Wiener N (1948) Cybernetics, or control and communication in the animal and the machine. Technology Press, London"},{"issue":"7","key":"856_CR82","doi-asserted-by":"publisher","first-page":"1317","DOI":"10.1016\/S0893-6080(98)00066-5","volume":"11","author":"D Wolpert","year":"1998","unstructured":"Wolpert D, Kawato M (1998) Multiple paired forward and inverse models for motor control. Neural Netw 11(7):1317\u20131329","journal-title":"Neural Netw"},{"issue":"6","key":"856_CR83","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/S1364-6613(97)01070-X","volume":"1","author":"DM Wolpert","year":"1997","unstructured":"Wolpert DM (1997) Computational approaches to motor control. Trends Cogn Sci 1(6):209\u2013216","journal-title":"Trends Cogn Sci"},{"issue":"1431","key":"856_CR84","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1098\/rstb.2002.1238","volume":"358","author":"DM Wolpert","year":"2003","unstructured":"Wolpert DM, Doya K, Kawato M (2003) A unifying computational framework for motor control and social interaction. Philos Trans R Soc Lond Ser B Biol Sci 358(1431):593\u2013602","journal-title":"Philos Trans R Soc Lond Ser B Biol Sci"},{"issue":"18","key":"856_CR85","doi-asserted-by":"publisher","first-page":"R729","DOI":"10.1016\/S0960-9822(01)00432-8","volume":"11","author":"DM Wolpert","year":"2001","unstructured":"Wolpert DM, Flanagan JR (2001) Motor prediction. Curr Biol 11(18):R729\u2013R732","journal-title":"Curr Biol"}],"updated-by":[{"DOI":"10.1007\/s00422-021-00869-7","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T00:00:00Z","timestamp":1616457600000}}],"container-title":["Biological Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00422-020-00856-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00422-020-00856-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00422-020-00856-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,29]],"date-time":"2023-01-29T09:06:26Z","timestamp":1674983186000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00422-020-00856-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2]]},"references-count":85,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,2]]}},"alternative-id":["856"],"URL":"https:\/\/doi.org\/10.1007\/s00422-020-00856-4","relation":{"correction":[{"id-type":"doi","id":"10.1007\/s00422-021-00869-7","asserted-by":"object"}]},"ISSN":["0340-1200","1432-0770"],"issn-type":[{"value":"0340-1200","type":"print"},{"value":"1432-0770","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2]]},"assertion":[{"value":"12 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 December 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 February 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2021","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s00422-021-00869-7","URL":"https:\/\/doi.org\/10.1007\/s00422-021-00869-7","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"We have no conflicts of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interests"}},{"value":"The code of our mechanics engine <i>demoa<\/i> is available on request.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}}]}}