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This has served as inspiration for optimising stiffness in robot arms during manipulation tasks. Endpoint stiffness is modelled in Cartesian space, as though the hand were in independent rigid body. But an arm is a series of rigid bodies connected by articulated joints. The contribution of the joints and arm configuration to the endpoint stiffness has not yet been quantified. In this paper we use mathematical optimisation to find conditions for maximum stiffness and compliance with respect to an externally applied force. By doing so, we can retroactively explain observations made about humans using these mathematically optimal conditions. We then show how this optimisation can be applied to robotic task planning and control. Experiments on a humanoid robot show similar arm posture to that observed in humans. This suggests there is an underlying physical principle by which humans optimise stiffness. 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IEEE; 2012. p. 363\u2013369.","DOI":"10.1109\/HUMANOIDS.2012.6651545"},{"issue":"6","key":"pone.0302987.ref023","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.1109\/TRO.2017.2708087","article-title":"Choosing Poses for Force and Stiffness Control","volume":"33","author":"A Ajoudani","year":"2017","journal-title":"IEEE Transactions on Robotics"},{"issue":"1","key":"pone.0302987.ref024","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1115\/1.1539514","article-title":"Geometric Interpretation of the Derivatives of Parallel Robots\u2019 Jacobian Matrix With Application to Stiffness Control","volume":"125","author":"N Simaan","year":"2003","journal-title":"Journal of Mechanical Design"},{"issue":"7","key":"pone.0302987.ref025","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":"pone.0302987.ref026","doi-asserted-by":"crossref","unstructured":"Pattacini U, Nori F, Natale L, Metta G, Sandini G. An Experimental Evaluation of a Novel Minimum-Jerk Cartesian Controller for Humanoid Robots. In: 2010 IEEE\/RSJ international conference on intelligent robots and systems. IEEE; 2010. p. 1668\u20131674.","DOI":"10.1109\/IROS.2010.5650851"},{"key":"pone.0302987.ref027","doi-asserted-by":"crossref","unstructured":"Matsui D, Minato T, MacDorman KF, Ishiguro H. Generating Natural Motion in an Android by Mapping Human Motion. In: 2005 IEEE\/RSJ International Conference on Intelligent Robots and Systems. 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A New Method of Robotic Rate Control Near Singularities. In: IEEE International Conference on Robotics and Automation. IEEE; 1991. p. 1708\u20131709.","DOI":"10.1109\/ICAR.1991.240619"},{"issue":"2","key":"pone.0302987.ref034","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/0094-114X(95)00069-B","article-title":"Symbolic Differentiation of the Velocity Mapping for a Serial Kinematic Chain","volume":"31","author":"H Bruyninckx","year":"1996","journal-title":"Mechanism and Machine Theory"},{"issue":"4","key":"pone.0302987.ref035","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1249\/01.MSS.0000058435.67376.49","article-title":"The metabolic cost of force generation","volume":"35","author":"BL Sih","year":"2003","journal-title":"Medicine & Science in Sports & Exercise"},{"issue":"2","key":"pone.0302987.ref036","doi-asserted-by":"crossref","first-page":"e2359","DOI":"10.1002\/rcs.2359","article-title":"Proof of Concept Study for Using UR10 Robot to Help Total Hip Replacement","volume":"18","author":"P Walker","year":"2022","journal-title":"The International Journal of Medical Robotics and Computer Assisted Surgery"},{"key":"pone.0302987.ref037","unstructured":"Hawkins K. Analytic Inverse Kinematics for the Universal Robots UR-5\/UR-10 Arms. Georgia Institute of Technology; 2013."},{"key":"pone.0302987.ref038","doi-asserted-by":"crossref","unstructured":"Bruyninckx H, Khatib O. Gauss\u2019 Principle and the Dynamics of Redundant and Constrained Manipulators. In: The International Conference on Robotics and Automation. vol. 3; 2000. p. 2563\u20132568.","DOI":"10.1109\/ROBOT.2000.846414"},{"key":"pone.0302987.ref039","doi-asserted-by":"crossref","unstructured":"Kang H, Freeman R. Joint Torque Optimization of Redundant Manipulators via the Null Space Damping Method. In: IEEE International Conference on Robotics and Automation. IEEE Computer Society; 1992. p. 520\u2013521.","DOI":"10.1109\/ROBOT.1992.220239"},{"key":"pone.0302987.ref040","unstructured":"L\u2019Istituto Italiano di Tecnologia. ergoCub: Ergonomics and Risk Reduction for Future Workers; 2023. https:\/\/ergocub.eu\/."}],"container-title":["PLOS ONE"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0302987","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,20]],"date-time":"2024-11-20T17:12:59Z","timestamp":1732122779000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0302987"}},"subtitle":[],"editor":[{"given":"Imre","family":"Cikajlo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2024,5,29]]},"references-count":40,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,5,29]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0302987","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,29]]}}}