{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:44:44Z","timestamp":1760240684881,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2019,8,2]],"date-time":"2019-08-02T00:00:00Z","timestamp":1564704000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish Government Projects","award":["DPI2014-57220-C2-1-P","PGC2018-095939-B-I00"],"award-info":[{"award-number":["DPI2014-57220-C2-1-P","PGC2018-095939-B-I00"]}]},{"name":"RoboCity2030 DIH-CM Madrid Robotics Digital Innovation Hub","award":["S2018\/NMT-4331"],"award-info":[{"award-number":["S2018\/NMT-4331"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Cable-driven parallel robots with a redundant configuration have infinite solutions for their cable tension distribution to provide a specific wrench to the end-effector. Redundancy is commonly used to increase the workspace and stiffness or to achieve secondary objectives like energetic minimization or additional movements. This article presents a method based on energy distribution to handle the redundancy of cable-driven parallel robots. This method allows the deformation and tension of each link to be related to the total energy available in the parallel robot. The study of energy distribution expression allows deformation, tension, and position to be combined. It also defines the range of tension and deformation that cables can achieve without altering the wrench exerted on the end-effector. This range is used with a passive reconfigurable end-effector to control the position of two grippers attached to some cables which act as compliant actuators. The relationship between the actuators\u2019 energy and their corresponding gripper positions is also provided. In this way, energy measurement from the actuators allows the grasping state to be sensed. The results are validated using multibody dynamic software.<\/jats:p>","DOI":"10.3390\/s19153403","type":"journal-article","created":{"date-parts":[[2019,8,2]],"date-time":"2019-08-02T11:58:16Z","timestamp":1564747096000},"page":"3403","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Potential Energy Distribution of Redundant Cable-Driven Robot Applied to Compliant Grippers: Method and Computational Analysis"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9710-7810","authenticated-orcid":false,"given":"Alejandro","family":"Rodriguez-Barroso","sequence":"first","affiliation":[{"name":"Centro de Autom\u00e1tica y Rob\u00f3tica, Universidad Polit\u00e9cnica de Madrid, C\/Jos\u00e9 Guti\u00e9rrez Abascal 2, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8009-5350","authenticated-orcid":false,"given":"Roque","family":"Saltaren","sequence":"additional","affiliation":[{"name":"Centro de Autom\u00e1tica y Rob\u00f3tica, Universidad Polit\u00e9cnica de Madrid, C\/Jos\u00e9 Guti\u00e9rrez Abascal 2, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4287-0800","authenticated-orcid":false,"given":"Gerardo","family":"A. Portilla","sequence":"additional","affiliation":[{"name":"Centro de Autom\u00e1tica y Rob\u00f3tica, Universidad Polit\u00e9cnica de Madrid, C\/Jos\u00e9 Guti\u00e9rrez Abascal 2, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3348-0533","authenticated-orcid":false,"given":"Juan","family":"S. Cely","sequence":"additional","affiliation":[{"name":"Centro de Autom\u00e1tica y Rob\u00f3tica, Universidad Polit\u00e9cnica de Madrid, C\/Jos\u00e9 Guti\u00e9rrez Abascal 2, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0934-6943","authenticated-orcid":false,"given":"Oz","family":"Yakrangi","sequence":"additional","affiliation":[{"name":"Centro de Autom\u00e1tica y Rob\u00f3tica, Universidad Polit\u00e9cnica de Madrid, C\/Jos\u00e9 Guti\u00e9rrez Abascal 2, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1002\/rob.4620100509","article-title":"The NIST robocrane","volume":"10","author":"Albus","year":"1993","journal-title":"J. Robot. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1109\/MMM.2018.2802178","article-title":"FAST in Space: Considerations for a Multibeam, Multipurpose Survey Using China\u2019s 500-m Aperture Spherical Radio Telescope (FAST)","volume":"19","author":"Li","year":"2018","journal-title":"IEEE Microw. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gagliardini, L., Gouttefarde, M., and Caro, S. (2018). Design of Reconfigurable Cable-Driven Parallel Robots. Mechatronics for Cultural Heritage and Civil Engineering, Springer.","DOI":"10.1007\/978-3-319-68646-2_4"},{"key":"ref_4","first-page":"4521","article-title":"On the connections between cable-driven robots, parallel manipulators and grasping","volume":"Volume 5","author":"Voglewede","year":"2004","journal-title":"Proceedings of the ICRA\u201904. 2004 IEEE International Conference on Robots"},{"key":"ref_5","unstructured":"Merlet, J.P. (2006). Parallel Robots, Springer Science & Business Media."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ottaviano, E., and Castelli, G. (2010). A study on the effects of cable mass and elasticity in cable-based parallel manipulators. ROMANSY 18 Robot Design, Dynamics and Control, Springer.","DOI":"10.1007\/978-3-7091-0277-0_17"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Rodriguez-Barroso, A., Saltaren, R., Portilla, G., Cely, J., and Carpio, M. (2018). Cable-Driven Parallel Robot with Reconfigurable End Effector Controlled with a Compliant Actuator. Sensors, 18.","DOI":"10.3390\/s18092765"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Abbasnejad, G., and Ren, H. (2017, January 18\u201320). Displacement analysis of under-constrained flexible-shaft driven parallel manipulator. Proceedings of the 2017 IEEE International Conference on Information and Automation (ICIA), Macau SAR, China.","DOI":"10.1109\/ICInfA.2017.8078989"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Austin, J., Schepelmann, A., and Geyer, H. (October, January 28). Control and evaluation of series elastic actuators with nonlinear rubber springs. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), 2015, Hamburg, Germany.","DOI":"10.1109\/IROS.2015.7354315"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"021020","DOI":"10.1115\/1.4029486","article-title":"Dynamic modeling of cable-driven parallel manipulators with distributed mass flexible cables","volume":"137","author":"Du","year":"2015","journal-title":"J. Vib. Acoust."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1115\/1.2114890","article-title":"Stiffness of cable-based parallel manipulators with application to stability analysis","volume":"128","author":"Behzadipour","year":"2006","journal-title":"J. Mech. Des."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1109\/TRO.2014.2298057","article-title":"Dynamic modeling and control of parallel robots with elastic cables: Singular perturbation approach","volume":"30","author":"Khosravi","year":"2014","journal-title":"IEEE Trans. Robot."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Baklouti, S., Caro, S., and Courteille, E. (2019). Elasto-Dynamic Model-Based Control of Non-Redundant Cable-Driven Parallel Robots. ROMANSY 22\u2013Robot Design, Dynamics and Control, Springer.","DOI":"10.1007\/978-3-319-78963-7_31"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Baklouti, S., Caro, S., and Courteille, E. (2018). Sensitivity Analysis of the Elasto-Geometrical Model of Cable-Driven Parallel Robots. Cable-Driven Parallel Robots, Springer.","DOI":"10.1007\/978-3-319-61431-1_4"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s11044-008-9144-0","article-title":"Vibration analysis of cable-driven parallel manipulators","volume":"21","author":"Diao","year":"2009","journal-title":"Multibody Syst. Dyn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1016\/j.ifacol.2015.06.265","article-title":"Adaptive vibration control of a flexible cable driven parallel robot","volume":"48","author":"Jamshidifar","year":"2015","journal-title":"IFAC-PapersOnLine"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Weber, X., Cuvillon, L., and Gangloff, J. (2015, January 25\u201330). Active vibration canceling of a cable-driven parallel robot in modal space. Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139402"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Khosravi, M.A., and Taghirad, H.D. (2013, January 13\u201315). Robust PID control of cable-driven robots with elastic cables. Proceedings of the 2013 First RSI\/ISM International Conference on Robotics and Mechatronics (ICRoM), Tehran, Iran.","DOI":"10.1109\/ICRoM.2013.6510128"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Weber, X., Cuvillon, L., and Gangloff, J. (2014, January 14\u201318). Active vibration canceling of a cable-driven parallel robot using reaction wheels. Proceedings of the 2014 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Chicago, IL, USA.","DOI":"10.1109\/IROS.2014.6942787"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"547416","DOI":"10.1155\/2013\/547416","article-title":"Research on longitudinal vibration characteristic of the six-cable-driven parallel manipulator in FAST","volume":"5","author":"Liu","year":"2013","journal-title":"Adv. Mech. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"El-Ghazaly, G., Gouttefarde, M., and Creuze, V. (2015). Adaptive terminal sliding mode control of a redundantly-actuated cable-driven parallel manipulator: Cogiro. Cable-Driven Parallel Robots, Springer.","DOI":"10.1007\/978-3-319-09489-2_13"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s11012-010-9369-x","article-title":"On the determination of the force distribution in overconstrained cable-driven parallel mechanisms","volume":"46","author":"Gosselin","year":"2011","journal-title":"Meccanica"},{"key":"ref_23","unstructured":"Merlet, J.P. (2015, January 25\u201330). On the robustness of cable configurations of suspended cable-driven parallel robots. Proceedings of the 14th IFToMM World Congress on the Theory of Machines and Mechanisms, Taipei, Taiwan."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1017\/S0263574701003332","article-title":"A new insight into the duality between serial and parallel non-redundant and redundant manipulators","volume":"19","author":"Gosselin","year":"2001","journal-title":"Robotica"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1109\/TRO.2004.837234","article-title":"Design and analysis of kinematically redundant parallel manipulators with configurable platforms","volume":"21","author":"Mohamed","year":"2005","journal-title":"IEEE Trans. Robot."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Berti, A., Merlet, J.P., and Carricato, M. (2015). Workspace analysis of redundant cable-suspended parallel robots. Cable-Driven Parallel Robots, Springer.","DOI":"10.1007\/978-3-319-09489-2_4"},{"key":"ref_27","unstructured":"Slotine, S.B. (1991, January 19\u201322). A general framework for managing multiple tasks in highly redundant robotic systems. In Proceeding of 5th International Conference on Advanced Robotics, Pisa, Italy."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1109\/TRO.2015.2418582","article-title":"Control of redundant robots under hard joint constraints: Saturation in the null space","volume":"31","author":"Flacco","year":"2015","journal-title":"IEEE Trans. Robot."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Lamaury, J., and Gouttefarde, M. (2013, January 6\u201310). Control of a large redundantly actuated cable-suspended parallel robot. Proceedings of the 2013 IEEE International Conference on Robots, Karlsruhe, Germany.","DOI":"10.1109\/ICRA.2013.6631240"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1444","DOI":"10.1109\/TRO.2015.2495005","article-title":"A Versatile Tension Distribution Algorithm for n-DOF Parallel Robots Driven by n+2 Cables","volume":"31","author":"Gouttefarde","year":"2015","journal-title":"IEEE Trans. Robot."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/s13538-011-0052-z","article-title":"The Moore\u2013Penrose pseudoinverse: A tutorial review of the theory","volume":"42","author":"Barata","year":"2012","journal-title":"Braz. J. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.1109\/TRO.2009.2032957","article-title":"Rapid computation of optimally safe tension distributions for parallel cable-driven robots","volume":"25","author":"Borgstrom","year":"2009","journal-title":"IEEE Trans. Robot."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1177\/0278364913512170","article-title":"Grasping deformable planar objects: Squeeze, stick\/slip analysis, and energy-based optimalities","volume":"33","author":"Jia","year":"2014","journal-title":"Int. J. Robot. Res."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Inoue, T., and Hirai, S. (2009, January 12\u201317). Parallel-distributed model in three-dimensional soft-fingered grasping and manipulation. Proceedings of the 2009 IEEE International Conference on Robotics and Automation, Kobe, Japan.","DOI":"10.1109\/ROBOT.2009.5152451"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1687814015622339","DOI":"10.1177\/1687814015622339","article-title":"Kinematic analysis of cable-driven parallel mechanisms based on minimum potential energy principle","volume":"7","author":"Liwen","year":"2015","journal-title":"Adv. Mech. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Pott, A., and Tempel, P. (2018, January 1\u20135). A Unified Approach to Forward Kinematics for Cable-Driven Parallel Robots Based on Energy. Proceedings of the International Symposium on Advances in Robot Kinematics, Bologna, Italy.","DOI":"10.1007\/978-3-319-93188-3_46"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zlatanov, D.S., Fenton, R.G., and Benhabib, B. (1998, January 13\u201316). Classification and interpretation of the singularities of redundant mechanisms. Proceedings of the ASME Design Engineering Technical Conference, Atlanta, GA, USA.","DOI":"10.1115\/DETC98\/MECH-5896"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1109\/9.847110","article-title":"Energy based control of the pendubot","volume":"45","author":"Fantoni","year":"2000","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Martinez-Martin, E., and Del Pobil, A.P. (2019). Vision for Robust Robot Manipulation. Sensors, 19.","DOI":"10.3390\/s19071648"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"137","DOI":"10.2478\/v10037-007-0015-6","article-title":"The rank+ nullity theorem","volume":"15","author":"Alama","year":"2019","journal-title":"Formaliz. Math."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/15\/3403\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:12:54Z","timestamp":1760188374000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/15\/3403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,2]]},"references-count":40,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["s19153403"],"URL":"https:\/\/doi.org\/10.3390\/s19153403","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,8,2]]}}}