{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T07:30:35Z","timestamp":1763105435840,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2015,10,15]],"date-time":"2015-10-15T00:00:00Z","timestamp":1444867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Government of Spain and European Regional Development Fund.","award":["TEC2012-38653"],"award-info":[{"award-number":["TEC2012-38653"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents a novel method to compensate for hysteresis nonlinearities observed in the response of a tactile sensor. The External Loop Adaptation Method (ELAM) performs a piecewise linear mapping of the experimentally measured external curves of the hysteresis loop to obtain all possible internal cycles. The optimal division of the input interval where the curve is approximated is provided by the error minimization algorithm. This process is carried out off line and provides parameters to compute the split point in real time. A different linear transformation is then performed at the left and right of this point and a more precise fitting is achieved. The models obtained with the ELAM method are compared with those obtained from three other approaches. The results show that the ELAM method achieves a more accurate fitting. Moreover, the involved mathematical operations are simpler and therefore easier to implement in devices such as Field Programmable Gate Array (FPGAs) for real time applications. Furthermore, the method needs to identify fewer parameters and requires no previous selection process of operators or functions. Finally, the method can be applied to other sensors or actuators with complex hysteresis loop shapes.<\/jats:p>","DOI":"10.3390\/s151026170","type":"journal-article","created":{"date-parts":[[2015,10,15]],"date-time":"2015-10-15T12:44:06Z","timestamp":1444913046000},"page":"26170-26197","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A New Model Based on Adaptation of the External Loop to Compensate the Hysteresis of Tactile Sensors"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8503-9593","authenticated-orcid":false,"given":"Jos\u00e9","family":"S\u00e1nchez-Dur\u00e1n","sequence":"first","affiliation":[{"name":"Universidad de M\u00e1laga, Andaluc\u00eda Tech, Departamento de Electr\u00f3nica, ETSI Inform\u00e1tica,  Campus de Teatinos, 29071 M\u00e1laga, Spain"},{"name":"Instituto de Investigaci\u00f3n Biom\u00e9dica de M\u00e1laga (IBIMA), 29010 M\u00e1laga, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fernando","family":"Vidal-Verd\u00fa","sequence":"additional","affiliation":[{"name":"Universidad de M\u00e1laga, Andaluc\u00eda Tech, Departamento de Electr\u00f3nica, ETSI Inform\u00e1tica,  Campus de Teatinos, 29071 M\u00e1laga, Spain"},{"name":"Instituto de Investigaci\u00f3n Biom\u00e9dica de M\u00e1laga (IBIMA), 29010 M\u00e1laga, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1185-4864","authenticated-orcid":false,"given":"\u00d3scar","family":"Oballe-Peinado","sequence":"additional","affiliation":[{"name":"Universidad de M\u00e1laga, Andaluc\u00eda Tech, Departamento de Electr\u00f3nica, ETSI Inform\u00e1tica,  Campus de Teatinos, 29071 M\u00e1laga, Spain"},{"name":"Instituto de Investigaci\u00f3n Biom\u00e9dica de M\u00e1laga (IBIMA), 29010 M\u00e1laga, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7167-2651","authenticated-orcid":false,"given":"Juli\u00e1n","family":"Castellanos-Ramos","sequence":"additional","affiliation":[{"name":"Universidad de M\u00e1laga, Andaluc\u00eda Tech, Departamento de Electr\u00f3nica, ETSI Inform\u00e1tica,  Campus de Teatinos, 29071 M\u00e1laga, Spain"},{"name":"Instituto de Investigaci\u00f3n Biom\u00e9dica de M\u00e1laga (IBIMA), 29010 M\u00e1laga, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9505-9141","authenticated-orcid":false,"given":"Jos\u00e9","family":"Hidalgo-L\u00f3pez","sequence":"additional","affiliation":[{"name":"Universidad de M\u00e1laga, Andaluc\u00eda Tech, Departamento de Electr\u00f3nica, ETSI Inform\u00e1tica,  Campus de Teatinos, 29071 M\u00e1laga, Spain"},{"name":"Instituto de Investigaci\u00f3n Biom\u00e9dica de M\u00e1laga (IBIMA), 29010 M\u00e1laga, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,10,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4121","DOI":"10.1109\/JSEN.2013.2279056","article-title":"Directions toward Effective Utilization of Tactile Skin: A Review","volume":"13","author":"Dahiya","year":"2013","journal-title":"IEEE Sens. J."},{"key":"ref_2","unstructured":"Cannata, G., and Maggiali, M. (2005, January 5\u20137). An embedded tactile and force sensor for robotic manipulation and grasping. Proceedings of the 5th IEEE-RAS International Conference on Humanoid Robots, Tsukuba, Japan."},{"key":"ref_3","unstructured":"G\u00f6ger, D., Wei\u00df, K., Burghart, C., and W\u00f6rn, H. (2006, January 6\u20137). Sensitive skin for a humanoid robot. Proceedings of the 2006 International Conference on Human-Centered Robotic Systems, Munich, Germany."},{"key":"ref_4","unstructured":"Barrett Technology. Available online: http:\/\/www.barrett.com\/robot\/products-hand.htm."},{"key":"ref_5","unstructured":"SDH servo-electric 3-Finger Gripping Hand. Available online: http:\/\/mobile.schunk-microsite.com\/en\/produkte\/produkte\/sdh-servo-electric-3-finger-gripping-hand.html."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.sna.2006.10.037","article-title":"Low cost thin film based piezoresistive MEMS tactile sensor","volume":"139","author":"Wisitsoraat","year":"2007","journal-title":"Sens. Actuators A Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1088\/1742-6596\/34\/1\/065","article-title":"A silicon-based flexible tactile sensor for ubiquitous robot companion applications","volume":"34","author":"Kim","year":"2006","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1109\/84.896763","article-title":"A traction stress sensor array for use in high-resolution robotic tactile imaging","volume":"9","author":"Kane","year":"2000","journal-title":"J. Microelectromec. Syst."},{"key":"ref_9","unstructured":"Lee, H.K., Chang, S.I., and Yoon, E. (2006, January 22\u201326). A Capacitive Proximity Sensor in Dual Implementation with Tactile Imaging Capability on a Single Flexible Platform for Robot Assistant Applications. Proceedings of the 19th IEEE International Conference on Micro Electro Mechanical Systems, Istanbul, Turkey."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/S0924-4247(98)00021-1","article-title":"A novel tactile sensor system for heavy-load applications based on an integrated capacitive pressure sensor","volume":"68","author":"Paschen","year":"1998","journal-title":"Sens. Actuators A Phys."},{"key":"ref_11","unstructured":"Pressure Profile Systems. Available online: http:\/\/www.pressureprofile.com\/."},{"key":"ref_12","unstructured":"Hellard, G., and Russell, R.A. (2006, January 6\u20138). A tactile sensor array that also grasps objects. Proceedings of the Australasian conference on robotics and automation, Auckland, New Zealand."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Dahiya, R.S., Valle, M., Metta, G., and Lorenzelli, L. (2007, January 11\u201314). POSFET Based Tactile Sensor Arrays. Proceedings of the 14th IEEE International Conference on Electronics, Circuits and Systems, Marrakech, Morocco.","DOI":"10.1109\/ICECS.2007.4511180"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TRO.2009.2033627","article-title":"Tactile Sensing\u2014From Humans to Humanoids","volume":"26","author":"Dahiya","year":"2010","journal-title":"IEEE Trans. Robot."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"20409","DOI":"10.3390\/s150820409","article-title":"Influence of Errors in Tactile Sensors on Some High Level Parameters Used for Manipulation with Robotic Hands","volume":"15","year":"2015","journal-title":"Sensors"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Oballe-Peinado, \u00d3., Castellanos-Ramos, J., Hidalgo-L\u00f3pez, J.A., and Vidal-Verd\u00fa, F. (2009, January 4). Direct interfaces for smart skins based on FPGAs. Proceedings of the SPIE Europe Microtechnologies for the New Millennium, Dresden, Germany.","DOI":"10.1117\/12.821642"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3249","DOI":"10.3390\/s110303249","article-title":"Three Realizations and Comparison of Hardware for Piezoresistive Tactile","volume":"11","year":"2011","journal-title":"Sensors"},{"key":"ref_18","unstructured":"Cofer, R.C., and Harding, B.F. (2005). Rapid System Prototyping with FPGAs: Accelerating the Design Process, Newnes."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1109\/TASE.2009.2028617","article-title":"Complete Open Loop Control of Hysteretic, Creeped, and Oscillating Piezoelectric Cantilevers","volume":"7","author":"Rakotondrabe","year":"2010","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/MCS.2008.930922","article-title":"Feedforward control of piezoactuators in atomic force microscope systems","volume":"29","author":"Leang","year":"2009","journal-title":"IEEE Control Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Smith, R. (2005). Smart Material Systems, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9780898717471"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Mayergoyz, I.D. (1991). Mathematical Models of Hysteresis, Springer New York.","DOI":"10.2172\/6911694"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Visintin, A. (1994). Differential Models of Hysteresis, Springer Berlin Heidelberg.","DOI":"10.1007\/978-3-662-11557-2"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"012028","DOI":"10.1088\/1742-6596\/138\/1\/012028","article-title":"Hysteresis modelling and compensation for smart sensors and actuators","volume":"138","author":"Visone","year":"2008","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Brokate, M., and Sprekels, J. (1996). Hysteresis and Phase Transitions, Springer New York.","DOI":"10.1007\/978-1-4612-4048-8"},{"key":"ref_26","first-page":"635","article-title":"Robust impedance control of a piezoelectric stage under thermal and external load disturbances","volume":"38","author":"Zareinejad","year":"2009","journal-title":"Control Cybern."},{"key":"ref_27","first-page":"74","article-title":"Inverse feedforward controller for complex hysteretic nonlinearities in smart-material systems","volume":"29","author":"Kuhnen","year":"2001","journal-title":"Control Intell. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1109\/TMECH.2010.2052366","article-title":"An Analytical Generalized Prandtl-Ishlinskii Model Inversion for Hysteresis Compensation in Micropositioning Control","volume":"16","author":"Janaideh","year":"2011","journal-title":"IEEEASME Trans. Mechatron."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1109\/TUFFC.2010.1533","article-title":"A modified prandtl-ishlinskii model for modeling asymmetric hysteresis of piezoelectric actuators","volume":"57","author":"Jiang","year":"2010","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1583","DOI":"10.1109\/TIE.2013.2257153","article-title":"Modeling and Compensation of Asymmetric Hysteresis Nonlinearity for Piezoceramic Actuators With a Modified Prandtl-Ishlinskii Model","volume":"61","author":"Gu","year":"2014","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"e498590","DOI":"10.1155\/2012\/498590","article-title":"A Memory-Based Hysteresis Model in Piezoelectric Actuators","volume":"2012","author":"Zhang","year":"2012","journal-title":"J. Control Sci. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1088\/0960-1317\/14\/11\/001","article-title":"Tracking control of piezoelectric actuator based on a new mathematical model","volume":"14","author":"Sun","year":"2004","journal-title":"J. Micromech. Microeng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1007\/s00542-009-0958-3","article-title":"Tactile sensors based on conductive polymers","volume":"16","author":"Macicior","year":"2010","journal-title":"Microsyst. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1007\/s00542-007-0453-7","article-title":"All-plastic distributed pressure sensors: Taylor-made performance by electroactive materials design","volume":"14","author":"Ochoteco","year":"2008","journal-title":"Microsyst. Technol."},{"key":"ref_35","unstructured":"Tekscan Pressure Mapping, Force Measurement, & Tactile Sensors. Available online: https:\/\/www.tekscan.com\/."},{"key":"ref_36","unstructured":"Pneumax. Available online: http:\/\/www.pneumaxspa.com."},{"key":"ref_37","unstructured":"Linear Slides and Linear Actuators from Zaber Technologies. Available online: http:\/\/www.zaber.com\/."},{"key":"ref_38","unstructured":"ATI Force Torque Sensor: Nano17. Available online: http:\/\/www.ati-ia.com\/products\/ft\/ft_models.aspx?id=Nano17."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"045001","DOI":"10.1088\/0964-1726\/18\/4\/045001","article-title":"A generalized Prandtl-Ishlinskii model for characterizing the hysteresis and saturation nonlinearities of smart actuators","volume":"18","author":"Janaideh","year":"2009","journal-title":"Smart Mater. Struct."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1834","DOI":"10.1109\/TCST.2012.2200896","article-title":"Development of an Approach toward Comprehensive Identification of Hysteretic Dynamics in Piezoelectric Actuators","volume":"21","author":"Liu","year":"2013","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.mechatronics.2007.04.006","article-title":"Hysteresis identification and compensation using a genetic algorithm with adaptive search space","volume":"17","author":"Chan","year":"2007","journal-title":"Mechatronics"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.sna.2012.10.029","article-title":"Parameter identification of the generalized Prandtl-Ishlinskii model for piezoelectric actuators using modified particle swarm optimization","volume":"189","author":"Yang","year":"2013","journal-title":"Sens. Actuators A Phys."},{"key":"ref_43","unstructured":"Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing Co., Inc.. [1st ed.]."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1007\/s00542-012-1455-7","article-title":"Hysteresis correction of tactile sensor response with a generalized Prandtl\u2013Ishlinskii model","volume":"18","year":"2012","journal-title":"Microsyst. Technol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"095111","DOI":"10.1063\/1.2052047","article-title":"Improving positioning accuracy of piezoelectric actuators by feedforward hysteresis compensation based on a new mathematical model","volume":"76","author":"Ru","year":"2005","journal-title":"Rev. Sci. Instrum."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"031008","DOI":"10.1115\/1.2907372","article-title":"A Polynomial-Based Linear Mapping Strategy for Feedforward Compensation of Hysteresis in Piezoelectric Actuators","volume":"130","author":"Bashash","year":"2008","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"ref_47","unstructured":"Lawrence, S., Giles, C.L., and Tsoi, A.C. (1997, January 27\u201331). Lessons in neural network training: Overfitting may be harder than expected. Proceedings of the Fourteenth National Conference on Artificial Intelligence, AAAI-97, Providence, RI, USA."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/10\/26170\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:50:09Z","timestamp":1760215809000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/10\/26170"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,15]]},"references-count":47,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2015,10]]}},"alternative-id":["s151026170"],"URL":"https:\/\/doi.org\/10.3390\/s151026170","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2015,10,15]]}}}