Robust control strategies based on fractional calculus for robotic platforms by Jorge Mu~nozY´a~nez-Barnuevo A dissertation submitted by in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical Engineering, Electronics and Automation Universidad Carlos III de Madrid Advisors: Concepci´onAlicia Monje Micharet Carlos Balaguer Bernaldo de Quir´os Tutor: Concepci´onAlicia Monje Micharet December, 2020 This thesis is distributed under license \Creative Commons Attribution { Non Commercial { Non Derivatives". A Juan, Luna y Aurora. i ii Acknowledgments First of all, I want to thank my children (Juan, Luna and Aurora) for all the support and encouragement they have given to me. This thesis would not have been possible without them for several reasons. Firstly, because they are my main motivation for embarking on any venture. And secondly because they have done the most important work of all. Any child requires constant attention, but they, with the help of their mother (Mar´ıaLaura) of course, have been able to give me the necessary peace of mind and time to develop this thesis. This shows me how great people they already are, and makes me feel very proud to be their father. Secondly, the invaluable help received from my thesis director, Concha Monje, an excellent person in all aspects, and of course, an academic of international standing, whose advice and guidance have made it possible to bring all the work of these years to a successful conclusion. Her help, both to encourage me in the most challenging moments and to put my feet on the ground, has been key throughout the development. Without her, I would probably now have nothing but a mountain of messy papers containing pencil calculations. I would also like to thank my other tutors, Carlos at the Robotics Lab, and Egidio at the Sant'anna Biorobotics Institute. Their support has been essential in certain key moments. The support of my colleagues has also been essential. Starting with the long and brilliant talks with Alvaro,´ which always resulted in more questions than answers, and which helped us grow as researchers and as persons. A good part of my research, and I suppose his too, advanced thanks to those good moments. The same could be said of many other former colleagues, such as Tamara, Nicol´as,Quijano, Silvia, Alejandro, David, and a very long list. Although they all took different paths that ended up distancing our professional lives, the friendship that was formed then will remain strong for many years to come. The colleagues Lisbeth, Luis, Juan Miguel, Carlos, Fernando and Santiago deserve a very special recognition. Their help during the long laboratory hours invested has been essential to achieve the extraordinary results obtained in the projects that we have developed together. Apart from the work in the laboratory, the collaboration with Vicente and Carlos, whose remarkable work gave and will give excellent results in the future, is also to be thanked. iii Finally, we must not forget that all this would not have been possible if it weren't for the support of all the people who are part of the Robotics Lab and Carlos III University. Both for trusting me, through scholarships or simply a place to work, and for providing me with the necessary facilities to carry out the research. And speaking of trusting and providing the necessary means, my parents, Andr´es and Mar´ıa,cannot be missed. They have always known how to support and motivate me (and often bear with me) in any of my endeavors, from my first steps, literally. Thank you all from the heart. iv Agradecimientos En primer lugar, quiero agradecer a mis hijos (Juan, Luna y Aurora) todo el apoyo y ´animoque me han dado. Esta tesis no habr´ıa sido posible sin ellos por varias razones. En primer lugar por ser mi motivaci´onprincipal para abordar cualquier aventura. Y en segundo lugar porque ellos han hecho el trabajo m´asimportante de todos. Cualquier ni~norequiere atenci´onconstante, pero ellos, con la ayuda de su madre (Mar´ıaLaura) por supuesto, han sabido darme la tranquilidad y el tiempo necesarios para poder desarrollar esta tesis. Eso me demuestra lo grandes personas que ya son, y me hace sentir muy orgulloso de ser su padre. En segundo lugar, la inestimable ayuda recibida de mi directora de tesis, Concha Monje, una excelente persona en todos los aspectos, y como no, una acad´emicade categor´ıainternacional, cuyo consejo y gu´ıahan hecho posible que todo el trabajo de estos a~noshaya llegado a buen puerto. Su ayuda, tanto para animarme en los momentos m´ascomplicados, como para ponerme los pies en la tierra, ha sido clave durante todo el desarrollo. Sin ella, probablemente ahora no tendr´ıam´asque una monta~nade papeles desordenados con c´alculosa l´apiz.Tambi´enquerr´ıaagradecer a mis otros tutores, a Carlos en el Robotics Lab, y a Egidio en el Instituto de biorob´otica de Sant'anna. Su apoyo ha sido indispensable en varios momentos clave. Tambi´enha sido imprescindible el apoyo de mis compa~neros. Empezando por las largas y geniales charlas con Alvaro,´ que siempre terminaban con m´aspreguntas que respuestas, y que nos vieron crecer como investigadores y como personas. Buena parte de mi investigaci´on,y supongo que la suya tambi´en,avanz´ogracias a aquellos buenos momentos. Lo mismo podr´ıadecir de muchos otros antiguos compa~neros, como Tamara, Nicol´as,Quijano, Silvia, Alejandro, David, Dorin y una largu´ısima lista. Aunque cada uno eligi´ocaminos distintos que terminaron por separar nuestras vidas profesionales, la amistad que surgi´oentonces se mantendr´aintacta por muchos a~nosque pasen. Merecen un reconocimiento muy especial los compa~neros Lisbeth, Luis, Juan Miguel, Carlos, Fernando y Santiago. Su ayuda durante las largas horas de labora- torio invertidas ha sido imprescindible para conseguir los extraordinarios resultados obtenidos en los proyectos que hemos desarrollado juntos. Aparte de los trabajos en el laboratorio, las colaboraciones mantenidas con Vicente y Carlos, cuyo admirable v trabajo, dio y dar´aexcelentes resultados en el futuro, son tambi´ende agradecer. Por ´ultimono hay que olvidar que todo esto no habr´ıasido posible sin el apoyo de todas las personas que forman parte del Robotics Lab y la universidad Carlos III. Tanto por depositar su confianza en m´ı, a trav´esde becas o simplemente un sitio en el que trabajar, como por proporcionarme los medios necesarios para realizar la investigaci´on. Y hablando de depositar su confianza y de proporcionarme los medios necesarios, no podr´ıanfaltar mis padres, Andr´esy Mar´ıa,que han sabido siempre apoyarme y motivarme ( y muchas veces aguantarme ) en cualquiera de mis peripecias, desde mis primeros pasos, en sentido literal. Gracias a todos, de coraz´on. vi Published and submitted content During the development of this thesis the following research works were published: A. Journals: 1. Mu~noz,J.; Monje, C. A.; Nagua, L. F. & Balaguer, C. (2020), 'A graphical tuning method for fractional order controllers based on iso-slope phase curves', ISA Transactions. (Q1, Impact Factor: 4.305). 2. Flores, C.; Mu~noz,J.; Monje, C. A.; Milan´es,V. & Lu, X.-Y. (2020), 'Iso- damping fractional-order control for robust automated car-following', Journal of Advanced Research 25, 181 - 189. (Q1, Impact Factor: 6.992). 3. Mena, L.; Monje, C. A.; Nagua, L.; Mu~noz,J. & Balaguer, C. (2020), 'Test Bench for Evaluation of a Soft Robotic Link', Frontiers in Robotics and AI 7, 27. 4. Mu~noz,J.; Monje, C. A.; Casa, S. M. d. l. & Balaguer, C. (2019), 'Joint Position Control Based on Fractional-Order PD and PI Controllers for the Arm of the Humanoid Robot TEO', International Journal of Humanoid Robotics 16(06), 1950042. (Q4, Impact Factor: 1.394). - Pending publications (accepted): 5. Mu~noz,J.; Copaci, D. S.; Monje, C. A.; Blanco D. & Balaguer, C. (2020), 'Iso-m based adaptive fractional order control with application to a soft robotic neck', IEEE Access. (Q1, Impact Factor: 4.098). 6. Copaci, D. S.; Mu~noz,J.; Gonz´alez,I.; Monje, C. A.; & Moreno, L. (2020), 'SMA-driven soft robotic neck: design, control and validation', IEEE Access. (Q1, Impact Factor: 4.098). B. Conferences: 1. Quevedo, F.; Munoz, J.; Castano, J.A.; Monje, C. A. & Balaguer, C. (2020), Model Identification of a Soft Robotic Neck, in '2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)', IEEE, , pp. {. 2. Mena, L.; Monje, C. A.; Nagua, L.; Mu~noz, J. & Balaguer, C. (2019), Sen- sorizaci´onde un sistema de eslab´onblando actuando como cuello rob´otico,in 'Actas de las Jornadas Nacionales de Rob´otica',Universidad de Alicante, , pp. 98-102. vii 3. Munoz, J.; Monje, C. A.; Martin, F. & Balaguer, C. (2018), A Robust Control Method for the Elbow of the Humanoid Robot TEO Based on a Fractional Order Controller, in '2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)', IEEE, , pp. 6378{6383. 4. Nagua, L.; Mu~noz,J.; Monje, C. A. & Balaguer, C. (2018), A first approach to a proposal of a soft robotic link acting as a neck, in 'Actas de las XXXIX Jornadas de Automatica, Badajoz, 5-7 de Septiembre de 2018', Area´ de Ingenier´ıade Sistemas y Autom´atica,Universidad de Extremadura, , pp. 522-529. 5. Nagua, L.; Monje, C.; Mu~nozYa~nez-Barnuevo, J. & Balaguer, C. (2018), Design and performance validation of a cable-driven soft robotic neck, in 'Actas de las Jornadas Nacionales de Rob´otica',Universidad de Valladolid, . Chapter 2 describes in detail the mathematical development of the iso-m method. The research contributions of this chapter have been published in the high impact paper [A1].