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Home   >  Master's & postgraduate courses  >  Education  >  Course in Singularities of Mechanisms and Robotic Manipulators
We advise you! Request information or admission
  • discount

    €100 discount for participants from member countries IFToMM

  • discount

    €50 discount for participants from non-IFToMM countries

Presentation

Edition
1st
Credits
3 ECTS
Delivery method
Face-to-face
Language of instruction
English
Fee
€525
Notes payment of enrolment fee and 0,7% campaign
Registration open until the beginning of the programme or until end of vacancies.
Start date
Start date: 15/09/2025
End date: 19/09/2025
Timetable
Monday: 9:30 am to 1:00 pm | 3:00 pm to 6:30 pm
Tuesday: 9:30 am to 1:00 pm | 3:00 pm to 6:30 pm
Wednesday: 9:30 am to 1:00 pm | 3:00 pm to 6:30 pm
Thursday: 9:30 am to 1:00 pm | 3:00 pm to 6:30 pm
Friday: 9:30 am to 1:00 pm
Taught at
Residència d'Investigadors
c/Hospital, 64
08001 Barcelona
Presentation video
Why this programme?
Singularities are fundamental in the kinematics of mechanisms and robots, with crucial implications for their design, analysis, and control. This course offers an intensive introduction to the theoretical and computational tools required to understand, calculate, and avoid singularities in robotic manipulators and mechanisms.

The course on Singularities of Mechanisms and Robotic Manipulators, now in its fifth edition after previous sessions in Udine, Linz, and Nantes, brings together international experts from academic and technical backgrounds, covering everything from the rigorous definition and mathematical classification of singularities to their symbolic and numerical calculation, as well as their geometric interpretation and topological implications in the configuration space.

Additionally, this learning experience addresses real-world applications in robotics, including strategies for avoiding singularities in trajectories and the analysis of phenomena such as cuspidal manipulators or constraint singularities. Participants will gain access to tools and methods such as algebraic geometry, Lie groups, and techniques for numerical continuation and pruning.

The course is supported by the Barcelona City Council. 
Promoted by:
Aims
The lectures will provide a wide overview of cutting-edge work around the following topics:

  • Definition of singularity. Singularity types.
  • Mathematical characterization of singularities.
  • Local and global topology of the singularity set and configuration space.
  • Symbolic and numerical tools for singularity set computation.
  • Methods to compute singularity-avoiding motions.
  • Applications to illustrative robots and mechanisms.
Who is it for?
Students who are interested in the mathematical theory necessary to deal with singularities, and also in the software tools to calculate and visualize them.

Training Content

  • Definition: Given the importance of kinematic singularity and the vast literature on the subject it may be surprising that one rarely encounters a clear general definition of the phenomenon. To provide one is the course’s first objective: singularity is defined rigorously and in simple terms.
  • Interpretation: Singularities are interpreted as silhouettes of configuration space when “seen” from the spaces of input or output coordinates of a mechanism. This provides a rich picture of singularities, and connects them to the notions of workspace boundary, workspace barrier, and reduced-dexterity locus. The interpretation allows one to visualise the various physical phenomena occurring at forward and inverse singularities.
  • Classification: Numerous singularity classifications exist. Since singularity is defined via instantaneous kinematics, the most fundamental taxonomy describes the types of degeneracy of the forward and inverse velocity problems. Finer distinctions exist for specific mechanism types, e.g., the important constraint singularities of parallel manipulators. When non-instantaneous properties are considered, other distinctions arise, such as between cusp-like and fold-like singularities, or the existence of self-motions.
  • Computation: One of the most practically-important problems of kinematic analysis is the explicit calculation of the singularity set. A general method using numerical partitioning of the ambient parameter space is outlined. Also, a powerful approach for formulating and solving symbolically the algebraic equations of the end-effector’s motion-pattern and singular-poses set is studied in detail.
  • Avoidance: The course explores the possibility of a singularity-free workspace and the ability to escape from singularity, issues of major practical importance for the design of path planning algorithms and singularity consistent control schemes.
  • Singularity-set and configuration-space topology: The singularity-free-connectivity properties of the configuration space are discussed, including the fascinating cuspidal manipulators, able to change posture while avoiding singularities. Related fundamental problems of genericity and configuration-space and singularity-set topology are explored. We examine the possibility of multiple operation modes, sometimes with strikingly different platform motion patterns, connected by constraint singularities.
  • Mathematical tools and formalisms: The course is a hands-on introduction to the various analytical and computational tools for dealing with singularities. We explore screw-geometrical techniques and Lie-group-based local-analysis methods. Algebraic-geometry formulations combined with either symbolic computation or numerical methods (branch-and-prune, and continuation methods) are used. Topology and differential geometry provide the basis for the definitions and formulations throughout the course.
The UPC School reserves the right to modify the contents of the programme, which may vary in order to better accommodate the programme objectives.
Degree
Certificate of Achievement issued by the Fundació Politècnica de Catalunya. Issued in accordance with the provisions of Article 8 of the Amendment to the Regulations of Lifelong Learning Studies, approved by Agreement CG/2025/02/35, of 25 March, by the Governing Council of the UPC.

Learning methodology

The teaching methodology of the programme facilitates the student's learning and the achievement of the necessary competences.



Learning tools
Participatory lectures
A presentation of the conceptual foundations of the content to be taught, promoting interaction with the students to guide them in their learning of the different contents and the development of the established competences.
Solving exercises
Solutions are worked on by practising routines, applying formulas and algorithms, and procedures are followed for transforming the available information and interpreting the results.
Assessment criteria
Attendance
At least 80% attendance of teaching hours is required.
Virtual campus
The students on this course will have access to the My_ Tech_Space virtual campus - an effective platform for work and communication between the programme's students, lecturers, directors and coordinators. My_Tech_Space provides the documentation for each training session before it starts, and enables students to work as a team, consult lecturers, check notes, etc.

Teaching team

Academic management
  • Perez Gracia, Maria Alba
    info

    Associate professor at the Polytechnic University of Catalonia, where she is also the Director of the Centre for the Design of Industrial Equipment, CDEI, and the head of the Computational Robotics research line at the IRI Robotics Institute. Her research is focused on theoretical kinematics and robot design. Her main contributions in these areas are the use of Clifford algebras for robot kinematics and robot design, the development of methods for grasping and for robot hand design, and the application of robotics to human-robot motion interaction through the design of exoskeletons. She has also contributed to the fusion of robotics and virtual/augmented reality, and is currently working on mobile robotics for agricultural applications. She is the author of approximately 20 peer-reviewed journal articles and book chapters, and more than 70 contributions in international conferences and recipient of National Science Foundation collaborative research awards, involving several universities. In addition to these awards, she has participated in around 10 more funded research projects.

    Her professional service includes being in the Scientific Committee of five international conferences, and also being associate editor of the ASME Journal of Mechanical Design. As a professor and advisor, Dr Perez-Gracia has taught more than 12 different undergraduate and graduate courses in robotics and mechanical engineering, and has advised 6 PhD and more than 20 MS graduate students.

Teaching staff
  • Carricato, Marco
    info

    Marco Carricato received the M.Sc. degree in Mechanical Engineering in 1998, and the Ph.D. degree in Mechanics of Machines in 2002. He has been with the University of Bologna since 2004. He is currently a Full Professor in the Dept. of Industrial Engineering, where he is the head of the IRMA L@B (Industrial Robotics, Mechatronics & Automation Lab @ Bologna), as well as scientific coordinator of the IMA-University of Bologna Joint Lab DIGIMECH (Digital and Mechatronic Research & Innovation for Automated Machinery and Systems). He is the Rector Delegate for the PhD Programs of the University of Bologna.
  • Jean-Pierre, Merlet
    info

    PhD in mechanical engineering from Paris VI University, engineer from Ecole Centrale de Nantes, Habilitation from Nice University, senior scientist emeritus at INRIA, IEEE Fellow, IFToMM Award of Merits, doctor Honoris Causa from Innsbruck University. Main activities: parallel robots, assistance robotics for frail people, ethics, numerical analysis (interval analysis, continuation, AI).
  • Manfred, Dr. Husty
    info

    Professor Manfred Husty is retired full professor of geometry of the University of Innsbruck, Austria. 1979 Master degree from University Graz, 1983 PhD from Technical University Graz. 1989 habilitation at Montan University Leoben, Austria and appointment to associate professor. 1993/94 he spent a successful research year at the Centre of Intelligent Machines, McGill University, Montreal Canada and is elected associate member of the institute since 1994. 2000 Full professor of geometry at University Innsbruck and in 2013 honorary doctorate of the Technical University Cluj-Napoca awarded.
  • Mueller, Andreas
    info

    PhD in Mechanical Engineering from Chemnitz University of Technology, Germany. Habilitation in Mechanics from University Duisburg-Essen, Germany. Currently full professor and chair of the Institute of Robotics, Johannes Kepler University Linz, Linz, Austria. Senior member of IEEE. Fellow of ASME. Member of Executive Council of IFToMM.
  • Perez Gracia, Maria Alba
    info

    Associate professor at the Polytechnic University of Catalonia, where she is also the Director of the Centre for the Design of Industrial Equipment, CDEI, and the head of the Computational Robotics research line at the IRI Robotics Institute. Her research is focused on theoretical kinematics and robot design. Her main contributions in these areas are the use of Clifford algebras for robot kinematics and robot design, the development of methods for grasping and for robot hand design, and the application of robotics to human-robot motion interaction through the design of exoskeletons. She has also contributed to the fusion of robotics and virtual/augmented reality, and is currently working on mobile robotics for agricultural applications. She is the author of approximately 20 peer-reviewed journal articles and book chapters, and more than 70 contributions in international conferences and recipient of National Science Foundation collaborative research awards, involving several universities. In addition to these awards, she has participated in around 10 more funded research projects.

    Her professional service includes being in the Scientific Committee of five international conferences, and also being associate editor of the ASME Journal of Mechanical Design. As a professor and advisor, Dr Perez-Gracia has taught more than 12 different undergraduate and graduate courses in robotics and mechanical engineering, and has advised 6 PhD and more than 20 MS graduate students.

  • Philippe, Wenger
    info

    Ph.D. in Automatics and Robotics, University of Nantes, France (1989). Research Habilitation, University of Nantes, France (1998). Professor qualification (2000). CNRS Research Director at IRCCyN (2002-2016) and LS2N (2017-). Professor at Ecole Centrale (2000-). 35 years of experience in research and teaching. 80 papers in international journals, 200 papers in international conferences. Research interests: Innovative design of robots, kinematic and design of mechanisms, trajectory optimization, tensegrity mechanisms, bio-inspired robotics.
  • Sébastien, Briot
    info

    Sébastien Briot received the B.S. and M.S. degrees in mechanical engineering in 2004 and the Ph.D. degree in roboticsin 2007, from the Institut National des Sciences Appliquées de Rennes, Rennes, France. He was a Postdoctoral Fellow with the Ecole de Technologie Supérieure, Montreal, QC, Canada, in 2008. In 2009, he has been recruited at CNRS as a researcher in the Laboratoire des Sciences du Numérique de Nantes, Nantes, France, where he has been the Head of the ARMEN Research Team since 2017. Since 2022, he is CNRS Director of Research in the same lab.
  • Thomas, Federico
    info
    /
    Federico Thomas received the B.Sc. degree in telecommunications engineering and the Ph.D. degree (with honors) in computer science from the Technical University of Catalonia (UPC), Barcelona, Spain, in 1984 and 1988. He has held distinguished visiting scholar positions with the University of Massachusetts (1991'1992) and Oxford University (1999'2000). In addition, he served as an invited Professor with the Institut de Recherche en Communications et Cybernétique de Nantes in 2009, and with the Department of Mechanical Engineering, University of Ferrara in 2010.

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Programme: Singularities of Mechanisms and Robotic Manipulators

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ACADEMIC AND ECONOMIC REGULATIONS

The Fundació Politècnica de Catalunya reserves the right to modify content, price, location, timetable and dates prior to the start of the course. Registration on the course will not be confirmed until payment has been made.

Registration rights. The interested party must make payment of the specified registration fee for the course. This fee will be deducted from the full course fee and will only be reimbursed if the applicant is not admitted.

Cancellation or deferment.The Fundació Politècnica de Catalunya reserves the right to cancel or defer a course if the minimum number of students is not met. In case of cancellation or non-admittance, the Fundació Politècnica de Catalunya will return all amounts paid in full, without any additional compensation. In case of deferment, applicants may request reimbursement of fees paid.

Cancellation of registration.
In the event of withdrawal or cancellation of the registration, the student must notify the UPC School in writing beforehand.
  • If this request for cancellation is made 45 days before the start of the programme, the UPC School will retain only 30% of the total registration fee and refund the difference paid.
  • In the event that the application request is made within 45 calendar days and the beginning of the programme, the UPC School will retain 60% of the registration fee.
  • No applications for refunds may be made after the programme has started.
Under exceptional circumstances, refunds of the registration fee will be made if the student's cancellation is due to one of the following circumstances:
  • Denial of a visa, subject to submission of supporting documentation. In this case, the UPC School will refund the registration fee less 300 Euros for administrative expenses.
  • Serious illness or accident accredited by an official medical certificate, stating the start date of the illness and the anticipated convalescence period. In this situation the UPC School's decision will be as follows:
    • If the notification takes place up to one month after the start of the programme, it will refund the amount actually paid, less 300 Euros as administrative expenses.
    • No refunds will be made after a month after the start of the programme. It will be only be possible to use the amount paid as a deposit for the registration fee of the next programme. This procedure entails no administrative fee for the student. The price difference between the new registration fee and the amount previously paid will be payable by the student under all circumstances.

Changes in registration. Any changes in registration, previously authorised by the Fundació Politècnica de Catalunya, will incur a 300 € administration fee.

Discounts.
  • Discounts are non-accumulable. The greater discount of those requested will be applied.
  • Discounts can only be applied under prior application and approval.
  • Once registration has been confirmed, no discount will be applied.
  • Students are responsible for placing applications for any discounts.

Qualification. In order to obtain the Qualification/Diploma issued by the Polytechnic University of Catalonia, the student must be in possession of a recognised university qualification or internal university qualification equivalent to a degree or diploma. If this is not the case, the student will receive a certificate of completion for the course, issued by the Fundació Politècnica de Catalunya. Students with outstanding payments due to the Fundació Politècnica de Catalunya or who has not approved all the credits necessary to overcome the program before the date of completion of this program will not be eligible to receive any qualification, diploma or certificate.

Barcelona, October 31, 2017


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