The one week course is organized in the form of several interactive lectures addressing the five topics where each lecturer will focus on one topic. However, common themes are identified and explored in each lecture from different viewpoints. This reinforces learning about the phenomena as well as understanding their importance, while providing the participants with varied conceptual and methodological tools applicable to the problems at hand.

The lectures will be given by the following renowned experts in the field (listed alphabetically):


Marco Carricato (Università di Bologna) is a full professor of Mechanics of Machines at the University of Bologna, where he is the head of the IRMA L@B (Industrial Robotics, Mechatronics & Automation Lab @ Bologna) and the Rector Delegate for PhD Programs of the University.

He is an associate editor of the journal Mechanism and Machine Theory, as well as a member of the scientific committees of several international conferences. He is the deputy Chair of the IFToMM Technical Committee for Computational Kinematics and a member of the IFToMM Technical Committee for Robotics and Mechatronics.

His research interests include robotic systems, servo-actuated automatic machinery and the theory of mechanisms, with a particular emphasis on parallel manipulators and screw theory. In the field of singularities, he presented a comprehensive taxonomy of singularities of parallel kinematic chains based on screw theory. This work earned him the 2011 IEEE I-RAS Young Author Best Paper Award. He was also awarded the AIMETA Junior Prize 2011 by the Italian Association of Theoretical and Applied Mechanics for outstanding research results in the field of Mechanics of Machines.

Lecture Title: Screw theory and its application to Singularity Analysis
Summary: In this session, the theory of screws will be introduced and it will be shown how they can find application in several fields of robotics, especially singularity analysis (but also mobility analysis, type synthesis, constraint design, etc.).
Screws are geometrical entities that represent both the instantaneous motion of a rigid body (in the form of a twist) and the set of generalized forces acting upon it (in the form of a wrench). Thus, screw theory naturally provides the geometrical and algebraic concepts and tools underlying the first-order kinematics and statics of rigid bodies. The importance of screw theory in robotics is widely recognized. Methods and formalisms based on the geometry and algebra of screws have been shown to be particularly effective and have led to significant advances in a variety of areas of robotics, including mobility analysis, constraint design, type synthesis and singularity analysis. The main reason for this success is the strong geometrical insight that screw theory sheds on many complex physical phenomena that roboticists have to deal with. This lecture will deliver an overview of the basic concepts of screw theory and its application to the study of singularities, with emphasis being given on geometrical interpretation and understanding, rather than on computational issues.



Alba Perez Gracia (Universitat Politecnica de Catalunya, Spain) is an 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.

Lecture Title: Using or avoiding singularities in the design of mechanisms
Summary: Characterization of singularities is usually done in order to avoid them in path planning or control algorithms. The topics covered here will focus on the use of singularity analysis theories during the design process. 
The lecture will start with a brief review of how designers have used the knowledge of singularities in order to avoid them or to enforce them for specific mechanisms. After that, we will define the kinematic design process and tools, and how singularities can be included within this process. We will also review the use of geometric algebra to define geometry and motion.

During the second part, we will discuss tools for the designer, based on singularity placement and the connection between singularity and symmetry. Some examples of kinematic synthesis with singularity considerations will be presented.

Manfred Husty (University of Innsbruck, Austria) is a full Professor of Geometry at the Leopold Franzens University of Innsbruck. He has been working on theoretical kinematics, robot kinematics workspace and singularity analysis for more than 35 years. His most important contributions are the solution of the forward kinematics of the general Stewart-Gough platform, an efficient (real time) algorithm for the inverse kinematics of general serial 6R robots, as well as on workspace and singularity analysis of different types of parallel mechanisms applying methods from algebraic geometry. He is scientific board member of Joanneum Research Institute of Robotics. He got the doctorate of technical sciences from the Technical University Graz in 1983 and the habiltiation in 1989. In the years 1993-94 he was Erwin Schrödinger fellow at McGill Center of Intelligent Machines in Montreal, Canada. From 2004 to 2008 he served as dean of the faculty of Technical Sciences at University of Innsbruck. He is long time chair of IFToMM Austria and past chair of the TC of Computational Engineering of IFToMM. In 2013 he obtained an honorary doctorate from Cluj Technical University and in 2017 he received the "Mechanism and Machine Theory 2017 Award for Excellence to celebrate and reward the top 10 most-cited papers since its first publication".

Lecture Title: Mechanism Constraints and Singularities -The Algebraic Formulation
: Kinematics of mechanisms and robots can be treated from local or from global point of view. Various mathematical formulations are used to describe mechanism and robot kinematics. This mathematical formulation is the basis for kinematic analysis and synthesis, i.e., determining displacements, velocities accelerations and singularities, on the one hand, and obtaining design parameters on the other. Vector/matrix formulation containing trigonometric functions is arguably the most favoured approach used in the engineering research community. For a global kinematic analysis a less well known but nevertheless very successful approach relies on an algebraic formulation. This involves describing mechanism constraints with algebraic (polynomial) equations and solving these equation sets, that pertain to some given mechanism or robot, with the powerful tools of algebraic and numerical algebraic geometry.For more than 20 years the lecturer and his collaborators have been applying algebraic formulation to kinematics in particular instances but wide range of analysis and synthesis problems. These instances include direct and inverse pose determination in general parallel (e.g., Stuart-Gough platform) and serial (e.g., 6R) robots, singularity distribution and workspace mapping. This has also been carried out in cases of lower degree of mobility parallel robots as well as for planar and spherical mechanisms. Fundamental to such formulations is the algebraic parametrization of the various displacement groups (planar, spherical, spatial). These parameters are usually elements of the group's quaternion algebra. We contend that this approach provides a most effective insight into the structure of the equations and what it reveals about the corresponding mechanical systems under investigation.

Topics to be addressed in the lectures are:  

  • Methods to establish the sets of equations - the canonical equations,
  • Solution methods for sets of polynomial equations, 
  • Adapting the algebraic formulation to the mechanism's degree of freedom, 
  • Jacobian and singularities, 
  • Some examples.

Jean-Pierre Merlet (INRIA Sophia Antipolis, France) is a full-time senior scientist and the scientific head of the HEPHAISTOS team. He graduated in control theory from Ecole Centrale de Nantes in 1980 and obtained his Ph.D in Robotics from the University Paris VI in 1986. He has worked on the theoretical aspects of parallel robots singularities together with their practical aspects. He has developed numerical methods to manage singularities both in the design phase and during control, taking into account unavoidable uncertainties in the modeling. He is currently extending this approach on cable-driven parallel robots and the use of AI for kinematics problems. He is an IFToMM Award of Merits, an IEEE Fellow and doctor honoris causae from Innsbruck University. He has served for two terms as member of IFToMM Executive Council, chairman of the IFToMM Technical Committee for Computational Kinematics and chairman of IFToMM France.

Lecture Title: Physical Singularities and relevant Numerical Methods
Summary: The geometrical characterization gives insight into the nature of singularities. For example for parallel robots this characterization involves lines in 3D space through their Plücker vectors, which will allow for an exhaustive enumeration of all singularity cases based on Grassman geometry that allows to determine an exploitable set of singularity conditions together with the resulting motion of the robot end-effector. However, this theoretical characterization only has a limited significance in practice, and a theoretical singularity cannot be reached or is not problematic. Hence we will present other singularity conditions that are more relevant for a practical exploitation that will be called physical singularities. In a second part we will address numerical methods that allow to determine if, for a given robot, there are physical singularities within a given workspace, taking into accounts the unavoidable uncertainties there are in the robot model or determine almost all robot design for which a prescribed workspace will be singularity-free even if uncertainties are taken into account. Established methods already exist to solve these types of problem, but we will also examine whether artificial intelligence (AI) may be an alternate method and under which conditions.

Andreas Müller (Institute of Robotics, Johannes Kepler University Linz, Austria) is a full professor and the head of the Institute of Robotics at the Johannes Kepler University, Linz, Austria. He has been working on singularities of mechanisms for more than 20 years, making fundamental contributions to the local analysis of linkage singularities and mobility identification. He is a member of the IFToMM Technical Committees for Computational Kinematics and Multibody Systems. He is also a member of the ASME Technical Committees on Mechanisms and Robotics and of Multibody Systems and Nonlinear Dynamics. He serves as associate Editor for the IEEE Transactions on Robotics, the IEEE Robotics and Automation Letters, and Meccanica. He has served as associate editor of the IFToMM journal Mechanism and Machine Theory.

Lecture Title: Topological Analysis of Singularities and Mobility with Screw and Lie Group Theory
Summary: In the first part of this lecture, the fundamental notion of kinematic singularities is introduced. The different types of singularities are clearly distinguished, and their consequences are discussed. Understanding the singularities of mechanisms and their consequences for the finite motion of mechanisms necessitates investigating the local topology of the configuration space and of the set of singularities. A powerful tool to this end is the higher-order local analysis, and the concept of kinematic tangent cone. In the second part of this lecture, the kinematic phenomenology is discussed upon an appropriate kinematic model. The latter is introduced using a Lie group formulation. This formulation naturally leads to efficient computational methods that can be pursued symbolically or numerically without the need for computer algebra systems. The approach is discussed and attendees will perform their own computation for various examples. Attendees can also pose their own example problem that will be used as examples in the course.

Philippe Wenger (IRCCyN, CNRS and École Centrale de Nantes, France) is a full-time CNRS Director of Research at Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN, until 2016) and Laboratoire des Sciences du Numérique de Nantes (LS2N, from 2017). Hegraduated in mechanical engineering from Ecole Centrale de Nantes in 1985 and obtained his Ph.D in Robotics from the University of Nantes in 1989. He was an Assistant Professor from 1989 to 1990. Since 1991, he has been a full-time CNRS researcher at Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN) until 2016 and Laboratoire des Sciences du Numérique de Nantes (LS2N) from 2017. He has been working on robot kinematics and singularities of serial and parallel manipulators for 30 years, both from a theoretical point of view and for industrial applications. He serves as a Professor at Ecole Centrale where he teaches courses to Master and Ph.D students.  He has been a vice-chair of the IFToMM Technical Commitee for Computational Kinematics from 2011 to 2021. He serves as an Associate Editor of the IFToMM journal Mechanisms and Machine Theory and has served as an Associate Editor of the ASME journal Mechanisms and Robotics until 2019.
Lecture Title: Identification, classification and trajectory planning of cuspidal robots
Summary: Cuspidal robots can move from one inverse or direct kinematic solution to another without ever passing through a singularity. These robots have remained unknown because almost all industrial robots do not have this feature. However, in fact, industrial robots are the exceptions. Some robots appeared recently in the industrial market can be shown to be cuspidal, but, surprisingly, almost nobody knows it and robot users meet difficulties in planning trajectories with these robots. This lesson proposes a review on the fundamental and application aspects of cuspidal robots. It addresses the important issues raised by these robots for the design and planning of trajectories. The identification of all cuspidal robots is still an open issue. This lesson recalls in details the case of serial robots with three joints, but it also addresses robots with more complex architectures such as 6-revolute-jointed robot and parallel robots.