Summer School on Singularities of Mechanisms and Robotic Manipulators (SIMERO 2019)

Motivation and Aims

Singularity analysis is a central topic of mechanism and robot kinematics. It provides an insight of major practical and theoretical importance for the design, control, and application of robot manipulators. In special configurations, known as singularities, the kinetostatic properties of a mechanism undergo sudden and dramatic change. Hence the enormous practical value of the careful study and thorough understanding of the phenomenon for the design and use of manipulators. The key role played by kinematic singularities in mechanism theory is analogous to, and in fact a consequence of, the critical importance of singularity in algebraic geometry and in the theory of differentiable mappings.

The purpose of the course is to introduce attendees to milestone results, key methods, and main problems in singularity analysis. The lectures provide a wide overview of cutting-edge work in this very active area of robotics research and focus in more detail on a few advanced topics of significant practical and theoretical value. The course is sequentially divided into five parts, presented by five lecturers. Each part contains lectures on several closely related topics. However, connections are also made between the parts and common themes are identified and explored from different viewpoints. This reinforces both learning about the phenomena and an understanding for their importance, while providing the participants with varied conceptual and methodological tools applicable to the problems at hand.

Main Themes

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.

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.

Identification. One of the most practically-important problems of kinematic analysis is the explicit calculation of the singularity set. Two general methods using numerical partitioning of the ambient parameter space are outlined.  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 (linear relaxations and interval analysis) are used. Topology and differential geometry provide the basis for the definitions and formulations throughout the course.

Intended Audience

The course delivers a comprehensive overview of singular phenomena in robots and mechanisms, and hence will be particularly attractive to doctoral students and young researchers in robotics, mechanical engineering, or applied mathematics. The advanced topics and the presentation of current progress in this very active field will also be of considerable interest to many senior researchers. The inescapable centrality of robot singularity in practical robot use and programming determines the value of the course material to robotics experts from industry.

List of Lecturers (confirmed)

• Oriol Bohigas
  Beta Robots, Barcelona, Spain
• Peter Donelan
  Victoria University of Wellington, New Zealand
• Manfred Husty
  University of Innsbruck, Austria
• Andreas Müller
  Institute of Robotics, Johannes Kepler University Linz, Austria
• Philippe Wenger
  IRCCyN, CNRS and École Centrale de Nantes, France
• Dimiter Zlatanov
  University of Genoa, Italy

More Information

Further information can be found here: https://www.simero.org/