Special configurations referred to as 'kinematic singularities' have always been central in mechanism theory and robotics. Besides being an intellectually appealing topic the study of kinematic singularities provides an insight of major practical and theoretical importance for the design, control, and application of robot manipulators. In such singularities, the kinetostatic properties of a mechanism undergo sudden and dramatic changes. This motivated the enormous practical value of a 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 singularities 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 the 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 such as

  • Definition and Classification
  • Singularity Identification
  • Singularity Avoidance
  • Local and global topology of the Singularity Set and Configuration-Space
  • Mathematical Tools and Formalisms

As this field of research is rapidly progressing these topics are updated and complemented as appropriate.
Attendees will be awarded with 1.5 ECTS credits for this course.

Colors indicate the number of inverse kinematics solutions of a manipulator with curved links (CUMA).
Colors indicate the number of inverse kinematics solutions of a manipulator with curved links (CUMA), whereby inaccurate results of the computation become visible.
Singularity surface of a 3-UPU operation mode.
Colors indicate the number of inverse kinematics solutions of a manipulator with curved links (CUMA).
Colors indicate the number of inverse kinematics solutions of a manipulator with curved links (CUMA).Courtesy of Mathias Brandstötter.