Summer Screws 2013 - International Summer School on Screw-Theory Based Methods in Robotics
Motivation and Objective
Applications of the theory of screws are based on a combined representation of angular and linear velocity, or similarly force and moment, as a single element of a six-dimensional vector space.
The importance of screw theory in robotics is widely recognised, in principle. In practice, almost nowhere is it taught to engineering students and few know how to use it. Yet, in a variety of areas of robotics, methods and formalisms based on the geometry and algebra of screws have been shown to be superior to other techniques and have led to significant advances. These include the development of fast and efficient dynamics algorithms, discoveries in the nature of robot compliance and mechanism singularity, and the invention of numerous parallel mechanisms.
The summer school instructors are the authors of many of these results. They will teach the participants to apply existing techniques and to develop new ones for their own research. The basic theoretical concepts will be introduced in a rigorous manner, but the emphasis will be on applications, with numerous examples and exercises.
The course delivers a comprehensive overview of the basic concepts and some of the main applications of screw-theory, and hence will be particularly attractive to doctoral students and young researchers in robotics, mechanical engineering, or applied mathematics. As has been the case in all previous editions of Summer Screws, 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 key role of the presented methods in robot design determines the value of the course material to robotics experts from industry.
Course Structure and Main Topics
The course is sequentially divided into six parts, presented by six lecturers, in six days. Each part contains lectures on several closely related topics with integrated exercise sessions.
Part 1. Basic vector-space properties of twists and wrenches: physical interpretation of the linear operations; linear dependence and independence, subspaces; bases and coordinates. (Lecturer: Dimiter Zlatanov)
Part 2. Scalar products, dual spaces, reciprocity. Constraint and freedom in mechanisms. Constraint analysis. Type synthesis of single-loop chains and parallel manipulators. (Lecturer: Xianwen Kong)
Part 3. Velocity and singularity analysis of parallel and interconnected-chain mechanisms. Derivation of input-output velocity equations and singularity conditions. (Lecturer: Matteo Zoppi)
Part 4. Mappings between screw spaces, stiffness and inertia. Structure of robot compliance. Eigenvalue problems and eigenscrews. Synthesis with springs. (Lecturer: Harvey Lipkin)
Part 5. 6D formulation of the dynamics of individual rigid bodies and rigid-body systems. Equations of motion. Dynamics algorithms. (Lecturer: Roy Featherstone)
Part 6. Basic Lie group theory, matrix representations of the group of rigid-body displacements.Lie algebras as related to screw theory. The exponential map and its applications in modern robotics (Lecturer: Jon Selig)
Connections between the parts are continuously emphasized by the lecturers. In this way, the shared fundamental ideas are communicated and exemplified as applied to different aspects of robot analysis and synthesis. Common themes are identified and explored from different viewpoints. All lecturers have excellent knowledge of the entire material and share the work to help with the better understanding of each section. This is done by direct participation in each other's lectures, by providing common assistance to the students during the exercise sessions, and by answering questions and engaging in informal discussions during the breaks.
On its last day, Summer Screws ends with an exam followed by an invited lecture on a related topic by an expert from the country or region where the school is held. This year's lecturer is Henrique Simas.