The Roles of Modern Screw Theory, Lie algebra, and Geometric Algebra in Robotics
Given our list of selected speakers, we believe that our workshop is uniquely positioned to bring together researchers from different applied fields of robotics research with geometers and researchers of core robotics' methods.
Frank Chongwoo Park (Seoul National University)
Title: Geometric Robot Learning: From Models to Representations
Differential geometry, particularly methods from Lie groups and Riemannian geometry, have contributed significantly to advances in robot kinodynamic modeling, planning, and control, and there is now great interest in determining what if any role geometric methods can play in leveraging machine learning techniques to problems in robotics. Obviously a robot model is only as good as the accuracy of its estimated parameters; the challenges in identifying accurate parameters -- especially for complex high-dimensional robot systems -- has led to the use of more generic statistical models in place of traditional physics-based models, in tandem with data-driven methods for learning lower-dimensional robot representations. Such methods can in practice be quite restrictive. We show that even for complex high-dof robots, accurate robot models can be identified by taking advantage of a robot's underlying geometric properties, e.g., link masses are positive and inertia tensors are positive-definite, and that that many representation learning problems in robotics can be naturally formulated as seeking a minimum distortion mapping between two Riemannian manifolds. Further challenges and open problems in developing geometric methods for robot model and representation learning are also highlighted.
Jon Selig (London South Bank University)
Title: Screw Systems and Their Classification
In this talk will the concept of a screw system will be reviewed. Several applications will be considered. Then the mathematical no- tion of a classification will be outlined. The Gibson-Hunt classifica- tion will be recalled with some sketch proofs given. Finally, some particular special types of screw system will be considered such as subalgebras and Lie triple systems. A few applications of such special system will be given.
Joan Lasenby (Cambridge University)
Gregory S. Chirikijian (National University of Singapore)
Title: Perspectives on Screws and Wrenches, and More
Abstract: In classical screw theory twists and wrenches are viewed as being in the same 6D space and are paired using the reciprocal product. In the more modern Lie-theoretic view, twists live in the tangent space to SE(3) and wrenches live in the cotangent space. Here it is explained that both views are valid. Moreover, it is shown how invariants of finite screw displacements are useful in calibration problems such as AX=XB. That said, despite the general usefulness of SE(3), there are some robotics domains such aerial vehicles where instead of SE(3), the pose-change group PCG(3) is more natural. This will be described. As time permits new work in convex geometry (closed-form parameterization of Minkowski sum boundaries) and motion planning will be discussed.
Leo Dorst (University of Amsterdam)
Steven De Keninck (Origami Digital LLC)
Noémie Jaquier (Karlsruhe Institute of Technology)
Eduardo Bayro Corrochano (CINVESTAV)
Title: Robot Modelling, Nonlinear Control and Trajectory Generation using the Geometric Algebra Framewor
We use Geometric Algebra (GA) to formulate screw theory along with screw line geometry (Plücker coordinates) and motor algebra (dual quaternions). We formulated the Lie groups SO(3) and SE(3) with rotor and motor algebra respectively and the related Lie algebras so(3)and se(3). The Lie Groups formulated with spinors, proof that there is no need to use matrices or tensors, which have redundant coefficients leading to complex formulations and slow algorithms. Newton-Euler dynamics is formulated using motor algebra.We use GA in robot mechanics, multi-body dynamics, mechanical design, robot control, and robot learning. We show the exploitation of geometric properties within Lie groups and Klein, Stiefel, Study and Riemannian manifolds has led to topological benefits, computational efficiency, and data-efficient learning. We will present GA algorithms in a variety of applications in medical robotics, robot vision, object manipulation and path planning geometric learning using Deep Learning, geometric controllers, deep learning for observes and control in the closed control loop.
Murilo M. Marinho (Tokyo University)
Tile: Using Dual Quaternion Algebra for Constrained Applications in Robots for Surgery, Science, and Space
Andreas Mueller (Johannes Kepler University Linz)
Title: The Role of Representation for Modeling and Control of Floating-Base and Space Robots
Dr. Luis Figueredo
Note: For further information, please contact the organizers or the corresponding organizers