Related papers: gafro: Geometric Algebra for Robotics
Setting up robot environments to quickly test newly developed algorithms is still a difficult and time consuming process. This presents a significant hurdle to researchers interested in performing real-world robotic experiments. RobotIO is…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
We introduce bindings that enable the convenient, efficient, and reliable use of software modules of CGAL (Computational Geometry Algorithm Library), which are written in C++, from within code written in Python. There are different tools…
This report provides an (updated) overview of {\sl Grafalgo}, an open-source library of graph algorithms and the data structures used to implement them. The programs in this library were originally written to support a graduate class in…
Traditional software development in robotics is about programming functionality in the CPU of a given robot with a pre-defined architecture and constraints. With adaptive computing, instead, building a robotic behavior is about programming…
Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable…
We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines…
We introduce PyTorch Geometric, a library for deep learning on irregularly structured input data such as graphs, point clouds and manifolds, built upon PyTorch. In addition to general graph data structures and processing methods, it…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
Recent researches on robotics have shown significant improvement, spanning from algorithms, mechanics to hardware architectures. Robotics, including manipulators, legged robots, drones, and autonomous vehicles, are now widely applied in…
Geometric algebra (GA) is a mathematical tool for geometric computing, providing a framework that allows a unified and compact approach to geometric relations which in other mathematical systems are typically described using different more…
Grasping objects of different shapes and sizes - a foundational, effortless skill for humans - remains a challenging task in robotics. Although model-based approaches can predict stable grasp configurations for known object models, they…
The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight…
This report provides an introduction to the Bandicoot C++ library for linear algebra and scientific computing on GPUs, overviewing its user interface and performance characteristics, as well as the technical details of its internal design.…
This article introduces PlaCo, a software framework designed to simplify the formulation and solution of Quadratic Programming (QP)-based planning and control problems for robotic systems. PlaCo provides a high-level interface that…
In this paper a new method for geometric robot calibration is introduced, which uses a calibration plate with precisely known distances between its measuring points. The relative measurement between two points on the calibration plate is…
Robots sense, move and act in the physical world. It is therefore natural that algorithmic problems in robotics and automation have a geometric component, often central to the problem. Below we review ten challenging problems at the…