Related papers: A micro Lie theory for state estimation in robotic…
After three decades of computational multibody system (MBS) dynamics, current research is centered at the development of compact and user friendly yet computationally efficient formulations for the analysis of complex MBS. The key to this…
Advances in quantum computing over the last two decades have required sophisticated mathematical frameworks to deepen the understanding of quantum algorithms. In this review, we introduce the theory of Lie groups and their algebras to…
This is an old article of 2000. Its aim is to illustrate how a Lie-theoretic result of Zelmanov enables one to treat various problems in group theory.
We study internal Lie algebras in the category of subshifts on a fixed group -- or Lie algebraic subshifts for short. We show that if the acting group is virtually polycyclic and the underlying vector space has dense homoclinic points, such…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
Series elastic actuators (SEA) were introduced for serial robotic arms. Their model-based trajectory tracking control requires the second time derivatives of the inverse dynamics solution, for which algorithms were proposed. Trajectory…
We generalize the common notion of descending and ascending central series. The descending approach determines a naturally graded Lie ring and the ascending version determines a graded module for this ring. We also link derivations of these…
We propose a new metric for robot state estimation based on the recently introduced $\text{SE}_2(3)$ Lie group definition. Our metric is related to prior metrics for SLAM but explicitly takes into account the linear velocity of the state…
A Lie system is a system of differential equations admitting a superposition rule, i.e., a function describing its general solution in terms of any generic set of particular solutions and some constants. Following ideas going back to the…
The special Galilean group, usually denoted SGal(3), is a 10-dimensional Lie group whose important subgroups include the special orthogonal group, the special Euclidean group, and the group of extended poses. We briefly describe SGal(3) and…
We describe the structure of the Lie groups endowed with a left-invariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
This thesis contains a collection of algorithms for working with the twisted groups of Lie type known as Suzuki groups, and small and large Ree groups. The two main problems under consideration are constructive recognition and constructive…
We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference…
Quantum mechanics of Hamiltonian (non-dissipative) systems uses Lie algebra and analytic group (Lie group). In order to describe non-Hamiltonian (dissipative) systems in quantum theory we need to use non-Lie algebra and analytic quasigroup…
In the article, we discuss the architecture of the polynomial neural network that corresponds to the matrix representation of Lie transform. The matrix form of Lie transform is an approximation of the general solution of the nonlinear…
In this paper, we describe procedures for computing higher-order time derivatives of the Lie-group Newton-Euler, Articulated-Body Inertia, and hybrid dynamics algorithms for floating-base trees, where the base configuration evolves on SE(3)…
This survey is about the fundamentals of the theory of finite dimensional Lie groups over the field of real numbers. The notion of the tangent space of a manifold at a point is considered to be defined via the well known chart and vector…
Incorporating prior knowledge of physics laws and structural properties of dynamical systems into the design of deep learning architectures has proven to be a powerful technique for improving their computational efficiency and…
A Lie system is a system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields: a so-called Vessiot-Guldberg Lie…