Related papers: Quantizing Euclidean motions via double-coset deco…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
The cosmological constant problem is usually considered an inevitable feature of any effective theory capturing well-tested gravitational and matter physics, without regard to the details of short-distance gravitational couplings. In this…
To represent motions from a mechanical point of view, this paper explores motion embedding using the motion taxonomy. With this taxonomy, manipulations can be described and represented as binary strings called motion codes. Motion codes…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…
Computing the epipolar geometry between cameras with very different viewpoints is often problematic as matching points are hard to find. In these cases, it has been proposed to use information from dynamic objects in the scene for…
The Kinematic Theory of rapid movements and its associated Sigma-Lognormal model have been extensively used in a large variety of applications. While the physical and biological meaning of the model have been widely tested and validated for…
Language-guided human motion synthesis has been a challenging task due to the inherent complexity and diversity of human behaviors. Previous methods face limitations in generalization to novel actions, often resulting in unrealistic or…
We find a two-degree-of-freedom Hamiltonian for the time-symmetric problem of straight line motion of two electrons in direct relativistic interaction. This time-symmetric dynamical system appeared 100 years ago and it was popularized in…
Robots that can manipulate objects in unstructured environments and collaborate with humans can benefit immensely by understanding natural language. We propose a pipelined architecture of two stages to perform spatial reasoning on the text…
This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…
We use molecular dynamics computer simulations to investigate the local motion of the particles in a supercooled simple liquid. Using the concept of the distance matrix we find that the alpha-relaxation corresponds to a small number of…
We develop a quantization method, that we name decomposable Weyl quantization, which ensures that the constants of motion of a prescribed finite set of Hamiltonians are preserved by the quantization. Our method is based on a structural…
The kinematics of a robot manipulator are described in terms of the mapping connecting its joint space and the 6-dimensional Euclidean group of motions $SE(3)$. The associated Jacobian matrices map into its Lie algebra $\mathfrak{se}(3)$,…
The compact groups such as $SU(n)$ and $SO(n)$ groups have been heavily studied and applied in the study of quantum many body systems. However, the non-compact groups such as the real symplectic groups are less touched. In this paper, we…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
Autonomous agents that perform everyday manipulation actions need to ensure that their body motions are semantically correct with respect to a task request, causally effective within their environment, and feasible for their embodiment. In…
We develop a method to bound the dynamic asymptotic dimension of isometric group actions $\Gamma\curvearrowright X$ in terms of the asymptotic dimension of a space of graphs similar to a box space of $\Gamma$ (which also determines…