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We consider the dynamics and symplectic reduction of the 2-body problem on a sphere of arbitrary dimension. It suffices to consider the case for when the sphere is 3-dimensional and where we take the group of symmetries to be $SO(4)$. As…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
The functional renormalisation group for the Einstein-Hilbert action is investigated for the case of four infinite (or large) and one compact dimension. The motivation for this study is given by the suggestion that gravity in more than four…
In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In this first one we present the…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
We demonstrate the definition of basic observables from physical operations, the key to overcome hidden stumbling blocks and apparent paradoxes from unscrutinized (classical) formalisms. We develop Helmholtz program of basic measurements…
We establish the existence of a class of asymptotically Euclidean solutions to Einstein's constraint equations, whose asymptotic behavior at infinity is arbitrarily prescribed. The proposed seed-to-solution method relies on iterations based…
Canonical quantization of gravitational systems is obstructed by the problem of time. Due to diffeomorphism symmetry the Hamiltonian vanishes: dynamics with respect to a background time parameter appears "frozen." Two strategies towards the…
Quantification of human movement is a challenge in many areas, ranging from physical therapy to robotics. We quantify of human movement for the purpose of providing automated exercise coaching in the home. We developed a model-based…
This paper unifies the concept of kinematic mappings by using geometric algebras. We present a method for constructing kinematic mappings for certain Cayley-Klein geometries. These geometries are described in an algebraic setting by the…
Often, robots are asked to execute primitive movements, whether as a single action or in a series of actions representing a larger, more complex task. These movements can be learned in many ways, but a common one is from demonstrations…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
Learning actions that are relevant to decision-making and can be executed effectively is a key problem in autonomous robotics. Current state-of-the-art action representations in robotics lack proper effect-driven learning of the robot's…
Computational chemistry at the atomic level has largely branched into two major fields, one based on quantum mechanics and the other on molecular mechanics using classical force fields. Because of high computational costs, quantum…
In this paper, we prove that an Adam-type algorithm with smooth clipping approaches the global minimizer of the regularized non-convex loss function. Adding smooth clipping and taking the state space as the set of all trajectories, we can…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
The purpose of this publication is to derive and discuss equations of motion of affinely rigid (homogeneously deformable) body moving in Euclidean space of general dimension $n$. Our aim is to present some analytical methods and to discuss…
Morphological computing, the use of the physical design of a robot to ease the realization of a given task has been proven to be a relevant concept in the context of swarm robotics. Here we demonstrate both experimentally and numerically,…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…