Related papers: DQ Robotics: a Library for Robot Modeling and Cont…
A many variable $q$-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The…
Restricted Boltzmann machines (RBM) and deep Boltzmann machines (DBM) are important models in machine learning, and recently found numerous applications in quantum many-body physics. We show that there are fundamental connections between…
It is known that the groups of Euclidean rotations in dimension 3 (isometries of $S^2$), general Lorentz transformations in dimension 4 (Hyperbolic isometries in dimension 3), and screw motions in dimension 3 can be represented by the…
This paper addresses two intertwined needs for collaborative robots operating in shop-floor environments. The first is the ability to perform complex manipulation operations, such as those on articulated or even flexible objects, in a way…
In this thesis, we consider two simple but typical control problems and apply deep reinforcement learning to them, i.e., to cool and control a particle which is subject to continuous position measurement in a one-dimensional quadratic…
This paper investigates the tracking problem of a smooth coordinate-invariant trajectory using dual quaternion algebra. The proposed architecture consists of a cascade structure in which the outer-loop MPC performs real-time smoothing of…
Quaternions, split quaternions, and hybrid numbers are very well-known number systems. These number systems are used to make geometry in Euclidean and Lorentz spaces. These number systems can be obtained with the help of a quadratic form.…
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…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
Learning from Demonstration offers great potential for robots to learn to perform agricultural tasks, specifically selective harvesting. One of the challenges is that the target fruit can be oscillating while approaching. Grasping…
This paper presents a new dual quaternion-based formulation for pose-based visual servoing. Extending our previous work on local contact moment (LoCoMo) based grasp planning, we demonstrate grasping of arbitrarily moving objects in 3D…
Recently, Zhuang, Roth, \& Sudhakar [1] proposed a method that allows simultaneous computation of the rigid transformations from world frame to robot base frame and from hand frame to camera frame. Their method attempts to solve a…
Constrained environments are common in practical applications of manipulating deformable linear objects (DLOs), where movements of both DLOs and robots should be constrained. This task is high-dimensional and highly constrained owing to the…
This paper addresses the analysis and design of quadratic neural networks, which have been recently introduced in the literature, and their applications to regression, classification, system identification and control of dynamical systems.…
Deep learning is an established framework for learning hierarchical data representations. While compute power is in abundance, one of the main challenges in applying this framework to robotic grasping has been obtaining the amount of data…
Quon language is a 3D picture language that we can apply to simulate mathematical concepts. We introduce the surface algebras as an extension of the notion of planar algebras to higher genus surface. We prove that there is a unique…
Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to…
This paper revisits the little-known Gibbs-Rodrigues representation of rotations in a three-dimensional space and demonstrates a set of algorithms for handling it. In this representation the rotation is itself represented as a…
This survey presents a necessarily incomplete (and biased) overview of results at the intersection of arithmetic circuit complexity, structured matrices and deep learning. Recently there has been some research activity in replacing…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…