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Depending of the geometry of the domain, one can define --at least-- three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to a converging…
Networks of coupled Kerr parametric oscillators (KPOs) are a leading physical platform for analog solving of complex optimization problems. These systems are colloquially known as ``Ising machines''. We experimentally and theoretically…
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…
Despite the potential benefits of collaborative robots, effective manipulation tasks with quadruped robots remain difficult to realize. In this paper, we propose a hierarchical control system that can handle real-world collaborative…
A basic task in the design of an industrial robot application is the relative placement of robot and workpiece. Process points are defined in Cartesian coordinates relative to the workpiece coordinate system, and the workpiece has to be…
This paper introduces an analytical framework for the derivation of hybrid equations of motion of a flexible quadrotor. This approach helps obtain rigid and elastic equations of motion simultaneously, in a decoupled form, which facilitates…
We propose a method for dual-arm manipulation of rigid objects, subject to external disturbance. The problem is formulated as a Cartesian impedance controller within a projected inverse dynamics framework. We use the constrained component…
Robotics is shifting from rigid, articulated systems to more sophisticated and heterogeneous mechanical structures. Soft robots, for example, have continuously deformable elements capable of large deformations. The flourishing of control…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
State-of-the-art impact dynamics models either apply for free-flying objects or do not account that a robotic manipulator is commonly high-stiffness controlled. Thus, we lack tailor-made models for manipulators mounted on a fixed base.…
This paper presents a sensitivity analysis of the Orthoglide, a 3-DOF translational Parallel Kinematic Machine. Two complementary methods are developed to analyze its sensitivity to its dimensional and angular variations. First, a linkage…
Estimating 3D poses and shapes in the form of meshes from monocular RGB images is challenging. Obviously, it is more difficult than estimating 3D poses only in the form of skeletons or heatmaps. When interacting persons are involved, the 3D…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
Calculating the inverse kinematics (IK) is a fundamental challenge in robotics. Compared to numerical or learning-based approaches, analytical IK provides higher efficiency and accuracy. However, existing analytical approaches are difficult…
Stewart platform-based Parallel Kinematic (PKM) Machines have been extensively studied by researchers due to their inherent finer control characteristics. This has opened its potential deployment opportunities in versatile critical…
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…
A class of optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is considered. We give some criteria under which the first and second-order optimality conditions are of KKT-type. We then prove…
The main objective of this paper is to present a general mathematical model and an associated numerical algorithm applicable to an arbitrary fixed-wing fixed-mass aircraft undergoing an arbitrary maneuver, based on the 3D nonlinear coupled…
Main objective of this paper is to describe the dynamic transition of the incompressible MHD equations in a rectangular domain in $\mathbb{R}^{3}$. Our analysis shows that the system undergoes a first dynamic transition either to multiple…
The basic formal and numerical aspects of different degree interpolated moving least-squares (IMLS) methods are studied using sixteen different combinations of coordinate system for fitting and weight functions. For the application we use…