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Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
This work addresses the inverse kinematics of serial robots using conformal geometric algebra. Classical approaches include either the use of homogeneous matrices, which entails high computational cost and execution time or the development…
Semidefinite programming (SDP) is a fundamental convex optimization problem with wide-ranging applications. However, solving large-scale instances remains computationally challenging due to the high cost of solving linear systems and…
A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This…
We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a…
Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is of great challenge. A useful approach, the projection method…
Stackelberg prediction games (SPGs) model strategic data manipulation in adversarial learning via a leader--follower interaction between a learner and a self-interested data provider, leading to challenging bilevel optimization problems.…
This article dives into the use of a 3-RRR Spherical Parallel Manipulator (SPM) for the purpose of inertial Line Of Sight (LOS) stabilization. Such a parallel robot provides three Degrees of Freedom (DOF) in orientation and is studied from…
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. After time discretization, we utilize collocation technique and implement a product integration method in order to simplify the…
This paper evaluates how laminated techniques may be used to replicate the performance of more traditionally manufactured robotic manipulators. In this case study, we introduce a laminated 2-DOF spherical, parallel manipulator. Taking…
In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the linear solver and its computational…
Consider the minimization of a nonconvex differentiable function over a polyhedron. A popular primal-dual first-order method for this problem is to perform a gradient projection iteration for the augmented Lagrangian function and then…
In this paper, we propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
This paper presents a novel approach for numerical solution of a class of fourth order time fractional partial differential equations (PDE's). The finite difference formulation has been used for temporal discretization, whereas, the space…
This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…
In this work we study a multi-step scheme on time-space grids proposed by W. Zhao et al. [28] for solving backward stochastic differential equations, where Lagrange interpolating polynomials are used to approximate the time-integrands with…
This paper studies the motion planning problem of the pick-and-place of an aerial manipulator that consists of a quadcopter flying base and a Delta arm. We propose a novel partially decoupled motion planning framework to solve this problem.…
This paper investigates singular configurations of planar 3-RPR parallel manipulators, which result from applying the averaging technique to solution pairs of their direct kinematic problem. Without computing the zeros of the corresponding…
An algorithm to compute the six distances between particles of a planar Four-Body central configuration is presented according to the following schema. An orthocentric tetrahedron is computed as a function of given masses. Each mass is…