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This paper presents a theoretical framework for analyzing the stability of higher-order geometric nonlinear control laws for attitude control on the Special Orthogonal Group $\mathrm{SO(3)}$. In particular, the paper extends existing…
In order for a bimanual robot to manipulate an object that is held by both hands, it must construct motion plans such that the transformation between its end effectors remains fixed. This amounts to complicated nonlinear equality…
Inverse Kinematics (IK) systems are often rigid with respect to their input character, thus requiring user intervention to be adapted to new skeletons. In this paper we aim at creating a flexible, learned IK solver applicable to a wide…
This paper presents the kinematic analysis of the 3-PPPS parallel robot with an equilateral mobile platform and a U-shape base. The proposed design and appropriate selection of parameters allow to formulate simpler direct and inverse…
Piecewise constant curvature is a popular kinematics framework for continuum robots. Computing the model parameters from the desired end pose, known as the inverse kinematics problem, is fundamental in manipulation, tracking and planning…
This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower-mobility parallel manipulators and parallel…
Soft robotic manipulators provide numerous advantages over conventional rigid manipulators in fragile environments such as the marine environment. However, developing analytic inverse models necessary for shape, motion, and force control of…
The aim of this paper is to characterize the notion of aspect in the workspace and in the joint space for parallel manipulators. In opposite to the serial manipulators, the parallel manipulators can admit not only multiple inverse kinematic…
A bounded linear Hilbert space operator $S$ is said to be a $2$-isometry if the operator $S$ and its adjoint $S^*$ satisfy the relation $S^{*2}S^{2} - 2 S^{*}S + I = 0$. In this paper, we study Hilbert space operators having liftings or…
The paper addresses the geometric synthesis of Orthoglide-type mechanism, a family of 3-DOF parallel manipulators for rapid machining applications, which combine advantages of both serial mechanisms and parallel kinematic architectures.…
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 $\mathfrak{se}(3)$,…
Methods for inverse kinematics computation and path planning of a three degree-of-freedom (DOF) manipulator using the algorithm for quantifier elimination based on Comprehensive Gr\"obner Systems (CGS), called CGS-QE method, are proposed.…
The orthoglide is a 3-DOF parallel mechanism designed at IRCCyN for machining applications. It features three fixed parallel linear joints which are mounted orthogonally and a mobile platform which moves in the Cartesian x-y-z space with…
This paper investigates a constrained inverse kinematic (IK) problem that seeks a feasible configuration of an articulated robot under various constraints such as joint limits and obstacle collision avoidance. Due to the high-dimensionality…
We derive general expressions for resonant inelastic x-ray scattering (RIXS) operators for $t_{2g}$ orbital systems, which exhibit a rich array of unconventional magnetism arising from unquenched orbital moments. Within the fast collision…
During complex object manipulation, manipulator systems often face the configuration disconnectivity problem due to closed-chain constraints. Although regrasping can be adopted to get a piecewise connected manipulation, it is a challenging…
We study parametric equations, which describe the position of an in-parallel planar manipulator. We discuss isometries in the Gauss plane, then we write the loop-closure equations in terms of the rotations as the parameters.
Inverse kinematics (IK) is central to robot control and motion planning, yet its nonlinear kinematic mapping makes it inherently nonconvex and particularly challenging under complex constraints. We present IKSPARK (Inverse Kinematics using…
Inverse dynamics is used extensively in robotics and biomechanics applications. In manipulator and legged robots, it can form the basis of an effective nonlinear control strategy by providing a robot with both accurate positional tracking…
This article provides a formalism making it possible to manage the solutions of the direct and inverse kinematic models of the fully parallel manipulators. We introduce the concept of working modes to separate the solutions from the…