A Computational Approach for Constructing the Reachable Workspaces for Redundant Manipulators

An efficient computation of 3D workspaces for redundant manipulators is based on a “hybrid” algorithm between direct kinematics and screw theory. Direct kinematics enjoys low computational cost, but needs edge detection algorithms when workspace boundaries are needed. Screw theory has exponential computational cost per workspace point, but does not need edge detection. Screw theory allows computing workspace points in prespecified directions, while direct kinematics does not. Applications of the algorithm are discussed

An inverse kinematics problem solver based on screw theory for manipulator arms

[Abstract] Several methodologies exist for solving the inverse kinematics of a manipulator arm. Basing on screw theory, it is possible to efficiently obtain complete and exact solutions. An open-source C++ implementation of an automated problem solver of this kind is introduced, and a comparative with selected known algorithms is established using the TEO humanoid robot platform by Universidad Carlos III de Madrid. The Orocos Kinematics and Dynamics Library is used for geometry and motion-related operationsThe research leading to these results has received funding from: European project “Human Centric Algebraic Machine Learning” (ALMA), H2020-EIC-FETPROACT-2019; ROBOASSET, “Sistemas robóticos inteligentes de diagnóstico y rehabilitación de terapias de miembro superior”, PID2020-113508RB-I00 funded by AGENCIA ESTATAL DE INVESTIGACION (AEI); RoboCity2030-DIHCM, Madrid Robotics Digital Innovation Hub, S2018/NMT-4331, funded by “Programas de Actividades I+D en la Comunidad de Madrid” and cofunded by the European Social Funds (FSE) of the EU; the R&D&I project PLEC2021-007819 funded by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR; and cofounded by Structural Funds of the EU.Comunidad de Madrid; S2018/NMT-433

A Hybrid System For Computing Reachable Workspaces For Redundant Manipulators

Copyright 1991 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.An efficient computation of 3D workspaces for redundant manipulators is based on a "hybrid" algorithm between direct kinematics and screw theory. Direct kinematics enjoys low computational cost, but needs edge detection algorithms when workspace boundaries are needed. Screw theory has exponential computational cost per workspace point, but does not need edge detection. Screw theory allows computing workspaces points in prespecfic directions, while direct kinematics does not. Applications of the algorithm are discussed.http://dx.doi.org/10.1117/12.2538

A geometrical introduction to screw theory

This work introduces screw theory, a venerable but yet little known theory aimed at describing rigid body dynamics. This formulation of mechanics unifies in the concept of screw the translational and rotational degrees of freedom of the body. It captures a remarkable mathematical analogy between mechanical momenta and linear velocities, and between forces and angular velocities. For instance, it clarifies that angular velocities should be treated as applied vectors and that, under the composition of motions, they sum with the same rules of applied forces. This work provides a short and rigorous introduction to screw theory intended to an undergraduate and general readership.Comment: Latex2e, 24 pages. v2: expanded introduction, added 2 figure

Modeling of the youBot in a serial link structure using twists and wrenches in a bond graph

We present a walk-through tutorial on the modeling of a complex robotic system, like the newly developed desktop mobile manipulator youBot developed by KUKA[5, 4]. The tutorial shows the design of models for typical robotic elements, done in a reusable object-oriented style. We employ an energy-based approach for modeling and its bondgraph notation to ensure encapsulation of functionality, extendability and reusability of each element of the model. The kinematic representation of mechanical elements is captured using screw theory. The modeling process is explained in two steps: first submodels of separate components are elaborated and next the model is constructed from these components

Vision based motion control for a humanoid head

This paper describes the design of a motion control algorithm for a humanoid robotic head, which consists of a neck with four degrees of freedom and two eyes (a stereo pair system) that tilt on a common axis and rotate sideways freely. The kinematic and dynamic properties of the head are analyzed and modeled using screw theory. The motion control algorithm is designed to receive, as an input, the output of a vision processing algorithm and to exploit the redundancy of the system for the realization of the movements. This algorithm is designed to enable the head to focus on and to follow a target, showing human-like motions. The performance of the control algorithm has been tested in a simulated environment and, then, experimentally applied to the real humanoid head

A constraint and position identification (CPI) approach for the synthesis of decoupled spatial translational compliant parallel manipulators

This paper introduces a screw theory based method termed constraint and position identification (CPI) approach to synthesize decoupled spatial translational compliant parallel manipulators (XYZ CPMs) with consideration of actuation isolation. The proposed approach is based on a systematic arrangement of rigid stages and compliant modules in a three-legged XYZ CPM system using the constraint spaces and the position spaces of the compliant modules. The constraint spaces and the position spaces are firstly derived based on the screw theory instead of using the rigid-body mechanism design experience. Additionally, the constraint spaces are classified into different constraint combinations, with typical position spaces depicted via geometric entities. Furthermore, the systematic synthesis process based on the constraint combinations and the geometric entities is demonstrated via several examples. Finally, several novel decoupled XYZ CPMs with monolithic configurations are created and verified by finite elements analysis. The present CPI approach enables experts and beginners to synthesize a variety of decoupled XYZ CPMs with consideration of actuation isolation by selecting an appropriate constraint and an optimal position for each of the compliant modules according to a specific application

A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework

In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory. Screw theory is an effective way to establish a global description of rigid body and avoids singularities due to the use of the local coordinates. In these three formulation methods, the first one is based on quaternion algebra, the second one is based on dual-quaternions, and the last one that is called exponential mapping method is based on matrix algebra. Compared with the matrix algebra, quaternion algebra based solutions are more computationally efficient and they need less storage area. The method which is based on dual-quaternion gives the most compact and computationally efficient solution. Paden-Kahan sub-problems are used to derive inverse kinematic solutions. 6-DOF industrial robot manipulator\u27s forward and inverse kinematic equations are derived using these formulation methods. Simulation and experimental results are given