A comprehensive dynamic model for class-1 tensegrity systems based on quaternions

Cefalo, Massimo; Mirats-Tur, Josep M.

doi:10.1016/j.ijsolstr.2010.11.015

Cited by 21 publications

(7 citation statements)

References 21 publications

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“…Mirats-Tur et al [ 23 ] developed dynamic equations for a 3-bar tensegrity mobile robot. Cefalo and Mirats-Tur [ 24 ] proposed a new dynamic model for a class-1 tensegrity system based on quaternions. The use of quaternions eliminates problems of singularities and allows to perform more precise calculations and simulation as they do not need to use trigonometric functions for the representation of angles.…”

Section: Literature Reviewmentioning

confidence: 99%

Design of a novel wheeled tensegrity robot: a comparison of tensegrity concepts and a prototype for travelling air ducts

Carreño

Post

2018

Robot. Biomim.

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Efforts in the research of tensegrity structures applied to mobile robots have recently been focused on a purely tensegrity solution to all design requirements. Locomotion systems based on tensegrity structures are currently slow and complex to control. Although wheeled locomotion provides better efficiency over distances there is no literature available on the value of wheeled methods with respect to tensegrity designs, nor on how to transition from a tensegrity structure to a fixed structure in mobile robotics. This paper is the first part of a larger study that aims to combine the flexibility, light weight, and strength of a tensegrity structure with the efficiency and simple control of a wheeled locomotion system. It focuses on comparing different types of tensegrity structure for applicability to a mobile robot, and experimentally finding an appropriate transitional region from a tensegrity structure to a conventional fixed structure on mobile robots. It applies this transitional structure to what is, to the authors’ knowledge, the design of the world’s first wheeled tensegrity robot that has been designed with the goal of traversing air ducts.

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Section: Literature Reviewmentioning

confidence: 99%

Design of a novel wheeled tensegrity robot: a comparison of tensegrity concepts and a prototype for travelling air ducts

Carreño

Post

2018

Robot. Biomim.

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“…In the above section, we noted that the rotation of a rigid body in space could be represented by Euler angles; however, the singularity of the transformation laws leads to adopt a new parametrization, the quaternions, with the aim of describing the orientation of the aircraft respect to the earth fixed frame [3,6,8]. Quaternions are commonly used in several application fields, such as computer game development and 3D virtual worlds, but also as a method for rigid body rotation in three-dimensional space.…”

Section: Quaternionsmentioning

confidence: 99%

Mathematical modeling of hexacopter

Artale¹,

Milazzo²,

Ricciardello³

2013

ams

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The purpose of this paper is to present the basic mathematical modeling of microcopters, which could be used to develop proper methods for stabilization and trajectory control. The microcopter taken into account consists of six rotors, with three pairs of counter-rotating fixedpitch blades. The microcopter is controlled by adjusting the angular velocities of the rotors which are spun by electric motors. It is assumed as a rigid body, so the differential equations of the microcopter dynamics can be derived from both the Newton-Euler and Euler-Lagrange equations. Euler-angle parametrization of three-dimensional rotations contains singular points in the coordinate space that can cause failure of both dynamical model and control. In order to avoid singularities, the rotations of the microcopter are parametrized in terms of quaternions. This choice has been made taking into consideration the linearity of quaternion formulation, their stability and efficiency.

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“…In other words, a 3D rigid bar has only five degrees of freedom (DoFs), one less than a 6-DoF 3D rigid body. Therefore, special treatments may be needed to determine the orientation parameters [22].…”

Section: Introductionmentioning

confidence: 99%

A Unified Framework for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars

Luo¹,

Wu²,

Xu³

2022

Preprint

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This paper develops a unified framework to study the dynamics of tensegrity systems with any arbitrary rigid bodies and rigid bars. The natural coordinates are adopted as a completely non-minimal modeling approach to describe both rigid bodies and rigid bars in terms of different combinations of basic points and base vectors. Various coordinate combinations are then unified into polymorphic expressions that succinctly encompass Class-1-to-k tensegrities. Then, the Lagranged'Alembert principle is employed to derive the dynamic equation, which has a constant mass matrix and is free from trigonometric functions as well as centrifugal and Coriolis terms. For numerical analysis of nonlinear dynamics, a modified symplectic integration scheme is derived, accommodating non-conservative forces and boundary conditions. Additionally, formulations for statics and linearized dynamics around static equilibrium states are derived to help determine cable actuation values and calculate natural frequencies and mode shapes, which are commonly needed for structural analyses. Numerical examples are given to demonstrate the proposed approach's abilities in modeling tensegrity structures composed of Class-1-to-k modules and conducting dynamic simulations with complex conditions, including slack cables, gravity loads, seismic grounds, and cable-based deployments. Finally, two novel designs of tensegrity structures exemplify new ways to create multi-functional composite structures.

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A comprehensive dynamic model for class-1 tensegrity systems based on quaternions

Cited by 21 publications

References 21 publications

Design of a novel wheeled tensegrity robot: a comparison of tensegrity concepts and a prototype for travelling air ducts

Design of a novel wheeled tensegrity robot: a comparison of tensegrity concepts and a prototype for travelling air ducts

Mathematical modeling of hexacopter

A Unified Framework for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars

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