A quaternion-based simulation of multirotor dynamics

The main problem addressed in this paper is the quaternion-based trajectory control of a microcopter consisting of six rotors with three pairs of counter-rotating fixed-pitch blades, known as hexacopter. If the hypothesis of rigid body condition is assumed, the Newton–Euler equations describe the translational and rotational motion of the drone. The standard 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, all the rotations of the microcopter are thus parametrized in terms of quaternions and an original proportional derivative (PD) regulator is proposed in order to control the dynamical model. Numerical simulations will be performed on symmetrical flight configuration, proving the reliability of the proposed PD control technique.

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Controlling Mixing Inside a Droplet by Time Dependent Rigid-Body Rotation

Volume 13: Nano-Manufacturing Technology; and Micro and Nano Systems, Parts A and B ◽

10.1115/imece2008-68026 ◽

2008 ◽

Author(s):

Rodolphe Chabreyrie ◽

Dmitri Vainchtein ◽

Cristel Chandre ◽

Pushpendra Singh ◽

Nadine Aubry

Keyword(s):

Rigid Body ◽

Liquid Droplet ◽

Three Dimensional ◽

Time Dependent ◽

Mixing Enhancement ◽

Body Rotation ◽

Rigid Body Rotation ◽

Digital Microfluidic ◽

And Control ◽

Time Periodic

The use of microscopic discrete fluid volumes (i.e., droplets) as microreactors for digital microfluidic applications often requires mixing enhancement and control within droplets. In this work, we consider a translating spherical liquid droplet to which we impose a time periodic rigid-body rotation which we model using the superposition of a Hill vortex and an unsteady rigid body rotation. This perturbation in the form of a rotation not only creates a three-dimensional chaotic mixing region, which operates through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of the mixing. Such a control is achieved by judiciously adjusting the three parameters that characterize the rotation, i.e., the rotation amplitude, frequency and orientation of the rotation. As the size of the mixing region is increased, complete mixing within the drop is obtained.

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Comparative Study of Two Pose Measuring Systems Used to Reduce Robot Localization Error

Sensors ◽

10.3390/s20051305 ◽

2020 ◽

Vol 20 (5) ◽

pp. 1305

Author(s):

Marek Franaszek ◽

Geraldine S. Cheok ◽

Jeremy A. Marvel

Keyword(s):

Rigid Body ◽

Body Condition ◽

Degrees Of Freedom ◽

Industrial Robot ◽

Substantial Reduction ◽

Three Dimensional ◽

Robot Localization ◽

Localization Error ◽

Measuring Systems ◽

The Difference

The performance of marker-based, six degrees of freedom (6DOF) pose measuring systems is investigated. For instruments in this class, the pose is derived from locations of a few three-dimensional (3D) points. For such configurations to be used, the rigid-body condition—which requires that the distance between any two points must be fixed, regardless of orientation and position of the configuration—must be satisfied. This report introduces metrics that gauge the deviation from the rigid-body condition. The use of these metrics is demonstrated on the problem of reducing robot localization error in assembly applications. Experiments with two different systems used to reduce the localization error of the same industrial robot yielded two conflicting outcomes. The data acquired with one system led to substantial reduction in both position and orientation error of the robot, while the data acquired with a second system led to comparable reduction in the position error only. The difference is attributed to differences between metrics used to characterize the two systems.

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Self-rotating 3D chiral mechanical metamaterials

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2020.0825 ◽

2021 ◽

Vol 477 (2251) ◽

pp. 20200825

Author(s):

K. K. Dudek ◽

A. Drzewiński ◽

M. Kadic

Keyword(s):

Rotational Motion ◽

Attitude Control ◽

Structural Unit ◽

Three Dimensional ◽

Point Of View ◽

Complex Structures ◽

Structural Elements ◽

Mechanical Metamaterials ◽

Potential Applications ◽

And Control

In this work, we demonstrate that three-dimensional chiral mechanical metamaterials are able to self-twist and control their global rotation. We also discuss the possibility of adjusting the extent of the global rotation manifested by the system in a programmable manner. In addition, we show that the effect of the global rotation can be observed both for small systems composed of a single structural unit as well as more complex structures incorporating several structural elements connected to each other. Finally, it is discussed that the results presented in this work are very promising from the point of view of potential applications such as satellites or telescopes in space, where appropriately designed mechanical metamaterials could be used for the attitude control as well as other systems where the control of the rotational motion is required.

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NPSNET: Flight Simulation Dynamic Modeling Using Quaternions

Presence Teleoperators & Virtual Environments ◽

10.1162/pres.1992.1.4.404 ◽

1992 ◽

Vol 1 (4) ◽

pp. 404-420 ◽

Cited By ~ 42

Author(s):

Joseph M. Cooke ◽

Michael J. Zyda ◽

David R. Pratt ◽

Robert B. McGhee

Keyword(s):

Real Time ◽

Low Cost ◽

Three Dimensional ◽

Euler Angle ◽

General Purpose ◽

Flight Simulation ◽

High Data ◽

Stability And Control ◽

Data Rates ◽

And Control

The Naval Postgraduate School (NPS) has actively explored the design and implementation of networked, real time, three-dimensional battlefield simulations on low-cost, commercially available graphics workstations. The most recent system, NPSNET, has improved in functionality to such an extent that it is considered a low-cost version of the Defense Advanced Research Project Agency's (DARPA) SIMNET system. To reach that level, it was necessary to economize in certain areas of the code so that real time performance occurred at an acceptable level. One of those areas was in aircraft dynamics. However, with “off-the-shelf” computers becoming faster and cheaper, real-time and realistic dynamics are no longer an expensive option. Realistic behavior can now be enhanced through the incorporation of an aerodynamic model. To accomplish this task, a prototype flight simulator was built that is capable of simulating numerous types of aircraft simultaneously within a virtual world. Besides being easily incorporated into NPSNET, such a simulator also provides the base functionality for the creation of a general purpose aerodynamic simulator that is particularly useful to aerodynamics students for graphically analyzing differing aircraft's stability and control characteristics. This system is designed for use on a Silicon Graphics workstation and uses the GL libraries. A key feature of the simulator is the use of quaternions for aircraft orientation representation to avoid singularities and high data rates associated with the more common Euler angle representation of orientation.

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A General Framework for Rigid Body Dynamics, Stability, and Control

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1468227 ◽

2002 ◽

Vol 124 (2) ◽

pp. 241-251 ◽

Cited By ~ 16

Author(s):

Hooshang Hemami

Keyword(s):

Rigid Body ◽

Three Dimensional ◽

Stability Control ◽

Rigid Bodies ◽

Rigid Body Dynamics ◽

Point Of View ◽

Body System ◽

Computationally Efficient ◽

Augmented State ◽

And Control

Augmented state spaces for the representation of systems that include rigid bodies, actuators, controllers, and integrate mechanical, electrical, sensory, and computational subsystems, are proposed here. The formulation is based on the Newton-Euler point of view, and has many advantages in stability, control, simulation, and computational considerations. The formulation is developed here for a one- and two-link three-dimensional rigid body system. Three simulations are presented to study stability of the system and to demonstrate feasibility and application of the formulation. The formulation affords an embedding of the system in a larger state space. The rigid body system can be stabilized, in the sense of Lyapunov, in this larger space with very general and minimally restricted feedback structures. The formulation is modular to implementation and is computationally efficient. The method offers alternative states that are easier to control and measure than Euler angles. Thus, the formulation offers advantages from a sensory and instrumentation point of view. The formulation is versatile, and yields conveniently to applications in studies of human neuro-musculo-skeletal systems, robotic systems, marionettes and humanoids for animation and simulation of crash and other injury prone maneuvers and sports. It offers a methodical and systematic procedure for formulation of large systems of interconnected rigid bodies.

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