Geometric Spectral Algorithms for the Simulation of Rigid Bodies

2019 ◽  
Vol 14 (12) ◽  
Author(s):  
Yiqun Li ◽  
Razikhova Meiramgul ◽  
Jiankui Chen ◽  
Zhouping Yin
Keyword(s):  
Lie Group ◽  
Spectral Methods ◽  
Rigid Bodies ◽  
Geometric Control ◽  
Homogeneous Manifolds ◽  
Practical Algorithms ◽  
Group Methods ◽  
Dynamics And Control ◽  
And Control ◽  
Geometric Dynamics

Abstract Lie group methods are an excellent choice for simulating differential equations evolving on Lie groups or homogeneous manifolds, as they can preserve the underlying geometric structures of the corresponding manifolds. Spectral methods are a popular choice for constructing numerical approximations for smooth problems, as they can converge geometrically. In this paper, we focus on developing numerical methods for the simulation of geometric dynamics and control of rigid body systems. Practical algorithms, which combine the advantages of Lie group methods and spectral methods, are given and they are tested both in a geometric dynamic system and a geometric control system.

Geometric Control of Quadrotor Attitude in Wind With Flow Sensing and Thrust Constraints

2017 ◽  
Author(s):  
William Craig ◽  
Derek A. Paley
Keyword(s):  
Exponential Stability ◽  
Global Exponential Stability ◽  
Initial Response ◽  
Geometric Control ◽  
Effective Control ◽  
System Control ◽  
Numerical Examples ◽  
Flow Sensing ◽  
Dynamics And Control ◽  
And Control

Quadrotor vehicles show great potential over a range of tasks, but effective control in windy environments continues to be a challenge. This paper develops a thrust-saturated controller on the Lie group SO (3) that uses flow sensing in order to reduce the effect of gusts on the vehicle. Designing the controller on SO (3) establishes almost-global exponential stability, and avoids the pitfalls of representing rigid-body kinematics using Euler angles. We prove that exponential stability is retained in the presence of thrust saturation. Aerodynamics are incorporated into the dynamics and control through a model of the blade-flapping phenomena experienced by rotorcraft. Numerical examples show that the system control remains effective despite thrust saturation, and that flow sensing improves both the initial response and steady-state error of the system in wind.

scholarly journals On the Hamel Coefficients and the Boltzmann–Hamel Equations for the Rigid Body

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Rigid Body ◽  
Nonholonomic Systems ◽  
Rigid Bodies ◽  
Body Motion ◽  
Floating Body ◽  
Lagrange Equations ◽  
Local Coordinates ◽  
Dynamics And Control ◽  
Boltzmann Hamel Equations ◽  
And Control

AbstractThe Boltzmann–Hamel (BH) equations are central in the dynamics and control of nonholonomic systems described in terms of quasi-velocities. The rigid body is a classical example of such systems, and it is well-known that the BH-equations are the Newton–Euler (NE) equations when described in terms of rigid body twists as quasi-velocities. It is further known that the NE-equations are the Euler–Poincaré, respectively, the reduced Euler–Lagrange equations on SE(3) when using body-fixed or spatial representation of rigid body twists. The connection between these equations are the Hamel coefficients, which are immediately identified as the structure constants of SE(3). However, an explicit coordinate-free derivation has not been presented in the literature. In this paper the Hamel coefficients for the rigid body are derived in a coordinate-free way without resorting to local coordinates describing the rigid body motion. The three most relevant choices of quasi-velocities (body-fixed, spatial, and hybrid representation of rigid body twists) are considered. The corresponding BH-equations are derived explicitly for the rotating and free floating body. Further, the Hamel equations for nonholonomically constrained rigid bodies are discussed, and demonstrated for the inhomogenous ball rolling on a plane.

PROJECT ON ELECTRONIC STEERING SYSYTEM

2018 ◽  
Vol 4 (5) ◽  
pp. 7
Author(s):  
Shivam Dwivedi ◽  
Prof. Vikas Gupta
Keyword(s):  
Steering System ◽  
Essential Elements ◽  
Variable Pressure ◽  
Passenger Cars ◽  
Control Techniques ◽  
Steering Mechanism ◽  
Dynamics And Control ◽  
Active Research ◽  
Electronic Steering ◽  
And Control

As the four-wheel steering (4WS) system has great potentials, many researchers' attention was attracted to this technique and active research was made. As a result, passenger cars equipped with 4WS systems were put on the market a few years ago. This report tries to identify the essential elements of the 4WS technology in terms of vehicle dynamics and control techniques. Based on the findings of this investigation, the report gives a mechanism of electronically controlling the steering system depending on the variable pressure applied on it. This enhances the controlling and smoothens the operation of steering mechanism.

Author response for "Dynamics and control of microgrids as a resiliency source"

2020 ◽  
Author(s):  
Lung-An Lee ◽  
Chen-Ching Liu ◽  
Yin Xu ◽  
Kevin P. Schneider ◽  
Francis K. Tuffner ◽  
...  
Keyword(s):  
Author Response ◽  
Dynamics And Control ◽  
And Control

Nonlinear Dynamics and Control of Flexible Structures

1989 ◽  
Author(s):  
Francis C. Moon ◽  
Peter Gergely ◽  
James S. Thorp ◽  
John F. Abel
Keyword(s):  
Nonlinear Dynamics ◽  
Flexible Structures ◽  
Dynamics And Control ◽  
And Control ◽  
Nonlinear Dynamics And Control
Sign in / Sign up

Export Citation Format

Share Document