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

2002 ◽  
Vol 124 (2) ◽  
pp. 241-251 ◽  
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.

Addenda to “On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models”

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Homin Choi ◽  
Bingen Yang
Keyword(s):  
Rigid Body ◽  
Inertial Frame ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Coordinate Systems ◽  
Body Frame ◽  
Modeling And Analysis ◽  
Body Dynamics

Although quaternions are singularity-free in modeling and analysis of rigid bodies in three-dimensional motion, description of torques may lead to unbounded response of a quaternion-based model. This paper gives theorems on the conditions of torque-induced singularity in four coordinate systems: inertial frame, body frame, Euler basis, and dual Euler basis. According to the theorems, torques applied in an inertial frame or a body frame or a Euler basis will never cause unbounded motion; torques applied in a dual Euler basis, however, may lead to unbounded motion.

Cyclopean Vision, Size Estimation, and Presence in Orthostereoscopic Images

2001 ◽  
Vol 10 (3) ◽  
pp. 312-330 ◽  
Author(s):  
Bernard Harper ◽  
Richard Latto
Keyword(s):  
Visual System ◽  
Three Dimensional ◽  
Point Of View ◽  
Psychophysical Experiment ◽  
Size Estimation ◽  
Human Form ◽  
Image Capture ◽  
Series Of Experiments ◽  
Abstract Shapes ◽  
And Control

Stereo scene capture and generation is an important facet of presence research in that stereoscopic images have been linked to naturalness as a component of reported presence. Three-dimensional images can be captured and presented in many ways, but it is rare that the most simple and “natural” method is used: full orthostereoscopic image capture and projection. This technique mimics as closely as possible the geometry of the human visual system and uses convergent axis stereography with the cameras separated by the human interocular distance. It simulates human viewing angles, magnification, and convergences so that the point of zero disparity in the captured scene is reproduced without disparity in the display. In a series of experiments, we have used this technique to investigate body image distortion in photographic images. Three psychophysical experiments compared size, weight, or shape estimations (perceived waist-hip ratio) in 2-D and 3-D images for the human form and real or virtual abstract shapes. In all cases, there was a relative slimming effect of binocular disparity. A well-known photographic distortion is the perspective flattening effect of telephoto lenses. A fourth psychophysical experiment using photographic portraits taken at different distances found a fattening effect with telephoto lenses and a slimming effect with wide-angle lenses. We conclude that, where possible, photographic inputs to the visual system should allow it to generate the cyclopean point of view by which we normally see the world. This is best achieved by viewing images made with full orthostereoscopic capture and display geometry. The technique can result in more-accurate estimations of object shape or size and control of ocular suppression. These are assets that have particular utility in the generation of realistic virtual environments.

Sensorless Modal Stabilization for Three-Link Robotic Arm With Elastic Wrist Drive Belt

2001 ◽  
Author(s):  
Martin Hosek
Keyword(s):  
Rigid Body ◽  
Robotic Manipulator ◽  
Vibration Damping ◽  
Rigid Body Dynamics ◽  
Limiting Factor ◽  
Direct Drive ◽  
Stability And Control ◽  
Body Dynamics ◽  
Improved Stability ◽  
And Control

Abstract A control system for a three-link direct-drive robotic manipulator with inherent structural flexibilities is presented. The structural flexibilities introduce undesirable vibration modes which may affect operation of the robot motion controller, resulting in destabilization of the closed-loop system. This represents a major limiting factor for implementation of a conventional controller designed solely for the rigid body dynamics of the robotic manipulator. The fundamental idea in the presented approach is to use a composite controller which consists of a trajectory-tracking section designed for the rigid-body dynamics and a vibration-damping compensator added for attenuation of the dominant flexible dynamics. The vibration damping compensator operates on estimated states of the dominant flexible dynamics obtained from a reduced-order state observer. A mechanism is implemented which allows the robotic manipulator to move through or hold in positions where the dominant flexible dynamics is unobservable and uncontrollable. Results of laboratory tests document that the presented approach leads to improved stability and control performance.

Contact-space resolution model for a physically consistent view of simultaneous collisions in articulated-body systems: theory and experimental results

2020 ◽  
Vol 39 (10-11) ◽  
pp. 1239-1258
Author(s):  
Shameek Ganguly ◽  
Oussama Khatib
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Null Space ◽  
Rigid Bodies ◽  
Computationally Efficient ◽  
Space Resolution ◽  
Resolution Model ◽  
Space Dynamics ◽  
Contact Space

Multi-surface interactions occur frequently in articulated-rigid-body systems such as robotic manipulators. Real-time prediction of contact-interaction forces is challenging for systems with many degrees of freedom (DOFs) because joint and contact constraints must be enforced simultaneously. While several contact models exist for systems of free rigid bodies, fewer models are available for articulated-body systems. In this paper, we extend the method of Ruspini and Khatib and develop the contact-space resolution (CSR) model by applying the operational space theory of robot manipulation. Through a proper choice of contact-space coordinates, the projected dynamics of the system in the contact space is obtained. We show that the projection into the dynamically consistent null space preserves linear and angular momentum in a subspace of the system dynamics complementary to the joint and contact constraints. Furthermore, we illustrate that a simultaneous collision event between two articulated bodies can be resolved as an equivalent simultaneous collision between two non-articulated rigid bodies through the projected contact-space dynamics. Solving this reduced-dimensional problem is computationally efficient, but determining its accuracy requires physical experimentation. To gain further insights into the theoretical model predictions, we devised an apparatus consisting of colliding 1-, 2-, and 3-DOF articulated bodies where joint motion is recorded with high precision. Results validate that the CSR model accurately predicts the post-collision system state. Moreover, for the first time, we show that the projection of system dynamics into the mutually complementary contact space and null space is a physically verifiable phenomenon in articulated-rigid-body systems.

scholarly journals Hamilton’s Equations With Euler Parameters for Rigid Body Dynamics Modeling

2004 ◽  
Vol 126 (1) ◽  
pp. 124-130 ◽  
Author(s):  
Ravishankar Shivarama ◽  
Eric P. Fahrenthold
Keyword(s):  
Rigid Body ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Potential Energy Function ◽  
Rigid Body Dynamics ◽  
Dynamics Modeling ◽  
Euler Parameters ◽  
Strongly Nonlinear ◽  
Body Dynamics ◽  
General Potential

A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

scholarly journals Towards a compact and computer-adapted formulation of the dynamics and stability of multi rigid body systems

2002 ◽  
Vol 12 (1) ◽  
pp. 64-70 ◽  
Author(s):  
Hooshang Hemami
Keyword(s):  
Nonlinear Systems ◽  
Rigid Body ◽  
Computer Simulations ◽  
Euler Method ◽  
Rigid Bodies ◽  
Lyapunov Methods ◽  
Full Detail ◽  
Stability And Control ◽  
Euler Methods ◽  
And Control

The dynamics of rigid bodies coupled by homonymic and non-homonymic constraints are formulated by the Newton - Euler method - employing a compact notation. The compact notation involves the use of two three by three matrices A and ? and the totality of constraint vector C. The Lagrangian and Newton - Euler methods are related for a one - link rigid body in order to introduce the methodology of the paper in full detail. Stability and control of the resulting nonlinear systems are investigated by the use of Lyapunov methods. Digital computer simulations of typical movements are carried out in order to demonstrate feasibility of the formulation and the approach.

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

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.

A Computationally Efficient Planar Rigid Body Velocity Measure

2009 ◽  
Author(s):  
Luis E. Criales ◽  
Joseph M. Schimmels
Keyword(s):  
Rigid Body ◽  
Rigid Bodies ◽  
Body Motion ◽  
Computationally Efficient ◽  
Straight Line ◽  
Body Velocity ◽  
Velocity Measure ◽  
Rigid Body Motions ◽  
Line Path ◽  
Planar Motions

A planar rigid body velocity measure based on the instantaneous velocity of all particles that constitute a rigid body is developed. This measure compares the motion of each particle to an “ideal”, but usually unobtainable, motion. This ideal motion is one that would carry each particle from its current position to its desired position on a straight-line path. Although the ideal motion is not a valid rigid body motion, this does not preclude its use as a reference standard in evaluating valid rigid body motions. The optimal instantaneous planar motions for general rigid bodies in translation and rotation are characterized. Results for an example planar positioning problem are presented.

Analysis of rigid-body dynamics for closed-loop mechanisms—its application to a novel satellite tracking device

2003 ◽  
Vol 217 (4) ◽  
pp. 285-298
Author(s):  
T P Jones ◽  
G R Dunlop
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Satellite Tracking ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Parallel Mechanisms ◽  
Body Dynamics ◽  
Tracking Device ◽  
General Method

A general method for analysing the velocity and acceleration kinematics of parallel mechanisms is introduced. A method for analysing the forces experienced by rigid bodies in parallel mechanisms is then introduced, which builds on the kinematics that result in a solution to the dynamics of rigid bodies in parallel mechanisms.

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