Estimation of Location and Orientation From Range Measurements

2015 ◽  
Author(s):  
Sai Krishna Kanth Hari ◽  
Swaroop Darbha
Keyword(s):  
Linear Programming ◽  
Rigid Body ◽  
Center Of Mass ◽  
Body Motion ◽  
Second Step ◽  
True Distance ◽  
Numerical Examples ◽  
Range Measurements ◽  
Motion Constraints

Localization is an important required task for enabling vehicle autonomy. Localization entails the determination of the position of the center of mass and orientation of a vehicle from the available measurements. In this paper, we focus on localization by using the range measurements available to a vehicle from the communication of its multiple onboard receivers with roadside beacons. The model proposed for measurement is as follows: the true distance between a receiver and a beacon is at most equal to a predetermined function of the range measurement. The proposed procedure for localization is as follows: Based on the range measurements specific to a receiver from the beacons, a finite LP (linear programming) is proposed to estimate the location of the receiver. The estimate is essentially the Chebychev center of the set of possible locations of the receiver. In the second step, the location estimates of the vehicle are corrected using rigid body motion constraints and the orientation of the rigid body is thus determined. Two numerical examples provided at the end corroborate the procedures developed in this paper.

Small Vibrations Superimposed on Non-Linear Rigid Body Motion

1997 ◽  
Author(s):  
A. L. Schwab ◽  
J. P. Meijaard
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rigid Motion ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Connecting Rod ◽  
Non Linear ◽  
Linear Differential

Abstract In the case of small elastic deformations in a flexible multi-body system, the periodic motion of the system can be modelled as a superposition of a small linear vibration and a non-linear rigid body motion. For the small deformations this analysis results in a set of linear differential equations with periodic coefficients. These equations give more insight in the vibration phenomena and are computationally more efficient than a direct non-linear analysis by numeric integration. The realization of the method in a program for flexible multibody systems is discussed which requires, besides the determination of the periodic rigid motion, the determination of the linearized equations of motion. The periodic solutions for the linear equations are determined with a harmonic balance method, while transient solutions are obtained by averaging. The stability of the periodic solution is considered. The method is applied to a pendulum with a circular motion of its support point and a slider-crank mechanism with flexible connecting rod. A comparison is made with previous non-linear results.

Momentum Balancing of Four-Bar Linkages

1976 ◽  
Vol 98 (4) ◽  
pp. 1289-1295 ◽  
Author(s):  
J. L. Wiederrich ◽  
B. Roth
Keyword(s):  
Angular Momentum ◽  
Center Of Mass ◽  
Primary Objective ◽  
Simple Design ◽  
Numerical Examples ◽  
Mass Distributions ◽  
Computer Based ◽  
Four Bar Linkage ◽  
Shaking Moment

The primary objective in this work is the determination of conditions for reducing the angular momentum fluctuations (i.e., vibration) transmitted to the frame of a completely force balanced four-bar linkage. This approach leads to relatively simple design equations for determining the inertial properties of the links for good momentum balancing. The essence of this procedure is that it yields analytical results as opposed to the computer-based search techniques required by most previously published methods, which are based on reducing the shaking forces and moments rather than the momentum fluctuations. Furthermore, this method allows for off-line mass distributions (i.e., the center of mass of the link is not on the line of pivots) and, as we show in the paper, this can result in better momentum balancing than the in-line case to which most previous works have been restricted. Some numerical examples are given and the results are compared to similar results obtained by minimizing the RMS shaking moment.

Vibration Centers for Planar Motion

1996 ◽  
Author(s):  
Pat Blanchet ◽  
Harvey Lipkin
Keyword(s):  
Free Vibration ◽  
Rigid Body ◽  
Center Of Mass ◽  
Planar Motion ◽  
Numerical Examples ◽  
Body Vibration ◽  
Principal Directions

Abstract A novel analysis is presented for the planar free vibration of an elastically suspended rigid body. Vibration centers describe the modes shapes and are shown to be constrained to regions specified by the center-of-elasticity, center-of-mass, and stiffness principal directions. Responses are classified by the number of pure translational modes and conditions for existence are given. Numerical examples illustrate the results.

On Dynamically Equivalent Force Systems and Their Application to the Balancing of a Broom or the Stability of a Shoe Box

2004 ◽  
Author(s):  
Just L. Herder ◽  
Arend L. Schwab
Keyword(s):  
Rigid Body ◽  
Center Of Mass ◽  
The Body ◽  
Resultant Force ◽  
Dynamic Equivalence ◽  
Force Systems ◽  
The Stability ◽  
Metacentric Height ◽  
The Given

The stability of a rigid body on which two forces are in equilibrium can be assessed intuitively. In more complex cases this is no longer true. This paper presents a general method to assess the stability of complex force systems, based on the notion of dynamic equivalence. A resultant force is considered dynamically equivalent to a given system of forces acting on a rigid body if the contributions to the stability of the body of both force systems are equal. It is shown that the dynamically equivalent resultant force of two given constant forces applies at the intersection of its line of action and the circle put up by the application points of the given forces and the intersection of their lines of action. The determination of the combined center of mass can be considered as a special case of this theorem. Two examples are provided that illustrate the significance of the proposed method. The first example considers the suspension of a body, by springs only, that is statically balanced for rotation about a virtual stationary point. The second example treats the roll stability of a ship, where the metacentric height is determined in a natural way.

scholarly journals Estimation of the Rigid-Body Motion From Three-Dimensional Images Using a Generalized Center-of-Mass Points Approach

2006 ◽  
Vol 53 (5) ◽  
pp. 2712-2718 ◽  
Author(s):  
B. Feng ◽  
P.P. Bruyant ◽  
P.H. Pretorius ◽  
R.D. Beach ◽  
H.C. Gifford ◽  
...  
Keyword(s):  
Rigid Body ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Three Dimensional Images ◽  
Generalized Center

On the Principle of Transference In Three-Dimensional Kinematics

1981 ◽  
Vol 103 (3) ◽  
pp. 652-656 ◽  
Author(s):  
L. M. Hsia ◽  
A. T. Yang
Keyword(s):  
Rigid Body ◽  
Three Dimensional ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Intrinsic Properties ◽  
Numerical Examples ◽  
Systematic Procedure ◽  
Point Trajectories

In this paper, the principle of transference is developed and applied to the establishment of a systematic procedure for the determination, via screw calculus, of a prescribed rigid body motion. This is an essential first step toward the study of the intrinsic properties of point trajectories in three-dimensional kinematics. Two numerical examples are presented for illustrative purposes.

scholarly journals The necessary and sufficient condition for the stability of a rigid body

2017 ◽  
Vol 13 (4) ◽  
pp. 4999-5003 ◽  
Author(s):  
W. S. Amer
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
First Integrals ◽  
Body Motion ◽  
Sufficient Condition ◽  
Stability Criteria ◽  
Necessary And Sufficient Condition ◽  
The Stability ◽  
Necessary And Sufficient

In this paper, the stability of the unperturbed rigid body motion close to conditions, related with the center of mass, is investigated. The three first integrals for the equations of motion are obtained. These integrals are used to achieve a Lyapunov function and to obtain the necessary and sufficient condition satisfies the stability criteria.

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