Design of Isotropic Accelerometer Strapdowns for Rigid-Body Pose-and-Twist Estimation

2013 ◽  
Author(s):  
Ting Zou ◽  
Jorge Angeles
Keyword(s):  
Rigid Body ◽  
Centripetal Acceleration ◽  
Numerical Example ◽  
Tangential Acceleration ◽  
Novel Design ◽  
Pose And Twist

Coupling of tangential and centripetal acceleration components occurs in the estimation of rigid-body pose and twist with current accelerometer strapdowns. To address this shortcoming and its pernicious effects, a novel design of biaxial accelerometer strapdown is proposed. By virtue of its inherent isotropy, point tangential acceleration is decoupled from its centripetal counterpart, thereby realizing a straightforward and accurate acceleration estimation. The algorithm associated with the strapdown is validated by means of a numerical example, which shows the precision of the strapdown in estimating rigid-body pose and twist.

Isotropic Accelerometer Strapdowns and Related Algorithms for Rigid-Body Pose and Twist Estimation

2014 ◽  
Vol 81 (11) ◽  
Author(s):  
Ting Zou ◽  
Jorge Angeles
Keyword(s):  
Kalman Filter ◽  
Angular Velocity ◽  
Rigid Body ◽  
Angular Acceleration ◽  
Estimation Algorithm ◽  
Velocity Fields ◽  
Excellent Performance ◽  
Simulation Results ◽  
Novel Design ◽  
Pose And Twist

A novel design of accelerometer strapdown, intended for the estimation of the rigid-body acceleration and velocity fields, is proposed here. The authors introduce the concept of isotropic-polyhedral layout of simplicial biaxial accelerometers (SBA), in which one SBA is rigidly attached at the centroid of each face of the polyhedron. By virtue of both the geometric isotropy of the layout and the structural planar isotropy of the SBA, the point tangential relative acceleration is decoupled from its centripetal counterpart, which is filtered out, along with the angular velocity. The outcome is that the rigid-body angular acceleration can be estimated independent of the angular velocity, thereby overcoming a hurdle that mars the estimation process in current accelerometer strapdowns. An estimation algorithm, based on the extended Kalman filter, is included. Simulation results show an excellent performance of the proposed strapdowns in estimating the acceleration and velocity fields of a moving object along with its pose.

scholarly journals An Algorithm for Rigid-Body Angular Velocity and Attitude Estimation Based on Isotropic Accelerometer Strapdowns

2018 ◽  
Vol 85 (6) ◽  
Author(s):  
Ting Zou ◽  
Jorge Angeles
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Industrial Robot ◽  
Attitude Estimation ◽  
Time Step ◽  
Integration Algorithm ◽  
Centripetal Acceleration ◽  
Inherent Nature ◽  
Gimbal Lock ◽  
Tangential Acceleration

A novel algorithm for the estimation of rigid-body angular velocity and attitude—the most challenging part of pose-and-twist estimation—based on isotropic accelerometer strapdowns, is proposed in this paper. Quaternions, which employ four parameters for attitude representation, provide a compact description without the drawbacks brought about by other representations, for example, the gimbal lock of Euler angles. Within the framework of quaternions for rigid-body angular velocity and attitude estimation, the proposed methodology automatically preserves the unit norm of the quaternion, thus improving the accuracy and efficiency of the estimation. By virtue of the inherent nature of isotropic accelerometer strapdowns, the centripetal acceleration is filtered out, leaving only its tangential counterpart, to be estimated and updated. Meanwhile, using the proposed integration algorithm, the angular velocity and the quaternion, which are dependent only on the tangential acceleration, are calculated and updated at appropriate sampled instants for high accuracy. This strategy, which brings about robustness, allows for relatively large time-step sizes, low memory demands, and low computational complexity. The proposed algorithm is tested by simulation examples of the angular velocity and attitude estimation of a free-rotating brick and the end-effector of an industrial robot. The simulation results showcase the algorithm with low errors, as estimated based on energy conservation, and high-order rate of convergence, as compared with other algorithms in the literature.

Novel MEMS Fabry-Perot Interferometric Pressure Sensors

2010 ◽  
Vol 638-642 ◽  
pp. 1009-1014 ◽  
Author(s):  
Ivan Padron ◽  
Anthony T. Fiory ◽  
Nuggehalli M. Ravindra
Keyword(s):  
Optical Fiber ◽  
Rigid Body ◽  
Pressure Sensors ◽  
Sensing Element ◽  
Micro Electro Mechanical Systems ◽  
Considerable Advantage ◽  
Fabry Perot ◽  
Mems Technology ◽  
Interferometric Sensor ◽  
Novel Design

A novel design for a Fabry-Perot Interferometric Sensor (FPIS) consisting of a Fabry-Perot cavity formed between two bonded surfaces is discussed. The Fabry-Perot cavity and the optical fiber to which it is coupled are used as the sensing element and interconnect, respectively. The Fabry-Perot cavity is fabricated using the Micro Electro Mechanical Systems (MEMS) technology. The introduction of a center rigid body diaphragm gives this sensor considerable advantage when compared with previous Fabry-Perot cavity based sensors.

On the Design of Spatial 4C Mechanisms for Rigid-Body Guidance Through 4 Positions

1995 ◽  
Author(s):  
Pierre M. Larochelle
Keyword(s):  
Rigid Body ◽  
Design Process ◽  
Design Procedure ◽  
Design Parameters ◽  
Two Dimensional ◽  
Dimensional Synthesis ◽  
Numerical Example ◽  
Cylindrical Joint ◽  
Free Parameters

Abstract This paper presents a procedure for determining the fixed and moving congruences associated with four finitely separated spatial positions. Furthermore, a methodology is derived for selecting the lines from the congruences which define the joint axes of a 4C mechanism. The result is a design procedure for performing the kinematic dimensional synthesis of spatial 4C mechanisms for four position rigid body guidance. Associated with four finitely separated positions in space are a fixed and a moving congruence. These congruences are a two dimensional set of lines, where each line defines the axis of a cylindrical joint that guides a body through the four prescribed positions. In order to uniquely determine a 4C mechanism from the congruences four free parameters must be specified. We present procedures for determining these free design parameters which result in mechanisms with joint axes that are nearest to some desired location. Moreover, included is a detailed numerical example illustrating the design process.

Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry

2011 ◽  
Vol 226 (5) ◽  
pp. 1254-1262 ◽  
Author(s):  
S-J Jang ◽  
J W Kim ◽  
Y J Choi
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Geometrical Properties ◽  
Plane Vibration ◽  
Numerical Example ◽  
Mass Centre ◽  
Out Of Plane ◽  
Triangular Relationship ◽  
Elastically Supported

The geometrical properties of vibration modes of a single rigid body with one plane of symmetry are presented. When in-plane vibration modes are represented by the axes normal to the plane of symmetry, three intersecting points of those axes and the plane of symmetry constitute two triangles whose orthocentres are coincident with the mass centre and planar couple point, while the induced wrenches of three out-of-plane modes are found to form two triangles whose orthocentres are lying on the mass centre and the perpendicular translation point. Examining these triangles reveals that the triangular areas are proportional to the distributions of the mass and stiffness in the vibrating system and the shapes of the triangles are related to the natural frequencies. A numerical example is provided to verify the proposed findings.

Rigid-body pose and twist estimation using an accelerometer array

2004 ◽  
Vol 74 (3-4) ◽  
pp. 223-236 ◽  
Author(s):  
K. Parsa ◽  
J. Angeles ◽  
A. K. Misra
Keyword(s):  
Rigid Body ◽  
Pose And Twist

The Kinematics of Conical Involute Gear Hobbing

2007 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Rigid Body ◽  
Numerical Example ◽  
Involute Gear ◽  
Gear Hobbing ◽  
Involute Gears ◽  
Setting Parameters

The paper is aimed at finding all relative rigid-body positions of two conical involute gears that mesh together with no backlash. The results are then specialized to determine two key setting parameters for a hobbing machine that has to cut a conical involute gear. A numerical example shows application of the presented results to a case study.

A Line Geometric Approach to Determining Displacements Based on Line Specifications

2008 ◽  
Author(s):  
Wuchang Kuo ◽  
Chintien Huang
Keyword(s):  
Rigid Body ◽  
Measurement Errors ◽  
Systematic Approach ◽  
Screw Theory ◽  
Geometric Approach ◽  
Line Geometry ◽  
Line Complex ◽  
Numerical Example ◽  
On Line ◽  
Best Fit

This paper presents a systematic approach to determining the displacements of a rigid body from line specifications. The underlying concept of the proposed approach pertains to screw theory and line geometry. We utilize the correspondence between a pair of homologous lines and a regulus and that between a screw and a linear line complex. In this paper, a displacement screw is obtained by fitting a linear line complex to two or more line reguli. When two exact pairs of homologous line are specified, we obtain a unique linear line complex, which determines the displacement screw correspondingly. When more than two pairs of homologous lines with measurement errors are specified, it becomes a redundantly specified problem, and a linear line complex that has the best fit to more than two reguli is determined. A numerical example with the specification of four pairs of homologous lines is provided.

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