Kinematic calibration using the product of exponentials formula

Robotica ◽  
1996 ◽  
Vol 14 (4) ◽  
pp. 415-421 ◽  
Author(s):  
Koichiro Okamura ◽  
F.C. Park
Keyword(s):  
Ad Hoc ◽  
Screw Theory ◽  
Geometric Interpretation ◽  
Kinematic Calibration ◽  
Kinematic Parameters ◽  
Open Chain ◽  
Calibration Algorithm ◽  
Forward Kinematic ◽  
Matrix Exponentials ◽  
Derivatives Of

SUMMARYWe present a method for kinematic calibration of open chain mechanisms based on the product of exponentials (POE) formula. The POE formula represents the forward kinematics of an open chain as a product of matrix exponentials, and is based on a modern geometric interpretation of classical screw theory. Unlike the kinematic representations based on the Denavit- Hartenberg (D-H) parameters, the kinematic parameters in the POE formula vary smoothly with changes in the joint axes, ad hoc methods designed to address the inherent singularities in the D-H parameters are therefore unnecessary. Another important advantage is that simple closed-form expressions can be obtained for the derivatives of the forward kinematic equations with respect to the kinematic parameters. After introducing the POE formula, we derive a least-squares kinematic calibration algorithm for general open chain mechanisms. Simulation results with a 6-axis open chain are presented.

scholarly journals Inverse kinematic solution of 6R robot manipulators based on screw theory and the Paden–Kahan subproblem

2018 ◽  
Vol 15 (6) ◽  
pp. 172988141881829 ◽  
Author(s):  
Rongbo Zhao ◽  
Zhiping Shi ◽  
Yong Guan ◽  
Zhenzhou Shao ◽  
Qianying Zhang ◽  
...  
Keyword(s):  
Inverse Kinematics ◽  
Matrix Theory ◽  
Screw Theory ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Kinematic Calibration ◽  
Kinematic Parameters ◽  
Kinematics Modeling ◽  
High Level ◽  
Kinematic Solution

The traditional Denavit–Hatenberg method is a relatively mature method for modeling the kinematics of robots. However, it has an obvious drawback, in that the parameters of the Denavit–Hatenberg model are discontinuous, resulting in singularity when the adjacent joint axes are parallel or close to parallel. As a result, this model is not suitable for kinematic calibration. In this article, to avoid the problem of singularity, the product of exponentials method based on screw theory is employed for kinematics modeling. In addition, the inverse kinematics of the 6R robot manipulator is solved by adopting analytical, geometric, and algebraic methods combined with the Paden–Kahan subproblem as well as matrix theory. Moreover, the kinematic parameters of the Denavit–Hatenberg and the product of exponentials-based models are analyzed, and the singularity of the two models is illustrated. Finally, eight solutions of inverse kinematics are obtained, and the correctness and high level of accuracy of the algorithm proposed in this article are verified. This algorithm provides a reference for the inverse kinematics of robots with three adjacent parallel joints.

Kinematic Calibration for Redundantly Actuated Parallel Mechanisms

2004 ◽  
Vol 126 (2) ◽  
pp. 307-318 ◽  
Author(s):  
Jay il Jeong ◽  
Dongsoo Kang ◽  
Young Man Cho ◽  
Jongwon Kim
Keyword(s):  
Optimization Algorithm ◽  
Parallel Mechanism ◽  
Kinematic Calibration ◽  
Parallel Mechanisms ◽  
Geometrical Constraint ◽  
Kinematic Parameters ◽  
Angle Error ◽  
Calibration Algorithm ◽  
Redundantly Actuated

We present a new kinematic calibration algorithm for redundantly actuated parallel mechanisms, and illustrate the algorithm with a case study of a planar seven-element 2-degree-of-freedom (DOF) mechanism with three actuators. To calibrate a nonredundantly actuated parallel mechanism, one can find actual kinematic parameters by means of geometrical constraint of the mechanism’s kinematic structure and measurement values. However, the calibration algorithm for a nonredundant case does not apply for a redundantly actuated parallel mechanism, because the angle error of the actuating joint varies with position and the geometrical constraint fails to be consistent. Such change of joint angle error comes from constraint torque variation with each kinematic pose (meaning position and orientation). To calibrate a redundant parallel mechanism, one therefore has to consider constraint torque equilibrium and the relationship of constraint torque to torsional deflection, in addition to geometric constraint. In this paper, we develop the calibration algorithm for a redundantly actuated parallel mechanism using these three relationships, and formulate cost functions for an optimization algorithm. As a case study, we executed the calibration of a 2-DOF parallel mechanism using the developed algorithm. Coordinate values of tool plate were measured using a laser ball bar and the actual kinematic parameters were identified with a new cost function of the optimization algorithm. Experimental results showed that the accuracy of the tool plate improved by 82% after kinematic calibration in a redundant actuation case.

Kinematic Analysis Based on Screw Theory of a 3-DOF Cable-Driven Surgical Instrument

2014 ◽  
Vol 490-491 ◽  
pp. 375-378
Author(s):  
Li Min Chang ◽  
Hong Qiang Sang ◽  
Li Ping Xu
Keyword(s):  
Kinematic Analysis ◽  
Screw Theory ◽  
Angular Displacement ◽  
Inverse Kinematic ◽  
Analysis Method ◽  
Surgical Instrument ◽  
Open Chain ◽  
End Effectors ◽  
Forward Kinematic ◽  
And Control

The Forward kinematic and the inverse kinematic were analyzed of 3-DOF cable-driven surgical instrument in this paper. Kinematics of open chain surgical instrument was derived by the product of exponentials formula, and Paden and Kahan subproblems. Kinematic analysis of the 3-DOF cable-driven surgical instrument can be analyzed by the map relationship between the end effectors and the joint angles of the surgical instrument after removal of cables and pulleys and the map relationship between the rotor angular displacement of the motor and joint angular displacement. The analysis method can be useful for motion analysis and control for cable-driven robotic mechanisms.

Preparation and Disulfide Interchange Reactions of Unsymmetrical Open-chain Derivatives of Cystine

1959 ◽  
Vol 81 (7) ◽  
pp. 1729-1734 ◽  
Author(s):  
Leonidas Zervas ◽  
Leo Benoiton ◽  
Ellinor Weiss ◽  
Milton Winitz ◽  
Jesse P. Greenstein
Keyword(s):  
Open Chain ◽  
Derivatives Of ◽  
Interchange Reactions

Identification of principal screws of two- and three-screw systems

2007 ◽  
Vol 221 (12) ◽  
pp. 1701-1715 ◽  
Author(s):  
J-S Zhao ◽  
F Chu ◽  
Z-J Feng
Keyword(s):  
Screw Theory ◽  
Coordinate Systems ◽  
Third Order ◽  
Analytical Methodology ◽  
Partial Derivatives ◽  
Spatial Mechanisms ◽  
Analysis Theory ◽  
Definition Of ◽  
Derivatives Of ◽  
Homogeneous Linear

The current paper proposes a unified analytical methodology to identify the principal screws of two- and three-screw systems. Based on the definition of the pitch of a screw, it first obtains an identical homogeneous quadric equation. According to functional analysis theory, it is known that the partial derivatives of an identical quadric equation with respect to its variables must be zero. Therefore, the paper deduces a set of linear homogeneous equations that are made up of the partial derivatives of the quadric equation. With the existing criteria of non-zero solutions for homogeneous linear algebra equations, it ultimately obtains the formulas of the principal pitches and the associated principal screws of the system. The most outstanding contribution of this methodology is that it proposes a unified analytical approach to identify the principal pitches and the principal coordinate systems of the second-order and the third-order screw systems. This should be a new contribution to the screw theory and will boost its applications to the kinematics analysis of robots and spatial mechanisms.

A New Measurement Device for Kinematic Calibration of Parallel Manipulators

2004 ◽  
Author(s):  
Abdul Rauf ◽  
Sung-Gaun Kim ◽  
Jeha Ryu
Keyword(s):  
Parallel Manipulators ◽  
Measurement Procedure ◽  
Initial Guess ◽  
Measurement Noise ◽  
Kinematic Calibration ◽  
Kinematic Parameters ◽  
End Effector ◽  
Experimental Procedure ◽  
New Device ◽  
Rotation Component

Kinematic calibration is a process that estimates the actual values of geometric parameters to minimize the error in absolute positioning. Measuring all the components of Cartesian posture assure identification of all parameters. However, measuring all components, particularly the orientation, can be difficult and expensive. On the other hand, with partial pose measurements, experimental procedure is simpler. However, all parameters may not be identifiable. This paper proposes a new device that can be used to identify all kinematic parameters with partial pose measurements. Study is performed for a 6 DOF (degree-of-freedom) fully parallel Hexa Slide manipulator. The device, however, is general and can be used for other parallel manipulators. The proposed device consists of a link with U joints on both sides and is equipped with a rotary sensor and a biaxial inclinometer. When attached between the base and the mobile platform, the device restricts the end-effector’s motion to 5 DOF and measures two position components and one rotation component of the end-effector. Numerical analyses of the identification Jacobian reveal that all parameters are identifiable. Computer simulations show that the identification is robust for the errors in the initial guess and the measurement noise. Intrinsic inaccuracies of the device can significantly deteriorate the calibration results. A measurement procedure is proposed and cost functions are discussed to prevent propagation of the inaccuracies to the calibration results.

Dynamic Calibration for Serial Robotic Manipulators Based on the Zero Position Analysis Method

1989 ◽  
Author(s):  
G. Z. Qian ◽  
K. Kazerounian
Keyword(s):  
Robotic Manipulators ◽  
Calibration Method ◽  
Dynamic Calibration ◽  
Calibration Model ◽  
Kinematic Calibration ◽  
Dynamic Parameters ◽  
Analysis Method ◽  
Kinematic Parameters ◽  
Position Analysis ◽  
Zero Position

Abstract In the continuation of a kinematic calibration method developed in a previous report, a new dynamic calibration model for serial robotic manipulators is presented in this paper. This model is based on the Zero Position Analysis Method. It entails the process of estimating the errors in the robot’s dynamic parameters by assuming that the kinematic parameters are free of errors. The convergence and effectiveness of the model are demonstrated through numerical simulations.

scholarly journals Turbulent outflows from [WC] nuclei

1997 ◽  
Vol 180 ◽  
pp. 108-108 ◽  
Author(s):  
Y. Grosdidier ◽  
A. Acker ◽  
A.F.J. Moffat ◽  
O. Chesneau ◽  
T. Dimeo
Keyword(s):  
Line Profile ◽  
Ad Hoc ◽  
Planetary Nebulae ◽  
Forthcoming Paper ◽  
Extensive Study ◽  
Kinematic Parameters ◽  
Average Motion ◽  
First Time

In the framework of the extensive study of [WC]-type nuclei of planetary nebulae undertaken since 1993 by Acker and collaborators, we report wind fluctuations for the two brightest late-type [WC] stars in the sky, observed at Observatoire de Haute-Provence (OHP, France) and Observatoire du mont Mégantic (OMM, Canada). In particular we confirm Balick et al.'s (1996, AJ, 111, 834) CIIIλ5696 line profile variations for the [WC8] nucleus of NGC 40. Moving features seen on the top of this line are interpreted as outflowing “blobs” which are accelerated in the WR wind. Kinematic parameters have been derived and compared to those observed for massive WR stars. This will be discussed in a forthcoming paper (Grosdidier et al., 1996, in preparation). Assuming the average motion of the blobs reflects the global wind expansion and adopting the ad hoc β velocity law, we find that the exponent β must be larger than 3 in order to fit the measured radial accelerations (up to ∼ 0.08 km s–2). Evidence for clumping in the wind of the [WC9] nucleus BD+30°3639 is shown for the first time and presented in Acker et al. (1996, A&ALetters, in press). In contrast to NGC 40, the clumps in this star show very low acceleration.

Investigation on Kane dynamic equations based on screw theory for open-chain manipulators

2005 ◽  
Vol 26 (5) ◽  
pp. 627-635 ◽  
Author(s):  
Liu Wu-fa ◽  
Gong Zhen-bang ◽  
Wang Qin-que
Keyword(s):  
Screw Theory ◽  
Dynamic Equations ◽  
Open Chain
Sign in / Sign up

Export Citation Format

Share Document