Self-calibration of parallel mechanisms with a case study on Stewart platforms
01 Jun 1997-Vol. 13, Iss: 3, pp 387-397
TL;DR: It is shown that by installing a number of redundant sensors on the Stewart platform, the system is able to perform self-calibration and the approach provides a tool for rapid and autonomous calibration of the parallel mechanism.
Abstract: Self-calibration has the potential of: 1) removing the dependence on any external pose sensing information; 2) producing high accuracy measurement data over the entire workspace of the system with an extremely fast measurement rate; 3) being automated and completely noninvasive; 4) facilitating on-line accuracy compensation; and 5) being cost effective. A general framework is introduced in this paper for the self-calibration of parallel manipulators. The concept of creating forward and inverse measurement residuals by exploring conflicting information provided with redundant sensing is proposed. Some of these ideas have been widely used for robot calibration when robot end-effector poses are available. By this treatment, many existing kinematic parameter estimation techniques can be applied for the self-calibration of parallel mechanisms. It is illustrated through a case study, i.e. calibration of the Stewart platform, that with this framework the design of a suitable self-calibration system and the formulation of the relevant mathematical model become more systematic. A few principles important to the system self-calibration are also demonstrated through the case study. It is shown that by installing a number of redundant sensors on the Stewart platform, the system is able to perform self-calibration. The approach provides a tool for rapid and autonomous calibration of the parallel mechanism.
Citations
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TL;DR: A review of the literature on the six-degree-of-freedom parallel manipulator commonly known as the Stewart platform can be found in this article, where the authors highlight the distinctions of this class from the conventional serial robot manipulators and the novel perspectives that are necessary for the analysis and design of the Stewart platforms in particular and parallel manipulators in general.
637Â citations
TL;DR: This paper presents closed-form solutions for the inverse and direct dynamic models of the Gough-Stewart parallel robot in terms of the Cartesian dynamic model elements of the legs and of the Newton-Euler equation of the platform.
Abstract: This paper presents closed-form solutions for the inverse and direct dynamic models of the Gough-Stewart parallel robot. The models are obtained in terms of the Cartesian dynamic model elements of the legs and of the Newton-Euler equation of the platform. The final form has an interesting and intuitive physical interpretation. The base inertial parameters of the robot, which constitute the minimum number of inertial parameters, are explicitly determined. The number of operations to compute the inverse and direct dynamic models are given.
156Â citations
01 Dec 1999
TL;DR: The calibration makes use of the motorized prismatic joint positions corresponding to some sets of configurations where in each set either a passive universal joint or a passive spherical joint is fixed using a lock mechanism.
Abstract: Presents a method for the autonomous calibration of six degrees-of-freedom parallel robots. The calibration makes use of the motorized prismatic joint positions corresponding to some sets of configurations where in each set either a passive universal joint or a passive spherical joint is fixed using a lock mechanism. Simulations give us an idea about the number of sets that must be used, the number of configurations by set and the effect of noise on the calibration accuracy. The main advantage of this method is that it can be executed rapidly without need to external sensors to measure the position or the orientation of the mobile platform.
152Â citations
Cites background from "Self-calibration of parallel mechan..."
...WhereXc is the current vector of position and orientation defining Fm into F0; qd is the given vector of the leg lengths,Jinv is the inverse Jacobian matrix; its rows are easy to obtain analytically [12], J+inv is the pseudo-inverse ofJinv, and" is the desired accuracy....
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TL;DR: In this paper, a vision-based self-calibration method for a serial robot manipulator, which only requires a ground-truth scale in the reference frame, is proposed.
Abstract: Unlike the traditional robot calibration methods, which need external expensive calibration apparatus and elaborate setups to measure the 3D feature points in the reference frame, a vision-based self-calibration method for a serial robot manipulator, which only requires a ground-truth scale in the reference frame, is proposed in this paper. The proposed algorithm assumes that the camera is rigidly attached to the robot end-effector, which makes it possible to obtain the pose of the manipulator with the pose of the camera. By designing a manipulator movement trajectory, the camera poses can be estimated up to a scale factor at each configuration with the factorization method, where a nonlinear least-square algorithm is applied to improve its robustness. An efficient approach is proposed to estimate this scale factor. The great advantage of this self-calibration method is that only image sequences of a calibration object and a ground-truth length are needed, which makes the robot calibration procedure more autonomous in a dynamic manufacturing environment. Simulations and experimental studies on a PUMA 560 robot reveal the convenience and effectiveness of the proposed robot self-calibration approach.
114Â citations
Cites methods from "Self-calibration of parallel mechan..."
...In [ 3 ], Zhuang proposed a self-calibration method for parallel mechanisms with a case study on Stewart platform....
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21 May 2001
TL;DR: A numerical method for the determination of the identifiable parameters of parallel robots based on QR decomposition of the observation matrix of the calibration system is presented.
Abstract: Presents a numerical method for the determination of the identifiable parameters of parallel robots. The special case of Stewart-Gough 6 degrees-of-freedom parallel robots is studied for classical and self calibration methods, but this method can be generalized to any kind of parallel robot. The method is based on QR decomposition of the observation matrix of the calibration system. Numerical relations between the parameters which are identified and those which are not identifiable can be obtained for each method.
109Â citations
Cites background or methods from "Self-calibration of parallel mechan..."
...Figure 3: Two different robots with the same orientation of one leg for a given configuration q Results are given in [9] with 6 extra sensors on 3 passive U-joint....
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...Self calibration methods using extra sensors on the passive joints have been also proposed for parallel robots [6] [7] [8] [9]....
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...Zhuang [9] has presented autonomous methods based on the use of extra sensors on some passive U-joints....
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References
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28,888Â citations
"Self-calibration of parallel mechan..." refers methods in this paper
..., and are positive definite weighting matrices whenever a nonlinear least estimation technique such as the Levenberg–Marquardt algorithm [22] is considered....
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Book•
01 Jan 1974
TL;DR: This is the first book on the optimal estimation that places its major emphasis on practical applications, treating the subject more from an engineering than a mathematical orientation, and the theory and practice of optimal estimation is presented.
Abstract: This is the first book on the optimal estimation that places its major emphasis on practical applications, treating the subject more from an engineering than a mathematical orientation. Even so, theoretical and mathematical concepts are introduced and developed sufficiently to make the book a self-contained source of instruction for readers without prior knowledge of the basic principles of the field. The work is the product of the technical staff of the The Analytic Sciences Corporation (TASC), an organization whose success has resulted largely from its applications of optimal estimation techniques to a wide variety of real situations involving large-scale systemsArthur Gelb writes in the Foreword that "It is our intent throughout to provide a simple and interesting picture of the central issues underlying modern estimation theory and practice. Heuristic, rather than theoretically elegant, arguments are used extensively, with emphasis on physical insights and key questions of practical importance."Numerous illustrative examples, many based on actual applications, have been interspersed throughout the text to lead the student to a concrete understanding of the theoretical material. The inclusion of problems with "built-in" answers at the end of each of the nine chapters further enhances the self-study potential of the text.After a brief historical prelude, the book introduces the mathematics underlying random process theory and state-space characterization of linear dynamic systems. The theory and practice of optimal estimation is them presented, including filtering, smoothing, and prediction. Both linear and non-linear systems, and continuous- and discrete-time cases, are covered in considerable detail. New results are described concerning the application of covariance analysis to non-linear systems and the connection between observers and optimal estimators. The final chapters treat such practical and often pivotal issues as suboptimal structure, and computer loading considerations.This book is an outgrowth of a course given by TASC at a number of US Government facilities. Virtually all of the members of the TASC technical staff have, at one time and in one way or another, contributed to the material contained in the work
6,015Â citations
"Self-calibration of parallel mechan..." refers background or methods in this paper
...A natural choice for the state equation in this case is the random walk model [24]....
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...If the extended Kalman filter is applied to estimate the kinematic error parameters, the measurement residuals must be augmented to include terms that represent system and measurement noises [24], [25]....
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01 Jun 1965
TL;DR: In this article, the authors describe a six-degree-of-freedom control with six motors, each having a ground abutment, for simulating flight conditions in the training of pilots.
Abstract: This paper describes a mechanism which has six degrees of freedom, controlled in any combination by six motors, each having a ground abutment. It is considered that by its particular arrangement, this mechanism may form an elegant design for simulating flight conditions in the training of pilots. Unlike most simulators, it has no fixed axes relative to the ground, and therefore within the limits of amplitude of the design it can truly simulate the conditions of banking by carrying the simulation of control surfaces into the axes of the new attitude.Variations in control arrangements are described and their respective design merits considered.Other possible uses for this mechanism are mentioned, including automation of production.
2,341Â citations
"Self-calibration of parallel mechan..." refers background in this paper
...PARALLEL manipulators, particularly the Stewart platform [1], [2], have recently attracted considerable interest....
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TL;DR: The Stewart Platform is one example of a parallel connection robot manipulator as discussed by the authors, and it has been used extensively in the past several years for a variety of tasks in the field of robotics.
Abstract: The Stewart Platform is one example of a parallel connection robot manipulator. This paper summarizes work that has been done at Oregon State University over the past several years on this topic. T...
820Â citations
"Self-calibration of parallel mechan..." refers background in this paper
...PARALLEL manipulators, particularly the Stewart platform [1], [2], have recently attracted considerable interest....
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Book•
19 Mar 1991
TL;DR: The details of the calibration process step-by-step are described, covering systems modeling, measurement, identification, correction and performance evaluation.
Abstract: From the Publisher:
Describes the details of the calibration process step-by-step, covering systems modeling, measurement, identification, correction and performance evaluation. Calibration techniques are presented with an explanation of how they interact with each other as they are modified. Shows the reader how to determine if, in fact, a robot problem is a calibration problem and then how to analyze it.
479Â citations
"Self-calibration of parallel mechan..." refers background or methods in this paper
...Kinematic calibration can significantly improve the manipulator accuracy [11], [12]....
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...The identification of these unknown geometric relationships is a subset of the standard calibration problems given in [11]....
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...Once the measurement residuals are constructed, these can be related to kinematic parameter errors by differential error odels, which resembles the practice in serial manipulator calibration using error-model-based techniques [11]....
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...of model-based robot calibration techniques [11], in which the...
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