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Journal ArticleDOI

A calibration procedure for reconfigurable Gough-Stewart manipulators

01 Oct 2020-Mechanism and Machine Theory (Pergamon)-Vol. 152, pp 103920
TL;DR: A calibration procedure for the identification of the geometrical parameters of a reconfigurable Gough-Stewart parallel manipulator is introduced and a numeric algorithm for an efficient solution to the problem is proposed.
About: This article is published in Mechanism and Machine Theory.The article was published on 2020-10-01 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Parallel manipulator & Calibration (statistics).

Summary (2 min read)

1 Introduction

  • Parallel robots are closed-loop mechanisms that are characterized by high stiffness, payload capability and repeatability [1].
  • Furthermore, the estimation of some parameters might not be available at all.
  • In his book, Merlet [1] identifies three main calibration methods for parallel kinematic machines: external calibrations, which are based on measurements with external devices; constrained calibrations, which analyse the motion of the robot in a constrained configuration; auto-calibrations, that only rely on the internal sensors of the robot.
  • While most of the works of the 1990s are focused on practical calibration methods, in the early 2000s several papers on calibration modelling were published.
  • The new decade was also characterized by the rise of new technologies, such as vision-based metrology.

2 Mechanism description

  • The Gough-Stewart mechanism, often called hexapod, is based on a 6-UPS parallel architecture with six identical limbs of varying length, which are controlled by linear motors.
  • The position of each joint on the base platform is expressed by position vector fi, while the relative position of each joint on the moving platform with respect to centre point H is expressed by position vector mi.
  • With reference to Fig. 1, the following parameters are used to define the geometry of the calibration system: .
  • The location of the jth distance sensor on the moving platform is defined by point Sj.
  • A simple iterative procedure based on the Newton-Raphson method with the steps in Fig. 2 is used to solve forward kinematics.

3 Calibration procedure

  • This section presents the mathematical modelling of a calibration procedure that identifies the geometry of a reconfigurable Gough-Stewart platform, which is characterized by a variable position of the joints of the fixed and mobile platform, defined by vectors fi and mi.
  • By assuming perfect passive joints, a general Gough-Stewart platform is characterized by 42 identifiable parameters, namely the xyz coordinates of the mobile joints (18) and fixed joints (18) and the limb offsets (6).
  • A priori estimates are available for the full set of parameters.
  • To compensate errors due to sensor positioning and assembly, the xyz coordinates of sensors (3nr) and of measurement targets (3nr) can be calibrated, for a total of 6nr additional parameters.

4 Calibration in unknown environments

  • The previous section assumes a known coordinate system for the identification of the position of the joints of the base platform.
  • This reference system can then be used to calibrate and identify the geometry of the fixed base and the position of the measuring targets.

5 Experimental validation

  • The proposed calibration procedure is applied to the Free-Hex robot, a reconfigurable Gough-Stewart machining tool, in order to identify the position of its passive joints.
  • Free-Hex, as explained in [33], is a parallel machine tool that is characterized by a mobile platform with fixed geometry and a reconfigurable base platform, with loose magnetic feet at the end of each limb.
  • A second partial calibration has been performed by including the location of all the passive joints as parameters.
  • When compared to the reference geometry of Table 1, the average correction is equal to 1.94 mm, with an average relative correction of 1.03% and a maximum relative correction of 1.63%.
  • A smaller number of poses does not increase the number of iterations to convergence, with 30 to 90 iterations needed for convergence with different subsets.

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Citations
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Journal ArticleDOI
TL;DR: In this paper, a cable-driven device for limb rehabilitation, CUBE2, with a novel end-effector (EE) design and autotuning capabilities to enable autonomous use is presented.
Abstract: Out of all the changes to our daily life brought by the COVID-19 pandemic, one of the most significant ones has been the limited access to health services that we used to take for granted. Thus, in order to prevent temporary injuries from having lingering or permanent effects, the need for home rehabilitation device is urgent. For this reason, this paper proposes a cable-driven device for limb rehabilitation, CUBE2, with a novel end-effector (EE) design and autotuning capabilities to enable autonomous use. The proposed design is presented as an evolution of the previous CUBE design. In this paper, the proposed device is modelled and analyzed with finite element analysis. Then, a novel vision-based control strategy is described. Furthermore, a prototype has been manufactured and validated experimentally. Preliminary test to estimate home position repeatability has been carried out.

16 citations

Journal ArticleDOI
Jiang Shujia1, Chi Changcheng1, Fang Hanliang1, Tang Tengfei1, Zhang Jun1 
TL;DR: A minimal-error-model based two-step kinematic calibration methodology for redundantly actuated parallel manipulators to relieve the influences of zero offsets and geometric source errors.

12 citations

Journal ArticleDOI
TL;DR: In this paper , a two-step kinematic calibration methodology for parallel manipulators is proposed to eliminate redundant geometric source errors in the manipulator to derive a minimal error model that includes the least number of geometric sources errors, and a sensitivity analysis is carried out using the Monte-Carlo simulation.

8 citations

Book ChapterDOI
08 Sep 2021
TL;DR: In this article, an underwater legged robot is modeled as a Gough-Stewart platform to enhance its ability to interact with the environment, and a strategy is provided to harness the redundancy of SILVER2 by finding the optimal posture to maximize forces/torques that it can resist along/around constrained directions.
Abstract: SILVER2 is an underwater legged robot designed with the aim of collecting litter on the seabed and sample the sediment to assess the presence of micro-plastics. Besides the original application, SILVER2 can also be a valuable tool for all underwater operations which require to interact with objects directly on the seabed. The advancement presented in this paper is to model SILVER2 as a Gough-Stewart platform, and therefore to enhance its ability to interact with the environment. Since the robot is equipped with six segmented legs with three actuated joints, it is able to make arbitrary movements in the six degrees of freedom. The robot’s performance has been analysed from both kinematics and statics points of view. The goal of this work is providing a strategy to harness the redundancy of SILVER2 by finding the optimal posture to maximize forces/torques that it can resist along/around constrained directions. Simulation results have been reported to show the advantages of the proposed method.

5 citations

Journal ArticleDOI
01 Dec 2022
TL;DR: In this article , a parallel reconfigurable walking machine tool with shape memory alloy actuation is presented to achieve reconfiguration capabilities, and the optimal walking gaits are determined by kinematic, stability and force analyses.
Abstract: Current research on walking robots strives to achieve a higher efficiency, a better load capacity, and an increased adaptability. Parallel kinematic manipulators (PKMs) are characterized by high payload and accuracy, but conventional PKMs with fixed configurations are limited to constrained workspaces in known structured environments. In this article, we propose a parallel reconfigurable walking machine tool that overcomes these limits by adapting its configuration and gaits to different scenarios. A lightweight and compact positioning system with shape memory alloy actuation is presented to achieve reconfiguration capabilities. Furthermore, kinematic, stability, and force analyses are reported to determine the optimal walking gaits in three different scenarios (with inclined slopes at different angles) and four robot configurations. Finally, a set of experiments with the physical prototype validates the proposed models. The results show that symmetric configurations present a better performance at lower ground inclinations (0.5% error), whereas asymmetric configurations can climb on slope conditions that would prevent the use of conventional PKMs (18% or 10°).

3 citations

References
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Journal ArticleDOI
01 Jun 1997
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.

224 citations

Journal ArticleDOI
01 Oct 1995
TL;DR: A unified formulation for the calibration of both serial-link robots and robotic mechanisms having kinematic closed-loops is presented and applied experimentally to two 6-degree-of-freedom devices: the RSI 6-DOF hand controller and the MEL "modified Stewart platform".
Abstract: A unified formulation for the calibration of both serial-link robots and robotic mechanisms having kinematic closed-loops is presented and applied experimentally to two 6-degree-of-freedom devices: the RSI 6-DOF hand controller and the MEL "modified Stewart platform". The unification is based on an equivalence between end-effector measurements and constraints imposed by the closure of kinematic loops. Errors are allocated to the joints such that the loop equations are satisfied exactly, which eliminates the issue of equation scaling and simplifies the treatment of multi-loop mechanisms. For the experiments reported here, no external measuring devices are used; instead we rely on measurements of displacements in some of the passive joints of the devices. Using a priori estimates of the statistics of the measurement errors and the parameter errors, the method estimates the parameters and their accuracy, and tests for unmodeled factors. >

173 citations

Journal ArticleDOI
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.

152 citations

Journal ArticleDOI
01 Mar 1998-Robotica
TL;DR: This article deals with the kinematic calibration of the Delta robot and a measurement set-up is presented which allows to determine the end-effector's position and orientation with respect to the base.
Abstract: This article deals with the kinematic calibration of the Delta robot. Two different calibration models are introduced: The first one takes into account deviations of all mechanical parts except the spherical joints, which are assumed to be perfect (“model 54”), the second model considers only deviations which affect the position of the end-effector, but not its orientation, assuming that the “spatial parallelogram” remains perfect (“model 24”). A measurement set-up is presented which allows to determine the end-effector's position and orientation with respect to the base. The measurement points are later be used to identify the parameters of the two calibration model resulting in an accuracy improvement of a factor of 12.3 for the position and a factor of 3.7 for the prediction of the orientation.

120 citations

Proceedings ArticleDOI
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.

109 citations

Frequently Asked Questions (2)
Q1. What contributions have the authors mentioned in the paper "A calibration procedure for reconfigurable gough-stewart manipulators" ?

This paper introduces a calibration procedure for the identification of the geometrical parameters of a reconfigurable Gough-Stewart parallel manipulator. Furthermore, an application of the proposed method is discussed with a numerical example, and the behaviour of the calibration procedure is analysed as a function of the number of acquisitions and the number of poses. 

Since the procedure follows a linear approximation with the assumption of small parameter variation, it is possible to study the dependency of limb length on position and geometry independently. A direct derivation of the total differential of Eq. ( 2. 2 ) yields the same result without decoupling the system and can be obtained by expanding Eq. ( A. 5 ) without applying conditions ( A. 6 ) or ( A. 9 ).