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Publication# Calibration of high-precision flexure parallel robots

Résumé

Over the last decades, calibration techniques have been widely used in robotics since they represent a cost-effective solution for improving the accuracy of robots and machine-tools. They only involve software modification without the necessity of revising the robot design or tightening the manufacturing tolerances. The goal of this thesis is to propose a procedure that guides the engineer through the calibration of a given multi-DOF flexure parallel robot within sub-µm accuracy. Two robots having 3 and 6 degrees of freedom have been considered as a case-study throughout the work. As in any calibration procedure, the work has been conducted on three different fronts: measurement, data processing and validation. The originality of this thesis in respect to published material lies in these three points. Measurements were carried out in a chamber inside which the measuring environment was protected against mechanical and thermal perturbations. In particular, the temperature variations experienced by the different parts of the measuring loop during a typical measurement session were stabilized within less than ± 0.1 °C. Proposed procedures allow the collection of reliable sets of data on the two robots. Delicate aspects of practical implementation are discussed. In particular, the problem of collecting a complete set of 6D data within accuracies in the nanometre range, for which there is still a lack of standard equipment, is solved using a procedure comprising several steps and making use of existing instrumentation. Suggestions for future investigations are given, regarding either long-term research problems or short-term industrial implementation issues. Data processing was performed using two different techniques in order to reach absolute accuracies after calibration better than ± 100 nm for translations and ± 3 arcsec for rotations (± 0.3 arcsec inside a more restricted range of ± 0.11°). The first method is called the "model-based approach" and requires the use of a known analytical relationship between the motor and operational coordinates of the robot. This relationship involves a certain number of parameters that can be related to the geometry of the robot (physical models) or simply mathematical coefficients of an approximating mathematical function (behavioural models). In the case of high-precision multi-DOF flexure parallel robots, we show that polynomial-based behavioural models are preferable to physical models in terms of accuracy for data processing tasks. In the second method, called the "model-free approach", the user does not need to model explicitly the main error sources (or their effect) affecting the robot accuracy. A model-free approach has been implemented using Artificial Neural Networks. We show that, using a heuristic search based on a decision-tree, the architecture of a network with satisfactory prediction capability can be found systematically. In particular, this algorithm can find a network able to predict the direct correspondence between the motor and operational coordinates (within the desired accuracy) without the help of the Inverse Geometric Model of the robot, i.e. even if the nominal geometry of the robot being calibrated remains unknown. This result contradicts conclusions reported by previous researchers. It is claimed that any robot (not necessarily a high-precision flexure parallel mechanism) can be calibrated by means of a "neural approach" in which the architecture of an appropriate network is determined with the help of our algorithm. Two examples (other than the robots measured in this thesis) are given to illustrate this universality. In the last part of this work, we provide a feasibility study on the use of indentation, a technique traditionally used for material testing, as a validation procedure to assess the accuracy of the calibrated degrees of freedom. The industrial interest of this technique lies in the fact that the robot is asked to execute similar motions to those involved in a real micro-machining operation.

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In the high-precision industry, most operations require the use of robots able to accomplish highly accurate and repeatable motions. In order to meet the desired level of absolute accuracy, one has to limit or even suppress the effects of different sources of inaccuracy by means of an appropriate calibration. However, calibration techniques cannot be applied to compensate inaccuracies occuring along passive (non-actuated) degrees of freedom (e.g orientation errors on the end-effector of a 3 degrees-of-freedom (DOF) in translation robot). The main goal of this thesis is to evaluate and benchmark the effects of these different sources of inaccuracy. Moreover, a set of design rules are proposed in order to optimize flexure parallel robots regarding their absolute accuracy. The robots studied in this work are of "Delta Cube" type, having their kinematic chains composed of translational stages and space parallelograms (acting as universal joints). These robots have the following features: their 3 DOF are the (x, y, z) translations on the Euclidean space, the stroke of each DOF goes from ±1 mm to ± 4 mm, their repeatabilities are at the nanometre range (thanks to the absence of dry friction and mechanical play), their resolutions are within a few nanometers (only limited by the captors used), their small sizes go from 1,5 dm3 to 13 dm3. The analysis of the effects of the different sources of inaccuracy has been focused on the following points: the basic elements composing the robot structure (translational stage, space parallelogram). Studying the influence on the absolute accuracy caused by a variation of a given geometric dimension provides knowledge on how to optimize the overall robot dimensions regarding absolute accuracy; the assembly of the different basic elements on the kinematic chain (in particular their relative orientation) is also critical for the absolute accuracy of the robot since it may cause parasitic effects such as orientation errors in the end-effector; the type and location of the different captors, motors and the frame can also influence accuracy. The analysis of the influence of each source of inaccuracy (manufacturing tolerances, temperature variations, assembly defaults, effect of external loads) and their coupling has been mainly performed numerically by means of Finite-Element Models. Theoretical results have been verified by experimental data. Considering the simulation results for each basic structure as well as the comparison of different assembly variants, general design rules have been proposed in order to optimize a given flexure parallel robot regarding absolute accuracy and considering also the application the robot is made for. This work is a contribution to the design of high-precision flexure parallel robots regarding absolute accuracy. It is also an important tool for the engineer in order to make the calibration work easier.

The main objective of this thesis is the accuracy improvement of parallel robots. Accuracy can be improved either by precise manufacturing and assembly or by calibration of each individual robot using a kinematic model which takes geometric deviations into account. The latter has the advantage of leading to low cost solutions but requires sophisticated modeling of the robot's structure which is usually considerably more complex than the derivation of its nominal model. To substantiate the theoretical tools proposed in this thesis two examples of parallel structures are chosen. One of them is the Delta robot with three translational degrees of freedom whereas the second example is a novel structure called Argos having three rotational degrees of freedom. For experimental verification a mock-up was built for each of the two structures. Four calibration steps, modeling, measurement, identification, and implementation are investigated. Investigations were restricted to static errors due to geometric deviations assuming rigid bodies. First a formula is proposed which allows to calculate the number of independent kinematic parameters required for a complete model of a parallel structure. Then a systematic parameterization is introduced and applied to derive four calibration models, two for each example. Two measurement devices are described which were built to determine the position and orientation (pose) of the end-effectors of the two robots. For the Delta robot two additional set-ups using no external (additional) measurement device are proposed. For parameter identification different methods were tested by simulation. Calibration based on the implicit model is proposed as a standard method to calibrate parallel robots. Another calibration method is introduced, referred to as semiparametric calibration, which leads to low computational effort. Fast solutions of the direct and inverse problems had to be found. For the first time al1 the solutions of the direct problem for the Delta robot were found by means of an algorithm introduced by Husty. In addition a fast numeric algorithm for the Delta's direct problem is proposed. The main contribution of this thesis is the experimental verification of calibration methods to improve the accuracy of parallel robots. Using these calibration methods for the two robots, ARGOS and DELTA, between a three- to a twelve-fold improvement of accuracy was achieved and experimentally verified.

In recent years nanotechnology has become an enabling technology for the development and fabrication of new innovative products. The growth of micro- and nano-manufacturing lies in the ability of converting micro- and nano-fabrication techniques into mass-production industrial processes, where small-scale products can be economically manufactured in a short period of time. When dealing with nano-scale objects and industrial processes it is necessary to take into account the physics acting at this level of precision. Phenomena such as friction, heat transfer, and adhesion forces have far more dramatic effects on the deformation of the robot geometry at the nano-scale than at macro- and micro-scales, thus affecting the industrial process that the robot will perform. The development of micro- and nano-fabrication techniques thus requires a thorough understanding of the physics behind nanorobotics. Specifically, to enable sub-micrometer accuracy for ultra-high-precision robots it is necessary to acquire a complete knowledge of how all sources of inaccuracy deform the robots at nano-scale. Furthermore, a way to compensate for such effects to maintain an acceptable level of accuracy has to be found. In this thesis we fulfill these needs by proposing a new calibration procedure specifically designed for industrial nano-systems working in a thermally unstable environment, a method to evaluate and compensate for external forces acting on ultra-high-precision robots and a method to relate the calibration of several robots working together. This is done by measuring how each source of inaccuracy deforms the robot, modeling this effect and compensating it in real-time. To allow this modus operandi, we propose a new calibration procedure summarized in the following six steps: Step 0 A judicious design of the robot that takes into account the calibration problem and the pose measurement, Step 1 Study of the sources of inaccuracy linked to the robot and the industrial process that it will perform, Step 2 Measurement of several end-effector poses, Step 3 Identification of a function that describes the robot geometry and its behavior when subjected to the sources of inaccuracy identified in Step 1, Step 4 Implementation of the model found in Step 3 into the robot controller, Step 5 Validation and potential return to Step 1 or Step 0. The effectiveness of this calibration procedure is proven by testing it on three case studies, examined in order of complexity: A 1 DOF (degree(s)-of-freedom) ultra-high-precision linear axis was calibrated while thermal effects were deforming it. The 3 DOF ultra-high-precision parallel robot Agietron Micro-Nano was calibrated while thermal effects and an external force were acting on it. An ultra-high-precision 2-robot system was calibrated while thermal effects were acting on it. Thus, an exhaustive study on relating the references of the two robots was carried out. For each case we developed an appropriate ultra-high-precision measuring system used to acquire the pose of the robot end-effector. We measured the end-effector position throughout the workspace while the sources of inaccuracy were acting on the robot to map how they affect the robot geometry. We used the Stepwise Regression algorithm to identify a mathematical model able to describe the geometric features of the robot while all the sources of inaccuracy are acting on it. The model is then implemented in the robot controller and a validation of the calibration accuracy is performed. For every ultra-high-precision robot considered in this work we reached an absolute accuracy of ±100 nm. We finished the coverage of this thesis by analyzing the nano-indentation process as a calibration confirmation tool and as an industrial process. Furthermore, we describe how to use a multiple ultra-high-precision concurrent system of robots. This work was financed by the FNS (Swiss National Foundation for research).