Calibration of high-precision flexure parallel robots

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.