Practical identifiability of the manipulator link stiffness parameters

International audienceThe paper addresses a problem of the manipulator stiffness modeling, which is extremely important for the precise manufacturing of contemporary aeronautic materials where the machining force causes significant compliance errors in the robot end-effector position. The main contributions are in the area of the elastostatic parameters identification. Particular attention is paid to the practical identifiability of the model parameters, which completely differs from the theoretical one that relies on the rank of the observation matrix only, without taking into account essential differences in the model parameter magnitudes and the measurement noise impact. This problem is relatively new in robotics and essentially differs from that arising in geometrical calibration. To solve the problem, several physical and statistical model reduction methods are proposed. They are based on the stiffness matrix sparseness taking into account the physical properties of the manipulator elements and also on the heuristic selection of the practically non-identifiable parameters that employs numerical analyses of the parameter estimates. The advantages of the developed approach are illustrated by an application example that deals with the stiffness modeling of an industrial robot used in aerospace industry

Calibration of Parallel Kinematic Machines: theory and applications

Introduction As already stated in the chapter addressing the calibration of serial manipulators, kinematic calibration is a procedure for the identification and the consequent compensation of the geometrical pose errors of a robot. This chapter extends the discussion to Parallel Manipulators (also called PKM Parallel Kinematic Machines). As described in the following (Section 2) this extension is not obvious but requires special care. Although for serial manipulators some procedures for the calibration based on automatic generation of a MCPC (Minimum Complete Parametrically Continuos) model exist, for PKMs only methodologies for individual manipulators have been proposed but a general strategy has not been presented since now. A few examples of the numerous approaches for the calibration of individual PKMs are proposed in (Parenti-Castelli & Di Gregorio, 1995), (Jokiel et al., 2000) for direct calibration and (Neugebauer et al., 1999), (Smollett, 1996) for indirect or self calibration techniques. This paper makes one significant step integrating available results with new ones and reordering them in simple rules that can be automatically applied to any PKM with general kinematic chains. In all the cases a MCPC kinematic model for geometrical calibration is automatically obtained. In Section 2 the main features of PKMs calibration is pointed out and the total number of the necessary parameters is determined; this is an original contribution. In Sections 3 and 4 two novel approaches for the generation of a MCPC model are described. Sections 5 and 6 are dedicated to the analysis of the singular cases and to the procedure for the elimination of the redundant parameters respectively; actual cases are discussed. Section 7 presents several examples of application of the two proposed procedures to many existing PKMs. Section 8 eventually draws the conclusions

A screw theory based approach to determining the identifiable parameters for calibration of parallel manipulators

Establishing complete, continuous and minimal error models is fundamentally significant for the calibration of robotic manipulators. Motivated by practical needs for models suited to coarse plus fine calibration strategies, this paper presents a screw theory based approach to determining the identifiable geometric errors of parallel manipulators at the model level. The paper first addresses two specific issues: (1) developing a simple approach that enables all encoder offsets to be retained in the minimal error model of serial kinematic chains; and (2) exploiting a fully justifiable criterion that allows the detection of the unidentifiable structural errors of parallel manipulators. Merging these two threads leads to a new, more rigorous formula for calculating precisely the number of identifiable geometric errors, including both encoder offsets and identifiable structural errors, of parallel manipulators. It shows that the identifiability of structural errors in parallel manipulators depends highly upon joint geometry and actuator arrangement of the limb involved. The process is used to determine the unidentifiable structural errors of two lower mobility parallel mechanisms to illustrate the effectiveness of the proposed approach

An Overview of Kinematic and Calibration Models Using Internal/External Sensors or Constraints to Improve the Behavior of Spatial Parallel Mechanisms

This paper presents an overview of the literature on kinematic and calibration models of parallel mechanisms, the influence of sensors in the mechanism accuracy and parallel mechanisms used as sensors. The most relevant classifications to obtain and solve kinematic models and to identify geometric and non-geometric parameters in the calibration of parallel robots are discussed, examining the advantages and disadvantages of each method, presenting new trends and identifying unsolved problems. This overview tries to answer and show the solutions developed by the most up-to-date research to some of the most frequent questions that appear in the modelling of a parallel mechanism, such as how to measure, the number of sensors and necessary configurations, the type and influence of errors or the number of necessary parameters

Design and implementation of robot skill programming and control

Abstract. Skill-based approach has been represented as a solution to the raising complicity of robot programming and control. The skills rely heavily on the use of sensors integrating sensor perceptions and robot actions, which enable the robot to adapt to changes and uncertainties in the real world and operate autonomously. The aim of this thesis was to design and implement a programming concept for skill-based control of industrial robots. At the theoretical part of this thesis, the industrial robot system is introduced as well as some basic concepts of robotics. This is followed by the introduction of different robot programming and 3D machine vision methods. At the last section of the theoretical part, the structure of skill-based programs is presented. In the experimental part, structure of the skills required for the “grinding with localization” -task are presented. The task includes skills such as global localization with 3D-depth sensor, scanning the object with 2D-profile scanner, precise localization of the object as well as two grinding skills: level surface grinding and straight seam grinding. Skills are programmed with an off-line programming tool and implemented in a robot cell, composed of a standard industrial robot with grinding tools, 3D-depth sensors and 2D-profile scanners. The results show that global localization can be carried out with consumer class 3D-depth sensors and more accurate local localization with an industrial high-accuracy 2D-profile scanner attached to the robot’s flange. The grinding experiments and tests were focused on finding suitable structures of the skill programs as well as to understand how the different parameters influence on the quality of the grinding.Robotin taitopohjaisten ohjelmien ohjelmointi ja testaus. Tiivistelmä. Robotin taitopohjaisia ohjelmia on esitetty ratkaisuksi robottien jatkuvasti monimutkaistuvaan ohjelmointiin. Taidot pohjautuvat erilaisten antureiden ja robotin toimintojen integroimiseen, joiden avulla robotti pystyy havainnoimaan muutokset reaalimaailmassa ja toimimaan autonomisesti. Tämän työn tavoitteena oli suunnitella ja toteuttaa taitopohjaisia ohjelmia teollisuusrobotille. Aluksi työn teoriaosuudessa esitellään teollisuusrobottijärjestelmään kuuluvia osia ja muutamia robotiikan olennaisimpia käsitteitä. Sen jälkeen käydään läpi eri robotin ohjelmointitapoja ja eri 3D-konenäön toimintaperiaatteita. Teoriaosuuden lopussa esitellään taitopohjaisten ohjelmien rakennetta. Käytännön osuudessa esitellään ”hionta paikoituksella” -tehtävän suoritukseen tarvittavien taitojen rakenne. Tehtävän vaatimia taitoja ovat muun muassa kappaleen globaalipaikoitus 3D-syvyyskameralla, kappaleen skannaus 2D-profiiliskannerilla, kappaleen tarkkapaikoitus ja kaksi eri hiontataitoa: tasomaisen pinnan ja suoran sauman hionta. Taidot ohjelmoidaan off-line ohjelmointityökalulla ja implementoidaan robottisoluun, joka muodostuu hiontatyökaluilla varustetusta teollisuusrobotista, 3D-kameroista ja 2D-profiiliskannereista. Työn tuloksista selviää, että kappaleen globaalipaikoitus voidaan suorittaa kuluttajille suunnatuilla 3D-syvyyskameroilla ja kappaleen tarkempi lokaalipaikoitus robotin ranteeseen kiinnitetyllä teollisuuden käyttämillä 2D-profiiliskannereilla. Hiontojen kokeellisessa osuudessa etsitään ohjelmien oikeanlaista rakennetta sekä muodostetaan käsitys eri parametrien vaikutuksesta hionnan laatuun

Automatic calibration of space based manipulators and mechanisms

Four tasks in manipulator kinematic calibration are summarized. Calibration of a seven degree of freedom manipulator was simulated. A calibration model is presented that can be applied on a closed-loop robot. It is an expansion of open-loop kinematic calibration algorithms subject to constraints. A closed-loop robot with a five-bar linkage transmission was tested. Results show that the algorithm converges within a few iterations. The concept of model differences is formalized. Differences are categorized as structural and numerical, with emphasis on the structural. The work demonstrates that geometric manipulators can be visualized as points in a vector space with the dimension of the space depending solely on the number and type of manipulator joint. Visualizing parameters in a kinematic model as the coordinates locating the manipulator in vector space enables a standard evaluation of the models. Key results include a derivation of the maximum number of parameters necessary for models, a formal discussion on the inclusion of extra parameters, and a method to predetermine a minimum model structure for a kinematic manipulator. A technique is presented that enables single point sensors to gather sufficient information to complete a calibration