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Sensor Fusion and Control Applied to Industrial Manipulators
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

One of the main tasks for an industrial robot is to move the end-effector in a predefined path with a specified velocity and acceleration. Different applications have different requirements of the performance. For some applications it is essential that the tracking error is extremely small, whereas other applications require a time optimal tracking. Independent of the application, the controller is a crucial part of the robot system. The most common controller configuration uses only measurements of the motor angular positions and velocities, instead of the position and velocity of the end-effector. The development of new cost optimised robots has introduced unwanted flexibilities in the joints and the links. The consequence is that it is no longer possible to get the desired performance and robustness by only measuring the motor angular positions. 

This thesis investigates if it is possible to estimate the end-effector position using Bayesian estimation methods for state estimation, here represented by the extended Kalman filter and the particle filter. The arm-side information is provided by an accelerometer mounted at the end-effector. The measurements consist of the motor angular positions and the acceleration of the end-effector. In a simulation study on a realistic flexible industrial robot, the angular position performance is shown to be close to the fundamental Cramér-Rao lower bound. The methods are also verified in experiments on an ABB IRB4600 robot, where the dynamic performance of the position for the end-effector is significantly improved. There is no significant difference in performance between the different methods. Instead, execution time, model complexities and implementation issues have to be considered when choosing the method. The estimation performance depends strongly on the tuning of the filters and the accuracy of the models that are used. Therefore, a method for estimating the process noise covariance matrix is proposed. Moreover, sampling methods are analysed and a low-complexity analytical solution for the continuous-time update in the Kalman filter, that does not involve oversampling, is proposed. 

The thesis also investigates two types of control problems. First, the norm-optimal iterative learning control (ILC) algorithm for linear systems is extended to an estimation-based norm-optimal ILC algorithm where the controlled variables are not directly available as measurements. The algorithm can also be applied to non-linear systems. The objective function in the optimisation problem is modified to incorporate not only the mean value of the estimated variable, but also information about the uncertainty of the estimate. Second, H controllers are designed and analysed on a linear four-mass flexible joint model. It is shown that the control performance can be increased, without adding new measurements, compared to previous controllers. Measuring the end-effector acceleration increases the control performance even more. A non-linear model has to be used to describe the behaviour of a real flexible joint. An H-synthesis method for control of a flexible joint, with non-linear spring characteristic, is therefore proposed.

Abstract [sv]

En av de viktigaste uppgifterna för en industrirobot är att förflytta verktyget i en fördefinierad bana med en specificerad hastighet och acceleration. Exempel på användningsområden för en industrirobot är bland annat bågsvetsning eller limning. För dessa typer av applikationer är det viktigt att banföljningsfelet är extremt litet, men även hastighetsprofilen måste följas så att det till exempel inte appliceras för mycket eller för lite lim. Andra användningsområden kan vara punktsvetsning av bilkarosser och paketering av olika varor. För dess applikationer är banföljningen inte det viktiga, istället kan till exempel en tidsoptimal banföljning krävas eller att svängningarna vid en inbromsning minimeras. Oberoende av applikationen är regulatorn en avgörande del av robotsystemet. Den vanligaste regulatorkonfigurationen använder bara mätningar av motorernas vinkelpositioner och -hastigheter, istället för positionen och hastigheten för verktyget, som är det man egentligen vill styra. 

En del av utvecklingsarbetet för nya generationers robotar är att reducera kostnaden men samtidigt förbättra prestandan. Ett sätt att minska kostnaden kan till exempel vara att minska dimensionerna på länkarna eller köpa in billigare växellådor. Den här utvecklingen av kostnadsoptimerade robotar har infört oönskade flexibiliteter i leder och länkar. Det är därför inte längre möjligt att få den önskade prestandan och robustheten genom att bara mäta motorernas vinkelpositioner och -hastigheter. Istället krävs det omfattande matematiska modeller som beskriver dessa oönskade flexibiliteter. Dessa modeller kräver mycket arbete att dels ta fram men även för att identifiera parametrarna. Det finns automatiska metoder för att beräkna modellparametrarna men oftast krävs det en manuell justering för att få bra prestanda. 

Den här avhandlingen undersöker möjligheterna att beräkna verktygspositionen med hjälp av bayesianska metoder för tillståndsskattning. De bayesianska skattningsmetoderna beräknar tillstånden för ett system iterativt. Med hjälp av en matematisk modell över systemet predikteras vad tillståndet ska vara vid nästa tidpunkt. Efter att mätningar av systemet vid den nya tidpunkten har genomförts justeras skattningen med hjälp av dessa mätningar. De metoder som har använts i avhandlingen är det så kallade extended Kalman filtret samt partikelfiltret. 

Informationen på armsidan av växellådan ges av en accelerometer som är monterad på verktyget. Med hjälp av accelerationen för verktyget och motorernas vinkelpositioner kan en skattning av verktygspositionen beräknas. I en simuleringsstudie för en realistisk vek robot har det visats att skattningsprestandan ligger nära den teoretiska undre gränsen, känd som Raooch mätstörningar som påverkar roboten. För att underlätta trimningen så har en metod för att skatta processbrusets kovariansmatris föreslagits. En annan viktig del som påverkar prestandan är modellerna som används i filtren. Modellerna för en industrirobot är vanligtvis framtagna i kontinuerlig tid medan filtren använder modeller i diskret tid. För att minska felen som uppkommer då de tidskontinuerliga modellerna överförs till diskret tid har olika samplingsmetoder studerats. Vanligtvis används enkla metoder för att diskretisera vilket innebär problem med prestanda och stabilitet. För att hantera dessa problem införs översampling vilket innebär att tidsuppdateringen sker med en mycket kortare sampeltid än vad mätuppdateringen gör. För att undvika översampling kan det motsvarande tidskontinuerliga filtret användas för att prediktera tillstånden vid nästa diskreta tidpunkt. En analytisk lösning med låg beräkningskomplexitet till detta problem har föreslagits. 

Vidare innehåller avhandlingen två typer av reglerproblem relaterade till industrirobotar. För det första har den så kallade norm-optimala iterative learning control styrlagen utökats till att hantera fallet då en skattning av den önskade reglerstorheten används istället för en mätning. Med hjälp av skattningen av systemets tillståndsvektor kan metoden nu även användas till olinjära system vilket inte är fallet med standardformuleringen. Den föreslagna metoden utökar målfunktionen i optimeringsproblemet till att innehålla inte bara väntevärdet av den skattade reglerstorheten utan även skattningsfelets kovariansmatris. Det innebär att om skattningsfelet är stort vid en viss tidpunkt ska den skattade reglerstorheten vid den tidpunkten inte påverka resultatet mycket eftersom det finns en stor osäkerhet i var den sanna reglerstorheten befinner sig. 

För det andra har design och analys av H-regulatorer för en linjär modell av en vek robotled, som beskrivs med fyra massor, genomförts. Det visar sig att reglerprestandan kan förbättras, utan att lägga till fler mätningar än motorns vinkelposition, jämfört med tidigare utvärderade regulatorer. Genom att mäta verktygets acceleration kan prestandan förbättras ännu mer. Modellen över leden är i själva verket olinjär. För att hantera detta har en H-syntesmetod föreslagits som kan hantera olinjäriteten i modellen.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2014. , 69 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1585
Keyword [en]
Industrial Robots, Sensor Fusion, Iterative Learning Control, H-infinity Controller, Controllability, Extended Kalman Filter, Particle Filter, Expectation Maximisation, Continuous-time Filtering, Norm-optimal ILC
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-105343DOI: 10.3384/diss.diva-105343ISBN: 978-91-7519-368-7 (print)OAI: oai:DiVA.org:liu-105343DiVA: diva2:706015
Public defence
2014-05-09, Visionen, B-huset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Projects
Vinnova Excellence Center LINK-SIC
Funder
Vinnova
Available from: 2014-04-11 Created: 2014-03-18 Last updated: 2014-04-14Bibliographically approved
List of papers
1. Bayesian State Estimation of a Flexible Industrial Robot
Open this publication in new window or tab >>Bayesian State Estimation of a Flexible Industrial Robot
2012 (English)In: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 20, no 11, 1220-1228 p.Article in journal (Refereed) Published
Abstract [en]

A sensor fusion method for state estimation of a flexible industrial robot is developed. By measuring the acceleration at the end-effector, the accuracy of the arm angular position, as well as the estimated position of the end-effector are improved. The problem is formulated in a Bayesian estimation framework and two solutions are proposed; the extended Kalman filter and the particle filter. In a simulation study on a realistic flexible industrial robot, the angular position performance is shown to be close to the fundamental Cramér-Rao lower bound. The technique is also verified in experiments on an ABB robot, where the dynamic performance of the position for the end-effector is significantly improved.

Place, publisher, year, edition, pages
Elsevier, 2012
Keyword
Industrial robot, Positioning, Estimation, Particle filter, Extended Kalman filter, Cramér–Rao lower bound
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-81988 (URN)10.1016/j.conengprac.2012.06.004 (DOI)000309847800015 ()
Projects
Vinnova Excellence Center LINK-SICSSF project Collaborative Localization
Funder
VinnovaSwedish Foundation for Strategic Research
Available from: 2012-09-27 Created: 2012-09-27 Last updated: 2017-12-07
2. Evaluation of Six Different Sensor Fusion Methods for an Industrial Robot using Experimental Data
Open this publication in new window or tab >>Evaluation of Six Different Sensor Fusion Methods for an Industrial Robot using Experimental Data
2012 (English)In: Proceedings of the 10th IFAC Symposium on Robot Control, 2012, 126-132 p.Conference paper, Published paper (Refereed)
Abstract [en]

Experimental evaluations for path estimation are performed on an ABB IRB4600 robot. Different observers using Bayesian techniques with different estimation models are proposed. The estimated paths are compared to the true path measured by a laser tracking system. There is no significant difference in performance between the six observers. Instead, execution time, model complexities and implementation issues have to be considered when choosing the method.

Keyword
Estimation, Extended Kalman filter, Particle filter, Accelerometer, Industrial robots
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-81456 (URN)10.3182/20120905-3-HR-2030.00003 (DOI)
Conference
10th IFAC Symposium on Robot Control, Dubrovnik, Croatia, 5-7 September 2012
Projects
Vinnova Excellence Center LINK-SIC
Funder
Vinnova
Available from: 2012-09-14 Created: 2012-09-14 Last updated: 2014-04-11
3. Discrete-time Solutions to the Continuous-time Differential Lyapunov Equation With Applications to Kalman Filtering
Open this publication in new window or tab >>Discrete-time Solutions to the Continuous-time Differential Lyapunov Equation With Applications to Kalman Filtering
2015 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 60, no 3, 632-643 p.Article in journal (Refereed) Published
Abstract [en]

Prediction and filtering of continuous-time stochastic processes often require a solver of a continuous-time differential Lyapunov equation (CDLE), for example the time update in the Kalman filter. Even though this can be recast into an ordinary differential equation (ODE), where standard solvers can be applied, the dominating approach in Kalman filter applications is to discretize the system and then apply the discrete-time difference Lyapunov equation (DDLE). To avoid problems with stability and poor accuracy, oversampling is often used. This contribution analyzes over-sampling strategies, and proposes a novel low-complexity analytical solution that does not involve oversampling. The results are illustrated on Kalman filtering problems in both linear and nonlinear systems.

Place, publisher, year, edition, pages
IEEE Press, 2015
Keyword
Continuous time systems, Discrete time systems, Kalman filters, Sampling methods
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-104790 (URN)10.1109/TAC.2014.2353112 (DOI)000350206000003 ()
Projects
Vinnova Excellence Center LINK-SIC
Funder
VINNOVA
Available from: 2014-02-26 Created: 2014-02-26 Last updated: 2017-12-05
4. ML Estimation of Process Noise Variance in Dynamic Systems
Open this publication in new window or tab >>ML Estimation of Process Noise Variance in Dynamic Systems
2011 (English)In: Proceedings of the 18th IFAC World Congress, 2011, 5609-5614 p.Conference paper, Published paper (Refereed)
Abstract [en]

The performance of a non-linear filter hinges in the end on the accuracy of the assumed non-linear model of the process. In particular, the process noise covariance Q is hard to get by physical modeling and dedicated system identification experiments. We propose a variant of the expectation maximization (EM) algorithm which iteratively estimates the unobserved state sequence and Q based on the observations of the process. The extended Kalman smoother (EKS) is the instrument to find the unobserved state sequence. Our contribution fills a gap in literature, where previously only the linear Kalman smoother and particle smoother have been applied. The algorithm will be important for future industrial robots with more flexible structures, where the particle smoother cannot be applied due to the high state dimension. The proposed method is compared to two alternative methods on a simulated robot.

Keyword
Robotic manipulators, Extended Kalman filters, Smoothing filters, Identification, Maximum likelihood, Covariance matrices
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-72219 (URN)10.3182/20110828-6-IT-1002.00543 (DOI)978-3-902661-93-7 (ISBN)
Conference
18th IFAC World Congress, Milano, Italy, 28 August-2 September, 2011
Projects
LINK-SIC
Available from: 2011-11-28 Created: 2011-11-23 Last updated: 2014-04-11Bibliographically approved
5. H-Controller Design Methods Applied to One Joint of a Flexible Industrial Manipulator
Open this publication in new window or tab >>H-Controller Design Methods Applied to One Joint of a Flexible Industrial Manipulator
2014 (English)In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Boje, Edward and Xia, Xiaohua, International Federation of Automatic Control , 2014, 210-216 p.Conference paper, Published paper (Refereed)
Abstract [en]

Control of a flexible joint of an industrial manipulator using H design methods is presented. The considered design methods are i) mixed-H design, and ii) H loop shaping design. Two different controller configurations are examined: one uses only the actuator position, while the other uses the actuator position and the acceleration of end-effector. The four resulting controllers are compared to a standard PID controller where only the actuator position is measured. The choices of the weighting functions are discussed in details. For the loop shaping design method, the acceleration measurement is required to improve the performance compared to the PID controller. For the mixed-H method it is enough to have only the actuator position to get an improved performance. Model order reduction of the controllers is briefly discussed, which is important for implementation of the controllers in the robot control system.

Place, publisher, year, edition, pages
International Federation of Automatic Control, 2014
Series
World Congress, ISSN 1474-6670 ; Volume# 19, Part# 1
Keyword
Robotics, Flexible, H-infinity control, Accelerometers
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-104785 (URN)10.3182/20140824-6-ZA-1003.00143 (DOI)978-3-902823-62-5 (ISBN)
Conference
19th IFAC World Congress, August 24-29, Cape Town, South Africa
Projects
Vinnova Excellence Center LINK-SICExcellence Center at Linköping-Lund in Information Technology, ELLIIT
Funder
VinnovaeLLIIT - The Linköping‐Lund Initiative on IT and Mobile Communications
Available from: 2014-02-26 Created: 2014-02-26 Last updated: 2014-10-23Bibliographically approved
6. H Synthesis Method for Control of Non-linear Flexible Joint Models
Open this publication in new window or tab >>H Synthesis Method for Control of Non-linear Flexible Joint Models
2014 (English)In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Boje, Edward and Xia, Xiaohua, International Federation of Automatic Control , 2014, 8372-8377 p.Conference paper, Published paper (Refereed)
Abstract [en]

An H synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shaping paradigm and a change of variables, the non-linear optimisation problem can be rewritten as a convex, yet conservative, LMI problem. The method is motivated by the assumption that the joint operates in a specific stiffness region of the non-linear spring most of the time, hence the performance requirements are only valid in that region. However, the controller must stabilise the system in all stiffness regions. The method is validated in simulations on a non-linear flexible joint model originating from an industrial robot.

Place, publisher, year, edition, pages
International Federation of Automatic Control, 2014
Series
World Congress, ISSN 1474-6670 ; Volume# 19, Part# 1
Keyword
Mechanical systems, Flexible, Robust, H-infinity Control
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-104789 (URN)10.3182/20140824-6-ZA-1003.00142 (DOI)978-3-902823-62-5 (ISBN)
Conference
19th IFAC World Congress, August 24-29, Cape Town, South Africa
Projects
Vinnova Excellence Center LINK-SICExcellence Center at Linköping-Lund in Information Technology, ELLIIT
Funder
VinnovaeLLIIT - The Linköping‐Lund Initiative on IT and Mobile Communications
Available from: 2014-02-26 Created: 2014-02-26 Last updated: 2014-10-23Bibliographically approved
7. Estimation-based Norm-optimal Iterative Learning Control
Open this publication in new window or tab >>Estimation-based Norm-optimal Iterative Learning Control
2014 (English)In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 73, 76-80 p.Article in journal (Refereed) Published
Abstract [en]

The norm-optimal iterative learning control (ilc) algorithm for linear systems is extended to an estimation-based norm-optimal ilc  algorithm where the controlled variables are not directly available as measurements. A separation lemma is presented, stating that if a stationary Kalman filter is used for linear time-invariant systems then the ilc  design is independent of the dynamics in the Kalman filter. Furthermore, the objective function in the optimisation problem is modified to incorporate the full probability density function of the error. Utilising the Kullback–Leibler divergence leads to an automatic and intuitive way of tuning the ilc  algorithm. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ilc  algorithm. Stability and convergence properties for the proposed scheme are also derived.

Place, publisher, year, edition, pages
Elsevier, 2014
Keyword
Iterative learning control; Estimation; Filtering; Non-linear systems
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-104791 (URN)10.1016/j.sysconle.2014.08.007 (DOI)000345108000010 ()
Projects
Vinnova Excellence Center LINK-SICExcellence Center at Linköping-Lund in Information Technology, ELLIITSSF project Collaborative Localization
Funder
VINNOVAeLLIIT - The Linköping‐Lund Initiative on IT and Mobile Communications
Available from: 2014-02-26 Created: 2014-02-26 Last updated: 2017-12-05
8. Controllability Aspects for Iterative Learning Control
Open this publication in new window or tab >>Controllability Aspects for Iterative Learning Control
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper discusses the aspects of controllability in the iteration domain for systems that are controlled using iterative learning control (ILC). The focus is on controllability for a proposed state space model in the iteration domain and it relates to an assumption often used to prove convergence of ILC algorithms. It is shown that instead of investigating controllability it is more suitable to use the concept of target path controllability (TPC), where it is investigated if a system can follow a trajectory instead of the ability to control the system to an arbitrary point in the state space. Finally, a simulation study is performed to show how the ILC algorithm can be designed using the LQ-method, if the state space model in the iteration domain is output controllable. The LQ-method is compared to the standard norm-optimal ILC algorithm, where it is shown that the control error can be reduced significantly using the LQ-method compared to the norm-optimal approach.

Keyword
Iterative Learning Control, Controllability, Output controllability, Target path controllability
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-105342 (URN)
Projects
Vinnova Excellence Center LINK-SICExcellence Center at Linköping-Lund in Information Technology, ELLIIT
Funder
VinnovaeLLIIT - The Linköping‐Lund Initiative on IT and Mobile Communications
Available from: 2014-03-18 Created: 2014-03-18 Last updated: 2016-08-31

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