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Modeling and Control of Flexible Manipulators
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology. (RT)
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Industrial robot manipulators are general-purpose machines used for industrial automation in order to increase productivity, flexibility, and product quality. Other reasons for using industrial robots are cost saving, and elimination of hazardous and unpleasant work. Robot motion control is a key competence for robot manufacturers, and the current development is focused on increasing the robot performance, reducing the robot cost, improving safety, and introducing new functionalities.  Therefore, there is a need to continuously improve the mathematical models and control methods in order to fulfil conflicting requirements, such as increased performance of a weight-reduced robot, with lower mechanical stiffness and more complicated vibration modes. One reason for this development of the robot mechanical structure is of course cost-reduction, but other benefits are also obtained, such as lower environmental impact, lower power consumption, improved dexterity, and higher safety.

This thesis deals with different aspects of modeling and control of flexible, i.e., elastic, manipulators. For an accurate description of a modern industrial manipulator, this thesis shows that the traditional flexible joint model, described in literature, is not sufficient. An improved model where the elasticity is described by a number of localized multidimensional spring-damper pairs is therefore proposed. This model is called the extended flexible joint model. The main contributions of this work are the design and analysis of identification methods, and of inverse dynamics control methods, for the extended flexible joint model.

The proposed identification method is a frequency-domain non-linear gray-box method, which is evaluated by the identification of a modern six-axes robot manipulator. The identified model gives a good description of the global behavior of this robot.

The inverse dynamics problem is discussed, and a solution methodology is proposed. This methodology is based on the solution of a differential algebraic equation (DAE). The inverse dynamics solution is then used for feedforward control of both a simulated manipulator and of a real robot manipulator.

The last part of this work concerns feedback control. First, a model-based nonlinear feedback control (feedback linearization) is evaluated and compared to a model-based feedforward control algorithm. Finally, two benchmark problems for robust feedback control of a flexible manipulator are presented and some proposed solutions are analyzed.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2010. , 101 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1349
Keyword [en]
Modeling, identification, control, robot manipulator, DAE, flexible multibody dynamics, inverse dynamics, benchmark
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-60831ISBN: 978-91-7393-289-9 (print)OAI: oai:DiVA.org:liu-60831DiVA: diva2:370497
Public defence
2010-12-03, Sal Visionen, Hus B, Campus Valla, Linköping University, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2010-11-18 Created: 2010-10-27 Last updated: 2010-11-18Bibliographically approved
List of papers
1. Modeling and Parameter Estimation of Robot Manipulators using Extended Flexible Joint Models
Open this publication in new window or tab >>Modeling and Parameter Estimation of Robot Manipulators using Extended Flexible Joint Models
2014 (English)In: Journal of Dynamic Systems Measurement, and Control, ISSN 0022-0434, E-ISSN 1528-9028, Vol. 136, no 3, 031005- p.Article in journal (Refereed) Published
Abstract [en]

This paper considers the problem of dynamic modeling and identification of robot manipulators with respect to their elasticities. The so-called flexible joint model, modeling only the torsional gearbox elasticity, is shown to be insufficient for modeling a modern industrial manipulator accurately. The extended flexible joint model, where non-actuated joints are added to model the elasticity of the links and bearings, is used to improve the model accuracy. The unknown elasticity parameters are estimated using a frequency domain gray-box identification method. The conclusion is that the obtained model describes the movements of the motors and the tool mounted on the robot with significantly higher accuracy. Similar elasticity model parameters are obtained when using two different output variables for the identification, the motor position and the tool acceleration.

Keyword
Modeling, flexible arms, calibration and identification, motion control, robot manipulator.
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-61667 (URN)10.1115/1.4026300 (DOI)000333588100005 ()
Available from: 2010-11-17 Created: 2010-11-17 Last updated: 2017-12-12
2. Nonlinear Gray-Box Identification Using Local Models Applied to Industrial Robots
Open this publication in new window or tab >>Nonlinear Gray-Box Identification Using Local Models Applied to Industrial Robots
2011 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 47, no 4, 650-660 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we study the problem of estimating unknown parameters in nonlinear gray-box models that may be multivariable, nonlinear, unstable, and resonant at the same time. A straightforward use of time-domain predication-error methods for this type of problem easily ends up in a large and numerically stiff optimization problem. We therefore propose an identification procedure that uses intermediate local models that allow for data compression and a less complex optimization problem. The procedure is based on the estimation of the nonparametric frequency response function (FRF) in a number of operating points. The nonlinear gray-box model is linearized in the same operating points, resulting in parametric FRFs. The optimal parameters are finally obtained by minimizing the discrepancy between the nonparametric and parametric FRFs. The procedure is illustrated by estimating elasticity parameters in a six-axes industrial robot. Different parameter estimators are compared and experimental results show the usefulness of the proposed identification procedure. The weighted logarithmic least squares estimator achieves the best result and the identified model gives a good global description of the dynamics in the frequency range of interest for robot control.

Place, publisher, year, edition, pages
Elsevier, 2011
Keyword
System identification, Multivariable systems, Nonlinear systems, Closed-loop identification, Frequency response methods, Industrial robots
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-61670 (URN)10.1016/j.automatica.2011.01.021 (DOI)000289968500002 ()
Available from: 2010-11-17 Created: 2010-11-17 Last updated: 2017-12-12
3. Inverse Dynamics of Flexible Manipulators
Open this publication in new window or tab >>Inverse Dynamics of Flexible Manipulators
2009 (English)In: Proceedings of the 2009 Conference on Multibody Dynamics, 2009, 1-20 p.Conference paper, Published paper (Refereed)
Abstract [en]

High performance robot manipulators, in terms of cycle time and accuracy, require well designed control methods, based on accurate dynamic models. Robot manipulators are traditionally described by the flexible joint model or the flexible link model. These models only consider elasticity in the rotational direction. When these models are used for control or simulation, the accuracy can be limited due to the model simplifications, since a real manipulator has a distributed flexibility inall directions. This work investigates different methods for the inverse dynamics of a more general manipulator model, called the extended flexible joint model. The inverse dynamics solution is needed for feedforward control, which is often used for high-precision robot manipulator control.

The inverse dynamics of the extended flexible joint model can be computed as the solution of a high-index differential algebraic equation (DAE). One method is to solve the discretized DAE using a constant stepsize constant-order backwards differentiation formula (BDF). This work shows that there is only a small difference between solving theoriginal high-index DAE and the index-reduced DAE. It is also concluded that scaling of the algebraic equations and their derivatives is important.

The inverse dynamics can be solved as an initial-value problem if the zero dynamics of the system is stable, i.e., minimum phase. For unstable zero dynamics, an optimization approach based on the discretized DAE is suggested. An optimization method, using a continuous DAE formulation, is also suggested and evaluated. The solvers are illustrated by simulation, using a manipulator with two actuators and five degrees-of-freedom.

Keyword
Manipulator, Control, Differential algebraic equation, Flexible multibody dynamics, Non-minimum phase, Inverse dynamics
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-61326 (URN)
Conference
2009 Conference on Multibody Dynamics, Warsaw, Poland, 29th June - 2nd July, 2009
Funder
Swedish Research Council
Available from: 2010-11-12 Created: 2010-11-12 Last updated: 2013-09-16
4. Inverse Dynamics of Robot Manipulators Using Extended Flexible Joint Models
Open this publication in new window or tab >>Inverse Dynamics of Robot Manipulators Using Extended Flexible Joint Models
(English)Manuscript (preprint) (Other academic)
Abstract [en]

High performance robot manipulators, in terms of cycle time and accuracy, require well designed control methods, based on accurate dynamic models. This work investigates different methods for the inverse dynamics of a general manipulator model, called the extended flexible joint model. This model can describe elasticity in all directions, unlike the traditionally used robot models. The inverse dynamics solution is needed for feedforward control, which is often used for high-precision robot manipulator control. The inverse dynamics of the extended flexible joint model can be computed as the solution of a high index differential algebraic equation (DAE). The obtained DAE is analyzed, and solvers for both minimum phase and nonminimum phase systems are suggested. The solvers are evaluated by simulation, using a manipulator with two actuators and five degrees-of-freedom. Finally, the suggested concept for inverse dynamics is experimentally evaluated using an industrial robot manipulator. In this experimental evalution, an identified model is used in the inverse dynamics computation. Simulations using the same identified model are in good agreement with the experimental results. The conclusion is that the extended flexible joint inverse dynamics method can improve the accuracy for manipulators with significant elasticities,

Keyword
Modeling, flexible arms, calibration and identification, motion control, robot manipulator
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-61594 (URN)
Available from: 2010-11-17 Created: 2010-11-17 Last updated: 2010-11-18
5. On Feedback Linearization for Robust Tracking Control of Flexible Joint Robots
Open this publication in new window or tab >>On Feedback Linearization for Robust Tracking Control of Flexible Joint Robots
2008 (English)In: Proceedings of the 17th IFAC World Congress, 2008, 12218-12223 p.Conference paper, Published paper (Refereed)
Abstract [en]

Feedback linearization is one of the major academic approaches for controlling flexible joint robots. This contribution investigates the discrete-time implementation of the feedback linearization approach for a realistic three-axis robot model. A simulation study of high speed tracking with model uncertainty is performed. It is assumed that full state measurements of the linearizing states are available. The feedback linearization approach is compared to a feedforward approach.

Keyword
Robotics, Manipulation, Control, Feedforward, Feedback linearization, Discrete-time, Flexible joints
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-43055 (URN)10.3182/20080706-5-KR-1001.02069 (DOI)71180 (Local ID)978-3-902661-00-5 (ISBN)71180 (Archive number)71180 (OAI)
Conference
17th IFAC World Congress, Seoul, South Korea, July, 2008
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-02-23Bibliographically approved
6. A Benchmark Problem for Robust Feedback Control of a Flexible Manipulator
Open this publication in new window or tab >>A Benchmark Problem for Robust Feedback Control of a Flexible Manipulator
2009 (English)In: IEEE Transactions on Control Systems Technology, ISSN 1063-6536, E-ISSN 1558-0865, Vol. 17, no 6, 1398-1405 p.Article in journal (Refereed) Published
Abstract [en]

A benchmark problem for robust feedback control of a flexible manipulator is presented. The system to be controlled is a four-mass system subject to input saturation, nonlinear gear elasticity, model uncertainties, and load disturbances affecting both the motor and the arm. The system should be controlled by a discrete-time controller that optimizes performance for given robustness requirements. Four suggested solutions are presented, and even though the solutions are based on different design methods, they give comparable results.

Keyword
Flexible structures, Manipulators, Position control, Robots, Robustness
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-51596 (URN)10.1109/TCST.2008.2006755 (DOI)
Available from: 2009-11-09 Created: 2009-11-09 Last updated: 2017-12-12
7. A Benchmark Problem for Robust Control of a Multivariable Nonlinear Flexible Manipulator
Open this publication in new window or tab >>A Benchmark Problem for Robust Control of a Multivariable Nonlinear Flexible Manipulator
2008 (English)In: Proceedings of the 17th IFAC World Congress, 2008, 1206-1211 p.Conference paper, Published paper (Refereed)
Abstract [en]

A benchmark problem for robust feedback control of a manipulator is presented. The system to be controlled is an uncertain nonlinear two link manipulator with elastic gear transmissions. The gear transmission is described by nonlinear friction and elasticity. The system is uncertain according to a parametric uncertainty description and due to uncertain disturbances affecting both the motors and the tool. The system should be controlled by a discrete-time controller that optimizes performance for given robustness requirements. The control problem concerns only disturbance rejection. The proposed model is validated by experiments on a real industrial manipulator.

Keyword
Robust control, Control, Benchmark examples, Manipulators, Disturbance rejection, Flexible arms, Robotics
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-43053 (URN)10.3182/20080706-5-KR-1001.00208 (DOI)71168 (Local ID)978-3-902661-00-5 (ISBN)71168 (Archive number)71168 (OAI)
Conference
17th IFAC World Congress, Seoul, South Korea, July, 2008
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-02-23

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