A Benchmark Problem for Robust Control of a Multivariable Nonlinear Flexible Manipulator

Moberg, Stig; Öhr, Jonas; Gunnarsson, Svante

doi:10.3182/20080706-5-kr-1001.00208

Cited by 32 publications

(23 citation statements)

References 7 publications

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“…The single joint model is based on the two-axes model in [20], where the model structure and the parameters are presented. To get a single joint model, the second joint for the two-axes model has been positioned in −π/2 and it is assumed rigidly attached to the first arm.…”

Section: Simulation Resultsmentioning

confidence: 99%

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Estimation-based norm-optimal iterative learning control

Axelsson¹,

Karlsson²,

Norrlöf³

2014

Systems & Control Letters

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The iterative learning control (ilc) method improves performance of systems that repeat the same task several times. In this paper the standard norm-optimal ilc control law for linear systems is extended to an estimation-based ilc algorithm where the controlled variables are not directly available as measurements. The proposed ilc algorithm is proven to be stable and gives monotonic convergence of the error. The estimationbased part of the algorithm uses Bayesian estimation techniques such as the Kalman lter. The objective function in the optimisation problem is modied to incorporate not only the mean value of the estimated variable, but also information about the uncertainty of the estimate. It is further shown that for linear time-invariant systems the ilc design is independent of the estimation method. 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. It is also discussed how the Kullback-Leibler divergence can be used if linearisation cannot be performed. Finally, the proposed solution for non-linear systems is applied and veried in a simulation study with a simplied model of an industrial manipulator system. AbstractThe iterative learning control (ilc) method improves performance of systems that repeat the same task several times. In this paper the standard norm-optimal ilc control law for linear systems is extended to an estimation-based ilc algorithm where the controlled variables are not directly available as measurements. The proposed ilc algorithm is proven to be stable and gives monotonic convergence of the error. The estimation-based part of the algorithm uses Bayesian estimation techniques such as the Kalman filter. 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. It is further shown that for linear time-invariant systems the ilc design is independent of the estimation method. 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. It is also discussed how the Kullback-Leibler divergence can be used if linearisation cannot be performed. Finally, the proposed solution for non-linear systems is applied and verified in a simulation study with a simplified model of an industrial manipulator system.

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Section: Simulation Resultsmentioning

confidence: 99%

“…The expression in (37) is the same as the one in (20). By interchanging the distributions p and q the result will be the norm of the mean error but now weighted with Σ −1 , which is a tuning parameter, hence no information of the covariance matrix of the control error is used.…”

mentioning

confidence: 99%

Estimation-based norm-optimal iterative learning control

Axelsson¹,

Karlsson²,

Norrlöf³

2014

Systems & Control Letters

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“…The model used is fully described in [13]. Each link has rigid body characteristics described by mass m, link length l, center of mass ξ and inertia j with respect to center of mass.…”

Section: A Original Nonlinear Robot Modelmentioning

confidence: 99%

ILC applied to a flexible two-link robot model using sensor-fusion-based estimates

Wallén

Gunnarsson

Henriksson

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Estimates from an extended Kalman filter (EKF) is used in an Iterative Learning Control (ILC) algorithm applied to a realistic two-link robot model with flexible joints. The angles seen from the arm side of the joints (arm angles) are estimated by an EKF in two ways: 1) using measurements of angles seen from the motor side of the joints (motor angles), which normally are the only measurements available in commercial industrial robot systems, 2) using both motor-angle and tool-acceleration measurements. The estimates are then used in an ILC algorithm. The results show that the actual arm angles are clearly improved compared to when only motor angles are used in the ILC update, even though model errors are introduced.Keywords: Iterative learning control; Robotics; Sensor fusion ILC applied to a flexible two-link robot model using sensor-fusion-based estimates Johanna Wallén, Svante Gunnarsson, Robert Henriksson, Stig Moberg and Mikael NorrlöfAbstract-Estimates from an extended Kalman filter (EKF) is used in an Iterative Learning Control (ILC) algorithm applied to a realistic two-link robot model with flexible joints. The angles seen from the arm side of the joints (arm angles) are estimated by an EKF in two ways: 1) using measurements of angles seen from the motor side of the joints (motor angles), which normally are the only measurements available in commercial industrial robot systems, 2) using both motorangle and tool-acceleration measurements. The estimates are then used in an ILC algorithm. The results show that the actual arm angles are clearly improved compared to when only motor angles are used in the ILC update, even though model errors are introduced.

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“…The robot model is a joint flexible two axes model from [15]. The model assumes rigid links and flexible joints.…”

Section: Robot and Accelerometer Modelsmentioning

confidence: 99%

Evaluation of Six Different Sensor Fusion Methods for an Industrial Robot using Experimental Data

Axelsson

2012

IFAC Proceedings Volumes

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This paper summarizes previous work on tool position estimation on industrial manipulators, and emphasize the problems that must be taken care of in order to get a satisfied result. The acceleration of the robot tool, measured by an accelerometer, togheter with measurements of motor angles are used. The states are estimated with an extended kalman filter. A method for tuning the covariance matrices for the noise, used in the observer, is suggested. The work has been focused on a robot with two degrees of freedom.

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A Benchmark Problem for Robust Control of a Multivariable Nonlinear Flexible Manipulator

Cited by 32 publications

References 7 publications

Estimation-based norm-optimal iterative learning control

Estimation-based norm-optimal iterative learning control

ILC applied to a flexible two-link robot model using sensor-fusion-based estimates

Evaluation of Six Different Sensor Fusion Methods for an Industrial Robot using Experimental Data

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