Gearbox failures cost thousands of lost production hours in plants that use industrial robots. In this context, an automated monitoring system that can warn the user of an impending failure can save precious resources. This problem has been addressed in many other domains through the use of machine learning approaches. However, standard machine learning algorithms are limited in their ability to detect gearbox failures, mainly due to task variability arises from robot-specific data. To improve detection performance of machine learning approaches, in this paper we propose techniques to curate the data prior to building a classification model. In a systematic hypothesis-driven study exploring the effect of different preprocessing techniques, we evaluate training data augmentation with estimated measurements, data differencing to suppress task dependence, inclusion of local variation, and selection of principal components on data collected from 26 industrial robots from the field. Our results show that preprocessing techniques improve the failure detection performance.

Some controllability aspects for iterative learning control (ILC) are discussed. Via a batch (lifted) description of the problem a state space model of the system to be controlled is formulated in the iteration domain. This model provides insight and enables analysis of the conditions for and relationships between controllability, output controllability and target path controllability. In addition, the property miminum lead target path controllability is introduced. This property, which is connected to the number of time delays, plays an important role in the design of ILC algorithms. The properties are illustrated by a numerical example.

This paper presents a data-driven approach to diagnostics of systems that operate in a repetitive manner. Considering that data batches collected from a repetitive operation will be similar unless in the presence of an abnormality, a condition change is inferred by comparing the monitored data against an available nominal batch. The method proposed considers the comparison of data in the distribution domain, which reveals information of the data amplitude. This is achieved with the use of kernel density estimates and the Kullback–Leibler distance. To decrease sensitivity to disturbances while increasing sensitivity to faults, the use of a weighting vector is suggested which is chosen based on a labeled dataset. The framework is simple to implement and can be used without process interruption, in a batch manner. The approach is demonstrated with successful experimental and simulation applications to wear diagnostics in an industrial robot gearbox and for diagnostics of gear faults in a rotating machine.

Boundary effects in iterative learning control (ILC) algorithms are considered in this article. ILC algorithms involve filtering of input and error signals over finite-time intervals, often using non-causal filters, and it is important that the boundary effects of the filtering operations are handled in an appropriate way. The topic is studied using both a proposed theoretical framework and simulations, and it is shown that the method for handling the boundary effects has impact on the stability and convergence properties of the ILC algorithm.

Input saturation is inevitable in many engineering applications. Most existing iterative learning control (ILC) algorithms that can deal with input saturation require that the reference signal is realizable within the saturation bound. For engineering systems without precise models, it is hard to verify this requirement. In this note, a "reference governor" (RG) is introduced and is incorporated with the available ILC algorithms (primary ILC algorithms). The role of the RG is to re-design the reference signal so that the modified reference signal is realizable. Two types of the RG are proposed: one modifies the amplitude of the reference signal and the other modifies the frequency. Our main results provide design guidelines for two RGs. Moreover, a design trade-off between the convergence speed and tracking performance is also discussed. A simple simulation result verifies the effectiveness of the proposed methods.

Iterative learning control (ILC) is applied to a robot arm with joint flexibility. The ILC algorithm uses an estimate of the arm angle, where the estimate is computed using measurements of the motor angle and the arm angular acceleration. The design of the ILC algorithm is evaluated experimentally on a laboratory scale robot arm with good results.

The convergence properties of causal and current iteration tracking error (CITE) discrete time iterative learning control (ILC) algorithms are studied using time and frequency domain convergence criteria. Of particular interest are conditions for monotone convergence, and these are evaluated using a discrete-time version of Bode's integral theorem.

Closed-loop identification of an industrial robot of the type ABB IRB 1400 is considered. Data are collected when the robot is subject to feedback control and moving around axis one. Both black-box and physically parameterized models are identified. A main purpose is to model the mechanical flexibilities. It is found that a model consisting of three-masses connected by springs and dampers gives a good description of the dynamics of the robot.

This letter gives an overview of classical iterative learning control algorithms. The presented algorithms are also evaluated on a commercial industrial robot from ABB. The presentation covers implicit to explicit model-based algorithms. The result from the evaluation of the algorithms is that performance can be achieved by having more system knowledge.

Iterative learning control (ILC) based on minimization of a quadratic criterion in the control error and the input signal is considered. The focus is on the frequency domain properties of the algorithm, and how it is able to handle non-minimum phase systems. Experiments carried out on a commercial industrial robot are also presented.

An iterative, learning based, feed-forward method for compensation offriction in industrial robots is studied. The method is put into an ILC framework by using a two step procedure proposed inliterature. The friction compensation method is based on ablack-box friction model which is learned from operational data,and this can be seen as the first step in the method. In the second step the learned model is usedfor compensation of the friction using the reference joint velocityas input. The approach is supported by simulation experiments.

Feedback linearization is compared to Jacobian linearization for LQ control of atwo-link industrial manipulator. A method for obtaining equivalent nominal performance forboth control designs is introduced. An experimentally verified benchmark model with industrialrelevance is used for comparing the designs. Results do not show any conclusive advantages ofFeedback linearization.

 In this work an Inertial Measurement Unit is used to improve tool position estimates for an ABB IRB 4600 industrial robot, starting from estimates based on motor angle forward kinematics. A Complementary Filter and an Extended Kalman Filter are investigated. The Complementary Filter is found to perform on par with the Extended Kalman Filter while having lower complexity both in the tuning process and the filtering computations.

Fault detection algorithms (FDAs) process data to generate a test quantity. Test quantities are used to determine presence of a fault in a monitored system, despite disturbances. Because only limited knowledge of the system can be embedded in an FDA, it is important to evaluate it in scenarios relevant in practice. In this paper, simulation based approaches are proposed in an attempt to determine: i) which disturbances affect the output of an FDA the most; ii) how to compare the performance of dierent FDAs; and iii) which combinations of fault change size and disturbances variations are allowed to achieve satisfactory performance. The ideas presented are inspired by the literature of design of experiments, surrogate models, sensitivity analysis and change detection. The approaches are illustrated for the problem of wear diagnosis in manipulators where three FDAs are considered. The application study reveals that disturbances caused by variations in temperature and payload mass error affect the FDAs the most. It is also shown how the size of these disturbances delimit the capacity of an FDA to relate to wear changes. Further comparison of the FDAs reveal which performs "best" in average.

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.

An estimation-based iterative learning control (ILC) algorithm is applied to a realistic industrial manipulator model. By measuring the acceleration of the end-effector, the arm angular position accuracy is improved when the measurements are fused with motor angle observations. The estimation problem is formulated in a Bayesian estimation framework where three solutions are proposed: one using the extended Kalman filter (EKF), one using the unscented  Kalman filter (UKF), and one using the particle filter (PF).  The estimates are used in an ILC method to improve the accuracy for following a given reference trajectory.  Since the ILC algorithm is repetitive no computational restrictions on the methods apply explicitly. In an extensive Monte Carlo simulation study it is shown that the PF method outperforms the other methods and that the ILC control law is substantially improved using the PF estimate.

A sensor fusion method for state estimation of a flexible industrial robot is presented. By measuring the acceleration at the end-effector, the accuracy of the arm angular position is improved significantly when these measurements are fused with motor angle observation. The problem is formulated in a Bayesian estimation framework and two solutions are proposed; one using the extended Kalman filter (EKF) and one using the particle filter (PF). The technique is verified on experiments on the ABB IRB4600 robot, where the accelerometer method is showing a significant better dynamic performance, even when model errors are present.

Three approaches of iterative learning control (ILC) applied to a Gantry-Tau parallel kinematic robot are studied; ILC algorithms using 1) measured motor angles, 2) tool-position estimates, and for evaluation purposes, 3) measured tool position. The approaches are compared experimentally, with the tool performance evaluated using external sensors. It is concluded that the tool performance can be improved using tool-position estimates in the ILC algorithm, compared to when using motor-angle measurements. Applying ILC algorithms to a system following trajectories with so-called lead-in/lead-out is also considered in the paper.

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.

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, together 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.

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.

This paper investigates methods for tool position estimation of industrial robots. It is assumed that the motor angular position and the tool acceleration are measured. The considered observers are different versions of the extended Kalman filter as well as a deterministic observer. A method for tuning the observers is suggested and the robustness of the methods is investigated. The observers are evaluated experimentally on a commercial industrial robot.

Experimental results from a first-order ILC algorithm applied to a large-size sixdegrees-of-freedom commercial industrial robot are presented. The ILC algorithm is based on measurements of the motor angles, but in addition to the conventional evaluation of the ILC algorithm based on the motor-side error, the tool-path error on the arm side is evaluated using a laser-measurement system. Experiments have been carried out in three operating points using movements that represent typical paths in a laser-cutting application and different choices of algorithm design parameters have been studied. The motor-angle error is reduced substantially in all experiments and the tool-path error is reduced in most of the cases. In one operating point, however, the error does not decrease as much and an oscillatory tool behaviour is observed. Changed filter variables can give worse error reduction in all operating points. To achieve even better performance, especially in difficult operating points, it is concluded that an arm-side measurement, from for example an accelerometer, needs to be included in the learning.

Experimental evaluation of an Iterative Learning Control (ILC) algorithm is presented. The ILC algorithm is applied to all motors of a large size commercial six degrees-of-freedom industrial robot in order to minimise the error measured on the motor angles. The performance of the algorithm is evaluated with respect to the operating point of the robot, the programmed tool velocity, and the design variables of the ILC algorithm. The chosen movements are intended to represent typical paths in a laser cutting application. Even though a fairly simple ILC algorithm is applied, the error reduction is substantial after only five iterations and the algorithm shows good robustness properties.

A first step towards making a toolbox in Maple for industrial robot modelling is taken. Position and orientation of the tool can be determined in terms of the Denavit-Hartenberg joint variables and also the Jacobian relating the linear and angular velocities to the joint velocities. Further on it will be possible to, eg, differentiate the Jacobian. Future work includes to evaluate different kinds of sensors and sensor locations and symbolically generate the kinematic models using Maple. It also means to incorporate the models in Matlab- or C-code for including the results, eg, in an Extended Kalman Filter algorithm for state estimation.

The CDIO (Conceive Design Implement Operate) Initiative is explained, and some of the results at the Applied Physics and Electrical Engineering program at Linköping University, Sweden, are presented. A project course in Automatic Control is used as an example. The projects within the course are carried out using the LIPS (Linköping interactive project steering) model. An example of a project, the golf playing industrial robot, and the results from this project are also covered.

A modern industrial robot control system is often only based upon measurements from the motors of the manipulator. To perform good tra-ectory tracking on the arm side of the robot a very accurate description of the system must therefore be used. In the paper a sensor fusion technique is presented to achieve good estimates of the position of the robotusing a very simple model. By using information from an accelerometer at the tool of the robot the effect of unmodelled dynamics can be measured. The estimate of the tool position can be improved to enhance accuracy. We formulate the computation of the position as a Bayesian estimation problem and propose two solutions. The first solution uses the extended Kalman fillter (EKF) as a fast but linearized estimator. The second uses the particle fillter which can solve the Bayesian estimation problem without linearizations or any Gaussian noise assumptions. Since the aim is to use the positions estimates to improve position with an iterative learning control method, no computational constraints arise. The methods are applied to experimental data from an ABB IRB1400 commercial industrialrobot and to data from a simulation of a realistic flexible robot model, showing a significant improvement in position accuracy.

A modern industrial robot control system is often based only upon measurements from the motors of the manipulator. Hence to follow a trajectory with the tool an accurate description of the system must be used. In the paper a sensor fusion technique is presented to achieve good estimates of the position of the robot using a simple model. By using information from an accelerometer the effect of unmodelled dynamics can be measured. Hence, the estimate of the tool position can be improved to enhance the positioning. We formulate the computation of the position as a Bayesian estimation problem and propose two solutions. First using the extended Kalman filter EKF as a fast but linearized estimator. Second the particle filter which can solve the Bayesian estimation problem without linearizations or any Gaussian noise assumptions. Since the aim is to use the estimates to improve position accuracy using an iterative learning control method, no computational constraints arises. The methods are applied to experimental data from an ABBIRB1400 commercial industrial robot. We also discuss some preliminary results from using a detailed simulation model.

Path generation in Cartesian space is discussed and the idea of using lines and arcs to create general paths is presented. To make smooth paths in Cartesian space zones are introduced and two different ways to interpolate zones are given. An algorithm for transforming a Cartesian path into a cubic spline representation in joint space is presented and also evaluated in an example. An important aspect of the proposed algorithm is that the resulting path in joint-space has a bounded Cartesian space error.

In this contribution we place ILC in the realm of numerical optimization. This clarifies the role played by the design variables and how they affect e.g. convergence properties. We give a model based interpretation of these design variables and also a sufficient condition for convergence of ILC which is similar in spirit to the sufficient and necessary condition previously derived for linear systems. This condition shows that the desired performance has to be traded against modelling accuracy. Finally, one of the main benefits of ILC when non-minimum phase systems are concerned, the possibility of non-causal control, is given a comprehensive coverage.

In this paper we study the problem of a modeling, identifying, and monitoring an industrial robot. We start by showing how a robot can be modeled in increasing degree of accuracy using high end tools such as MathModelica. This model can be transformed semi-automatically into a minimal state-space form which in turn can be used for identification. Moreover, the physically connected equations can be identified recursively, making it possible to monitor critical parts of the robot. When attached to a well trimmed detection scheme this provides a big help for operators, who easily can track problems with the process.

Frequency domain convergence conditions for Current Iteration Tracking Error (CITE) Iterative Learning Control (ILC) algorithms are presented. The convergence conditions together with a discrete-time version of Bodes integral theorem imply a strong restriction upon the kind of systems that can be controlled using a CITE ILC algorithm. The restriction is caused by the fact that the filter in the ILC algorithm has to be causal and and part of a closed loop system that has to be stable.

In this contribution it is shown how an iterative learning control algorithm can be found for a disturbance rejection application where a repetitive disturbance is acting on the output of a system. It is also assumed that there is additive noise on the measurements from the system. When applying iterative learning control to a system where measurement disturbances are present it is shown that it is optimal to use iteration varying filters in the learning law. To achieve a good transient behavior it is also necessary to have an accurate model of the system. The results are also verified in simulations.

Aspects on the behavior of a general second order iterative learning control (ILC) algorithm are presented from a frequency domain perspective. This includes stability as well as performance and robustness issues. The basis for the analysis is linear iterative systems and these are briefly described. A design algorithm for second order ILC schemes is proposed and analyzed both theoretically as well as in an experiment. In the experiment, done on a commercial industrial robot control system, the second order ILC design is compared with a first order ILC design. The result from both the analysis and the experiment is that the second order design is not better with respect to performance or robustness.

An adaptive approach to Iterative Learning Control (ILC) based on Kalman filters and optimization of a quadratic criterion is presented. The idea is to estimate one of the design parameters in the Kalman filter and hence create an adaptive gain in the ILC updating formula. The proposed ILC design is compared with two other ILC schemes and they are all implemented on an industrial robot. The results show that the proposed adaptive ILC scheme is fast, and also robust since the gain is reduced as the error is decreased.

Aspects on the behavior of a general second order iterative learning control (ILC) algorithm is presented from a frequency domain perspective. This includes stability as well as performance and robustness issues. The basis for the analysis is linear iterative systems and these are briefly described. A design algorithm for second order ILC schemes is proposed and analyzed both theoretically as well as in an experiment. In the experiment, done on a commercial industrial robot control system, the second order ILC design is compared with a first order ILC design. The result from both the analysis and the experiment is that the second order design is not better with respect to performance or robustness.

Control of a flexible mechanical system using Iterative Learning Control (ILC) is studied using a linear two-mass model. The available signals are position of the first mass and acceleration of the second mass. An ILC algorithm using an estimate of the position of the second mass is evaluated in simulations showing promising properties.

A synthesis algorithm for the filters in a first order ILC is presented and applied on an industrial robot. The proposed ILC synthesis method is evaluated using two experiments on the robot. The first is a one-axis experiment where the system can be seen as a single servo. A modeling experiment is done to give input to the synthesis algorithm and then ILC is applied to the single axis showing a dramatic improvement in trajectory following. In the second experiment ILC is applied to a more complex multi axes motion where the robot draws a circle in a plane. The evaluation of the result is done using a pen mounted on the robot and it is evident that also on the arm-side an improved motion can be achieved. In both experiments the error converges to a stable level in about 5 iterations. Since a model is desired for the synthesis, an extra iteration has to be done for the modeling experiment. In this particular case a good path following can therefore be achieved after 6 iterations.

An optimization approach to Iterative Learning Control (ILC) is considered. The ILC algorithm is formed by minimizing a quadratic criterion in the control error and input signal. A frequency domain interpretation of the derived updating algorithm is given. Experiments carried out on an ABB IRB 1400 are presented.

Iterative learning control applied to a simplified model of a robot arm is studied. The iterative learning control input signal is used in combination with conventional feed-back and feed-forward control, and the aim is to let the learning control signal handle the effects of unmodeled dynamics and friction. Convergence and robustness aspects of the choice of filters in the updating scheme of the iterative learning control signal are studied.

Some aspects of the use of learning control for improved performance in robot control systems are studied. The learning control signal is used in combination with conventional feed-back and feed-forward control. The effects of disturbances, unmodeled dynamics and friction are studied theoretically and in simulations of a simplified model of a robot arm. Convergence and robustness aspects of the choice of filters in the updating scheme of the learning control signal are studied.

In many industrial robot applications it is a fact that the robot is programmed to do the same task repeatedly. By observing the control error in the different iterations of the same task it becomes clear that it is actually highly repetitive. Iterative Learning Control (ILC) allows to iteratively compensate for and, hence, remove this repetitive error.

In the thesis different aspects of iterative learning control are covered. Although stability is the most important in practice the design aspect is also highlighted. Several design schemes for iterative learning control methods are presented, including first order as well as second order iterative learning control. An adaptive approach to iterative learning control is also discussed. Many of the suggested design methods are also given with stability and robustness results.

The application, industrial robot control, that has been used as a testbed throughout the thesis is described. The description includes a general discussion on robot modeling and control as well as a specific discussion on the implementation of the functions needed in the commercial robot control software in order to make it possible to apply iterative learning control.

The suggested iterative learning control design methods are all tested on the robot. Some practical aspects on the path following problem for industrial robots using iterative learning control are discussed. A potential solution to the path tracking problem using additional sensors is given, although it is not yet implemented on the robot.

The iterative learning control (ILC) method improvesperformance 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.

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.

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.

A sensor fusion method for state estimation of a flexible industrial robot is presented. By measuring the acceleration at the end-effector, the accuracy of the arm angular position is improved significantly when these measurements are fused with motor angle observation. The problem is formulated in a Bayesian estimation framework and two solutions are proposed; one using the extended Kalman filter (EKF) and one using the particle filter (PF). The technique is verified on experiments on the ABB IRB4600 robot, where the accelerometer method is showing a significant better dynamic performance, even when model errors are present.

Three different approaches of iterative learning control (ILC) applied to a parallel kinematic robot are studied. First, the ILC algorithm is based on measured motor angles only. Second, tool-position estimates are used in the ILC algorithm. For evaluation, the ILC algorithm finally is based on measured tool position. Model-based tuning of the ILC filters enables learning above the resonance frequencies of the system. The approaches are compared experimentally on a Gantry-Tau prototype, with the tool performance being evaluated by using external sensors. It is concluded that the tool performance can be improved by using tool-position estimates in the ILC algorithm, compared to when using motor-angle measurements. In the paper applying ILC algorithms to a system following trajectories with so-called lead-in/lead-out is also considered, as well as dynamic modelling of the Gantry-Tau prototype.

Some implementation aspects of Iterative Learning Control (ILC) are considered. Since the ILC algorithm involves filtering of various signals over finite time intervals, often using non-causal filters, it is important that the boundary effects of the filtering operations are handled in an appropriate way when implementing the ILC algorithm. The paper illustrates in both theoretical analysis using the matrix description and in simulations of a twomass system that the method of implementation for handling the boundary effects can have large influence over stability and convergence properties of the ILC algorithm.

This paper investigates methods for tool position estimation of industrial robots. It is assumed that the motor angular position and the tool acceleration are measured. The considered observers are different versions of the extended Kalman filter as well as a deterministic observer. A method for tuning the observers is suggested and the robustness of the methods is investigated. The observers are evaluated experimentally on a commercial industrial robot.

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.

When an ILC algorithm is applied to an industrial robot, the goal is to move the tool along a desired trajectory, while only the motor position canbe measured. In this paper aspects of robustness and performance are discussed when an ILC algorithm is applied to a flexible two-mass system. It is shown that the stabilising controller of the two-mass system also directly affects the robustness properties of the ILC algorithm. A classical noncausa lP-ILC algorithm and a model-based ILC design using optimisation are applied to the system, based on the error for the first mass. Performance and robustness of the algorithms are compared when model errors are introduced in the system, showing that the optimisation-based approach can handle larger model uncertainties. It is illustrated that the performance of the overall system, when considering position of the second mass, is the practical limit compared to the limiting factor of the robustness of the ILC algorithms.

In this paper a step toward making a toolbox for industrial robot modelling based on the computer algebra tool Maple is taken. It can be seen as a modelling platform for efficient derivation of the necessary equations for doing, eg, sensor fusion or state estimation by an Extended Kalman Filter (EKF) algorithm. Forward kinematics is studied and the position and orientation of the robot tool are determined in terms of the Denavit-Hartenberg joint variables. Linear and angular velocities and accelerations are derived using the Jacobian. The toolbox is exemplified using an IRB1400 from ABB Robotics with a so called parallelogram linkage structure. The kinematic relations received are verified using the robot IRB1400 with an accelerometer placed on the robot tool and it is shown that measured acceleration and theoretical acceleration derived from the kinematics agree well. However no flexibilities in the modelling are taken into account, which results in differences between measured and derived acceleration when several motors of the robot cooperate in the motion.

A first step towards making a toolbox in Maple for industrial robot modelling is taken. Position and orientation of the tool can be determined in terms of the Denavit-Hartenberg joint variables and also the Jacobian relating the linear and angular velocities to the joint velocities. Further on it will be possible to, eg, differentiate the Jacobian. Future work includes to evaluate different kinds of sensors and sensor locations and symbolically generate the kinematic models using Maple. It also means to incorporate the models in Matlab- or C-code for including the results, eg, in an Extended Kalman Filter algorithm for state estimation.

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.

A modern industrial robot control system is often only based upon measurements from the motors of the manipulator. To perform good tra-ectory tracking on the arm side of the robot a very accurate description of the system must therefore be used. In the paper a sensor fusion technique is presented to achieve good estimates of the position of the robotusing a very simple model. By using information from an accelerometer at the tool of the robot the effect of unmodelled dynamics can be measured. The estimate of the tool position can be improved to enhance accuracy. We formulate the computation of the position as a Bayesian estimation problem and propose two solutions. The first solution uses the extended Kalman fillter (EKF) as a fast but linearized estimator. The second uses the particle fillter which can solve the Bayesian estimation problem without linearizations or any Gaussian noise assumptions. Since the aim is to use the positions estimates to improve position with an iterative learning control method, no computational constraints arise. The methods are applied to experimental data from an ABB IRB1400 commercial industrialrobot and to data from a simulation of a realistic flexible robot model, showing a significant improvement in position accuracy.

A sensor fusion technique is presented and it is shown to achieve good estimates of the position for a 3 degrees-of-freedom industrial robot model. By using an accelerometer the estimate of the tool position accuracy can be improved. The computation of the position is formulated as a Bayesian estimation problem and two solutions are proposed. One using the extended Kalman filter and one using the particle filter. Since the aim is to use the positions estimates to improve trajectory tracking with an iterative learning control method, no computational constraints arise. In an extensive simulation study the performance is compared to the Cramér-Rao lower bound. A significant improvement in position accuracy is achieved using the sensor fusion technique.

This paper presents a gain scheduling control of a nonlinear system in which the reference trajectory is given in advance. Multiple frozen operating times are chosen on the reference trajectory and a linear time invariant model is obtained at each operating time. A linear parameter varying model is then constructed by interpolating the region between the neighbor frozen operating times. A gain scheduling state feedback law is designed by a linear matrix inequality formulation. The effectiveness is demonstrated in a numerical simulation of a traing control of a two-link robot arm.

Some fundamental limitations of causal and Current Iteration Tracking Error (CITE) discrete time Iterative Learning Control (ILC) algorithms are stud- ied using time and frequency domain convergence criteria. Of particular interest are conditions for monotone convergence, and these are evaluated using a discrete- time version of Bode's integral theorem. A relation between the frequency domain convergence conditions and the time-domain monotone convergence criterion is also discussed.

Time and frequency domain convergence properties of causal and Current Iteration Tracking Error (CITE) discrete time Iterative Learning Control (ILC) algorithms are discussed. Considering necessary and sufcient convergence conditions basic matrix properties can be utilized to show that causal as well as CITE ILC algorithms converge to zero error in only very restrictive special cases. The frequency domain convergence conditions, sucient for monotone convergence, are studied using a discrete-time version of Bode's integral theorem. The result is that causal and CITE ILC algorithms will not satisfy the frequency domain conditions except if the system has relative degree zero or it is accepted that the algorithms do not converge to zero error.

Path generation in Cartesian space is discussed and the idea of using lines and arcs to create general paths is presented. To make smooth paths in Cartesian space zones are introduced and two different ways to interpolate zones are given. An algorithm for transforming a Cartesian path into a cubic spline representation in joint space is presented and also evaluated in an example. An important aspect of the proposed algorithm is that the resulting path in joint-space has a bounded Cartesian space error.

This report covers many aspects of path and trajectory generation for industrial robots. Path generation in Cartesian space is discussed, with the limitation that only linear motion is considered. Path generation in joint space is also discussed and in particular representation of the joint path using cubic splines is presented. Different algorithms for spline generation are also discussed and tested on an example.The last step, the trajectory generation is also covered. Two preliminary algorithms that gives limited speed and acceleration in Cartesian space and in joint space are given. It is also indicated that there is more to be done in order to reach an optimal trajectory. At the end of the report a simple spline toolbox for MatLab is described.

In this contribution it is shown how an iterative learning control algorithm can be found for a disturbance rejection application where a repetitive disturbance is acting on the output of a system. It is also assumed that there is additive noise on the measurements from the system. When applying iterative learning control to a system where measurement disturbances are present it is shown that it is optimal to use iteration varying filters in the learning law. To achieve a good transient behavior it is also necessary to have an accurate model of the system. The results are also verified in simulations.

This paper gives an overview of classical Iterative Learning Control algorithms. The presented algorithms are also evaluated on a commercial industrial robot from ABB. The presentation covers implicit to explicit model based algorithms. The result from the evaluation of the algorithms is that performance can be achieved by having more system knowledge.

In this contribution we place ILC in the realm of numerical optimization. This clarifies the role played by the design variables and how they affect e.g. convergence properties. We give a model based interpretation of these design variables and also a sufficient condition for convergence of ILC which is similar in spirit to the sufficient and necessary condition previously derived for linear systems. This condition shows that the desired performance has to be traded against modelling accuracy. Finally, one of the main benefits of ILC when non-minimum phase systems are concerned, the possibility of non-causal control, is given a comprehensive coverage.

Some initial results on the disturbance properties of high order iterative learning control (ILC) algorithms are presented. Of particular interest is to investigate how high order ILC algorithms cope with measurement and load disturbances of different character. Some results are obtained by assuming statistical properties of the involved disturbances and deriving equations for the covariance matrix of the control error vector. The results are illustrated by analytic derivation of the covariance matrix for a second order ILC algorithm with a particular choice of design variables.

Closed-loop identification of an industrial robot of the type ABB IRB 1400 is considered. Data are collected when the robot is subject to feedback control and moving around axis one. Both black-box and physically parameterized models are identified. A main purpose is to model the mechanical flexibilities. It is found that a model consisting of three-masses connected by springs and dampers gives a good description of the dynamics of the robot.

Aspects on the behavior of a general second order iterative learning control (ILC) algorithm are presented from a frequency domain perspective. This includes stability as well as performance and robustness issues. The basis for the analysis is linear iterative systems and these are briefly described. A design algorithm for second order ILC schemes is proposed and analyzed both theoretically as well as in an experiment. In the experiment, done on a commercial industrial robot control system, the second order ILC design is compared with a first order ILC design. The result from both the analysis and the experiment is that the second order design is not better with respect to performance or robustness.

Design of Iterative Learning Control (ILC) algorithms using optimization is considered. By forming a quadratic criterion in the control error and the input signal using a nominal model of the system an ILC algorithm is derived. Special attention is paid to the frequency domain properties of the algorithm and to how it is able to handle non-minimum phase systems. A numerical example and an experiment carried out on an real industrial robot are presented.

Disturbance aspects of iterative learning control (ILC) are considered. By using a linear framework it is possible to investigate the influence of the disturbances in the frequency domain. The effects of the design filters in the ILC algorithm on the disturbance properties can then be analyzed. The analysis is supported by simulations and experiments.

Control of a flexible mechanical system using Iterative Learning Control (ILC) is studied using a linear two-mass model. The available signals are position of the first mass and acceleration of the second mass. An ILC algorithm using an estimate of the position of the second mass is evaluated in simulations showing promising properties.

A general theory for modeling of industrial robots is presented and, based on the theory, some algorithms for the actual modeling process are derived and described. As an example of an application of the theory an industrial manipulator, an IRB1400 from ABB Robotics Products, is used. A kinematic model and a dynamical model for the first three joints of the IRB1400 manipulator is found. One part of the report is also devoted to flexible manipulators, especially manipulators with joint flexibilities. Finally, an identification experiment using data from the IRB1400 is discussed.

A frequency domain analysis method of a second order iterative learning control (ILC) algorithm is considered. Using the notion of iterative systems bounds for stability are presented in the frequency domain for the second order term. The bounds are found using a geometrical approach based on the special structure of the transfer matrix in the iterative system. Two examples are included showing how the analysis method can be used in an application.

An introduction to Iterative Learning Control (ILC) is given. The basic principle behind ILC in both open loop and closed loop problems is explained. A general class of algorithms for updating of the ILC input signal is presented and the choice of the filters in the update algortihm is discussed with respect to convergence, robustness and disturbance sensitivity.

Many manipulators at work in factories today repeat their motions over and over in cycles and if there are errors in following the trajectory these errors will also be repeated cycle after cycle. The basic idea behind iterative learning control (ILC) is that the controller should learn from previous cycles and perform better every cycle. Iterative learning control is used in combination with conventional feed-back and feed-forward control, and it is shown that learning control signal can handle the effects of unmodeled dynamics and friction. Convergence and disturbance effects as well as the choice of filters in the updating scheme are also addressed.