Foreword

This paper considers identification of unknown parameters in elastic dynamic models of industrial robots. Identifying such models is a challenging task since an industrial robot is a multivariable, nonlinear, resonant, and unstable system. Unknown parameters (mainly spring-damper pairs) in a physically parameterized nonlinear dynamic model are identified in the frequency domain, using estimates of the nonparametric frequency response function (FRF) in different robot configurations/positions. The nonlinear parametric robot model is linearized in the same positions and the optimal parameters are obtained by minimizing the discrepancy between the nonparametric FRFs and the parametric FRFs (the FRFs of the linearized parametric robot model). In order to accurately estimate the nonparametric FRFs, the experiments must be carefully designed. The selection of optimal robot configurations for the experiments is also part of the design. 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

Improving (Software) Patent Quality Through the Administrative Process

The available evidence indicates that patent quality, particularly in the area of software, needs improvement. This Article argues that even an agency as institutionally constrained as the U.S. Patent and Trademark Office (“PTO”) could implement a portfolio of pragmatic, cost-effective quality improvement strategies. The argument in favor of these strategies draws upon not only legal theory and doctrine but also new data from a PTO software examination unit with relatively strict practices. Strategies that resolve around Section 112 of the patent statute could usefully be deployed at the initial examination stage. Other strategies could be deployed within the new post-issuance procedures available to the agency under the America Invents Act. Notably, although the strategies the Article discusses have the virtue of being neutral as to technology, they are likely to have a very significant practical impact in the area of software

State-Dependent Probability Distributions in Non Linear Rational Expectations Models

In this paper, we provide solution methods for non-linear rational expectations models in which regime-switching or the shocks themselves may be "endogenous", i.e. follow state-dependent probability distributions. We use the perturbation approach to find determinacy conditions, i.e. conditions for the existence of a unique stable equilibrium. We show that these conditions directly follow from the corresponding conditions in the exogenous regime-switching model. Whereas these conditions are diffcult to check in the general case, we provide for easily verifiable and sufficient determinacy conditions and first-order approximation of the solution for purely forward-looking models. Finally, we illustrate our results with a Fisherian model of inflation determination in which the monetary policy rule may change across regimes according to a state-dependent transition probability matrix.Dans ce papier, nous proposons une méthode de résolution de modèles non linéaires à anticipations rationnelles dans lesquels les changements de régimes ou les chocs eux-même peuvent être "endogènes", c'est-à-dire suivre des distributions de probabilités dépendant de l'état de l'économie. Par une méthode de perturbation, nous trouvons des conditions de détermination, i.e. des conditions d'existence d'un unique équilibre stable. Nous montrons que ces conditions découlent directement des conditions correspondantes dans le modèle à changements de régimes exogènes. Bien que ces conditions soient difficiles à vérifier dans le cas général, nous donnons, dans le cas des modèles à changements de régimes purement tournés vers le futur, des conditions de détermination faciles à calculer et une approximation au premier ordre de la solution. Enfin, nous illustrons nos résultats avec un modèle de Fisher de détermination d'inflation dans lequel la règle de politique monétaire change entre les régimes selon une matrice de transition dépendant de l'état de l'économie

Multivariable Frequency-Domain Identification of Industrial Robots

Industrirobotar är idag en väsentlig del i tillverkningsindustrin där de bland annat används för att minska kostnader, öka produktivitet och kvalitet och ersätta människor i farliga eller slitsamma uppgifter. Höga krav på noggrannhet och snabbhet hos robotens rörelser innebär också höga krav på de matematiska modeller som ligger till grund för robotens styrsystem. Modellerna används där för att beskriva det komplicerade sambandet mellan robotarmens rörelser och de motorer som orsakar rörelsen. Tillförlitliga modeller är också nödvändiga för exempelvis mekanisk design, simulering av prestanda, diagnos och övervakning. En trend idag är att bygga lättviktsrobotar, vilket innebär att robotens vikt minskas men att den fortfarande kan hantera en lika tung last. Orsaken till detta är främst att minska kostnaden, men också säkerhetsaspekter spelar in. En lättare robotarm ger dock en vekare struktur där elastiska effekter inte längre kan försummas i modellen om man kräver hög prestanda. De elastiska effekterna beskrivs i den matematiska modellen med hjälp av fjädrar och dämpare. Denna avhandling handlar om hur dessa matematiska modeller kan tas fram genom systemidentifiering, vilket är ett viktigt verktyg där mätningar från robotens rörelser används för att bestämma okända parametrar i modellen. Det som mäts är position och moment hos robotens alla motorer. Identifiering av industrirobotar är ett utmanande problem bland annat eftersom robotens beteende varierar beroende på armens position. Den metod som föreslås i avhandlingen innebär att man först identifierar lokala modeller i ett antal positioner. Var och en av dessa beskriver robotens beteende kring en viss arbetspunkt. Sedan anpassas parametrarna i en global modell, som är giltig för alla positioner, så att den så väl som möjligt beskriver det lokala beteendet i de olika positionerna. I avhandlingen analyseras olika metoder för att ta fram lokala modeller. För att få bra resultat krävs att experimenten är omsorgsfullt utformade. För att minska osäkerheten i den globala modellens identifierade parametrar ingår också valet av optimala positioner för experimenten. Olika metoder för att identifiera parametrarna jämförs i avhandlingen och experimentella resultat visar användbarheten av den föreslagna metoden. Den identifierade robotmodellen ger en bra global beskrivning av robotens beteende. Resultatet av forskningen har även gjorts tillgängligt i ett datorverktyg för att noggrant kunna ta fram lokala modeller och identifiera parametrar i dynamiska robotmodeller.Industrial robots are today essential components in the manufacturing industry where they are used to save costs, increase productivity and quality, and eliminate dangerous and laborious work. High demands on accuracy and speed of the robot motion require that the mathematical models, used in the motion control system, are accurate. The models are used to describe the complicated nonlinear relation between the robot motion and the motors that cause the motion. Accurate dynamic robot models are needed in many areas, such as mechanical design, performance simulation, control, diagnosis, and supervision. A trend in industrial robots is toward lightweight robot structures, where the weight is reduced but with a preserved payload capacity. This is motivated by cost reduction as well as safety issues, but results in a weaker (more compliant) mechanical structure with enhanced elastic effects. For high performance, it is therefore necessary to have models describing these elastic effects. This thesis deals with identification of dynamic robot models, which means that measurements from the robot motion are used to estimate unknown parameters in the models. The measured signals are angular position and torque of the motors. Identifying robot models is a challenging task since an industrial robot is a multivariable, nonlinear, unstable, and resonant system. In this thesis, the unknown parameters (typically spring-damper pairs) in a physically parameterized nonlinear dynamic model are identified, mainly in the frequency domain, using estimates of the nonparametric frequency response function (FRF) in different robot configurations/positions. Each nonparametric FRF then describe the local behavior around an operating point. The nonlinear parametric robot model is linearized in the same operating points and the optimal parameters are obtained by minimizing the discrepancy between the nonparametric FRFs and the parametric FRFs (the FRFs of the linearized parametric robot model). Methods for estimating the nonparametric FRF from experimental data are analyzed with respect to bias, variance, and nonlinearities. In order to accurately estimate the nonparametric FRF, the experiments must be carefully designed. To minimize the uncertainty in the estimated parameters, the selection of optimal robot configurations/positions for the experiments is also part of the design. Different parameter estimators are compared in the thesis and experimental results show the usefulness of the proposed identification procedure. The identified nonlinear robot model gives a good global description of the dynamics in the frequency range of interest. The research work is also implemented and made easily available in a software tool for accurate estimation of nonparametric FRFs as well as parametric robot models

Detection and Estimation of Nonlinear Distortions in Industrial Robots

System identification in robotics often involves the estimation of linear models characterizing the behavior in certain operating points. In this paper, a method for the detection and estimation of nonlinear distortions in an estimated frequency response function (FRF) has successfully been applied to experimental data from an industrial robot. The results show that nonlinear distortions areindeed present and cause larger variability in the FRF than the measurement noise contributions

Nonlinear Identification of a Physically Parameterized Robot Model

In the work presented here, a three-step identification procedure for rigid body dynamics, friction, and flexibilities, introduced in (Wernholt and Gunnarsson, 2005), will be utilized and extended. Using the procedure, the parameters can be identified only using motor measurements. In the first step, rigid body dynamics and friction will be identified using a separable least squares method, where a friction model describing the Striebeck effect is used. In the second step, initial values for flexibilities are obtained using inverse eigenvalue theory. Finally, in the last step, the remaining parameters of a nonlinear physically parameterized model are identified directly in the time domain. The procedure is exemplified using real data from an experimental industrial robot

On the Use of a Multivariable Frequency Response Estimation Method for Closed Loop Identification

A method for estimating the Multivariable Frequency Response Function using closed loop data is studied. An approximate expression for the estimation error is derived, and using this expression some properties of the estimation error can be explained. Of particular interest is how the model quality is affected by the properties of the disturbances, the choice of excitation signal in the different input channels, the feedback and the properties of the system itself. The expression is illustrated by simulation data from an industrial robot

Experiment Design for Identification of Nonlinear Gray-box Models with Application to Industrial Robots

Experiment design involving selection of optimal experiment positions for nonlinear gray-box models is studied. From the derived Fisher information matrix, a convex optimization problem is posed. By considering the dual problem, the experiment design is efficiently solved with linear complexity in the number of candidate positions, compared to cubic complexity for the primal problem. In the numerical illustration, using an industrial robot, the parameter covariance is reduced by a factor of six by using the 15 optimal positions compared to using the optimal single position in all experiments