A Sensitivity Analysis Based Method for Robot Calibration

1992 ◽  
Author(s):  
S. Kaizerman ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
G. Zak
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Model ◽  
Calibration Procedure ◽  
Inverse Kinematic ◽  
Model Parameters ◽  
Robot Calibration ◽  
Adjoint Sensitivity ◽  
Analysis Methods ◽  
The Matrix ◽  
Direct Sensitivity

Abstract A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two degree of freedom revolute-joint planar manipulator.

A Sensitivity Analysis Based Method for Robot Calibration

1994 ◽  
Vol 116 (2) ◽  
pp. 607-613 ◽  
Author(s):  
S. Kaizerman ◽  
G. Zak ◽  
B. Benhabib ◽  
R. G. Fenton
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Model ◽  
Calibration Procedure ◽  
Inverse Kinematic ◽  
Model Parameters ◽  
Robot Calibration ◽  
Adjoint Sensitivity ◽  
Analysis Methods ◽  
The Matrix ◽  
Direct Sensitivity

A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two-degree-of-freedom revolute-joint planar manipulator.

Optimization of the Robot Calibration Process

1992 ◽  
Author(s):  
G. Zak ◽  
R. G. Fenton ◽  
B. Benhabib
Keyword(s):  
Optimization Problem ◽  
Kinematic Model ◽  
Optimization Procedure ◽  
Calibration Procedure ◽  
Residual Error ◽  
Industrial Robots ◽  
Multiple Objective Optimization ◽  
Robot Calibration ◽  
Calibration Process ◽  
The Cost

Abstract Most industrial robots cannot be off-line programmed to carry out a task accurately, unless their kinematic model is suitably corrected through a calibration procedure. However, proper calibration is an expensive and time-consuming procedure due to the highly accurate measurement equipment required and due to the significant amount of data that must be collected. To improve the efficiency of robot calibration, an optimization procedure is proposed in this paper. The objective of minimizing the cost of the calibration is combined with the objective of minimizing the residual error after calibration in one multiple-objective optimization. Prediction of the residual error for a given calibration process presents the main difficulty for implementing the optimization. It is proposed that the residual error is expressed as a polynomial function. This function is obtained as a result of fitting a response surface to either experimental or simulated sample estimates of the residual error. The optimization problem is then solved by identifying a reduced set of possible solutions, thus greatly simplifying the decision maker’s choice of an effective calibration procedure. An application example of this method is also included.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

Determination of the Optimum Cost-Residual Error Trade-off in Robot Calibration

1994 ◽  
Vol 116 (1) ◽  
pp. 28-35 ◽  
Author(s):  
G. Zak ◽  
R. G. Fenton ◽  
B. Benhabib
Keyword(s):  
Kinematic Model ◽  
Optimization Procedure ◽  
Calibration Procedure ◽  
Residual Error ◽  
Industrial Robots ◽  
Multiple Objective Optimization ◽  
Robot Calibration ◽  
Optimum Cost ◽  
The Cost

Most industrial robots cannot be off-line programmed to carry out a task accurately, unless their kinematic model is suitably corrected through a calibration procedure. However, proper calibration is an expensive and time-consuming procedure due to the highly accurate measurement equipment required and due to the significant amount of data that must be collected. To improve the efficiency of robot calibration, an optimization procedure is proposed in this paper. The objective of minimizing the cost of the calibration is combined with the objective of minimizing the residual error after calibration in one multiple-objective optimization. Prediction of the residual error for a given calibration process presents the main difficulty for implementing the optimization. It is proposed that the residual error is expressed as a polynomial function. This function is obtained as a result of fitting a response surface to either experimental or simulated sample estimates of the residual error. The optimization problem is then solved by identifying a reduced set of possible solutions, thus greatly simplifying the decision maker’s choice of an effective calibration procedure. An application example of this method is also included.

scholarly journals Analysis of Open Architecture 6R Robot Forward and Inverse Kinematics Adaptive to Structural Variations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Chong Wang ◽  
Dongxue Liu ◽  
Qun Sun ◽  
Tong Wang
Keyword(s):  
Inverse Kinematics ◽  
Industrial Robot ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Open Architecture ◽  
Model Parameters ◽  
Structural Variations ◽  
Robot Controller ◽  
Kinematic Models ◽  
Kinematic Studies

This paper presents a kinematic analysis for an open architecture 6R robot controller, which is designed to control robots made by domestic manufactures with structural variations. Usually, robot kinematic studies are often introduced for specific robot types, and therefore, difficult to apply the kinematic model from one to another robot. This study incorporates most of the robot structural variations in one model so that it is convenient to switch robot types by modifying model parameters. By combining an adequate set of parameters, the kinematic models, especially the inverse kinematics, are derived. The kinematic models are proved to be suitable for many classic industrial robot types, such as Puma560, ABB IRB120/1600, KAWASAKI RS003N/RS010N, FANUC M6iB/M10iA, and therefore be applicable to those with similar structures. The analysis and derivation of the forward and inverse kinematic models are presented, and the results are proven to be accurate.

Computing Sensitivity Analysis of Vehicle Dynamics Based on Multibody Models

2013 ◽  
Author(s):  
Yitao Zhu ◽  
Daniel Dopico ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Vehicle Dynamics ◽  
Multibody Systems ◽  
Dynamics Simulation ◽  
Adjoint Sensitivity ◽  
Analysis And Design ◽  
Systems Analysis And Design ◽  
Dynamics Of Multibody Systems ◽  
Direct Sensitivity ◽  
Vehicle Suspension System

Vehicle dynamics simulation based on multibody dynamics techniques has become a powerful tool for vehicle systems analysis and design. As this approach evolves, more and more details are required to increase the accuracy of the simulations, to improve their efficiency, or to provide more information that will allow various types of analyses. One very important direction is the optimization of multibody systems. Sensitivity analysis of the dynamics of multibody systems is essential for design optimization. Dynamic sensitivities, when needed, are often calculated by means of finite differences but, depending of the number of parameters involved, this procedure can be very demanding in terms of time and the accuracy obtained can be very poor in many cases if real perturbations are used. In this paper, several ways to perform the sensitivity analysis of multibody systems are explored including the direct sensitivity approaches and the adjoint sensitivity ones. Finally, the techniques proposed are applied to the dynamical optimization of a five bar mechanism and a vehicle suspension system.

scholarly journals Sensitivity analysis and parameter estimation for the distributed modeling of infiltration excess overland flow

2007 ◽  
Vol 4 (1) ◽  
pp. 363-405 ◽  
Author(s):  
W. Castaings ◽  
D. Dartus ◽  
F.-X. Le Dimet ◽  
G.-M. Saulnier
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Overland Flow ◽  
Flash Flood ◽  
Parametric Uncertainty ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Adjoint Sensitivity ◽  
Gradient Based ◽  
Infiltration Excess

Abstract. The variational methods widely used for other environmental systems are applied to a spatially distributed flash flood model coupling kinematic wave overland flow and Green Ampt infiltration. Using an idealized configuration where only parametric uncertainty is addressed, the potential of this approach is illustrated for sensitivity analysis and parameter estimation. Adjoint sensitivity analysis provides an extensive insight into the relation between model parameters and the hydrological response and enables the use of efficient gradient based optimization techniques.

Sensitivity of Input Epistemic Uncertainty on Nondeterministic Performance Estimates Using Nondeterministic Simulations

2017 ◽  
Vol 2 (2) ◽  
Author(s):  
Lawrence Hale ◽  
Mayuresh Patil ◽  
Christopher J. Roy
Keyword(s):  
Sensitivity Analysis ◽  
Epistemic Uncertainty ◽  
Model Parameters ◽  
Local Sensitivity ◽  
Local Sensitivity Analysis ◽  
Analysis Methods ◽  
Plot Analysis ◽  
Computational Speed ◽  
Input Uncertainties ◽  
Performance Estimates

This paper examines various sensitivity analysis methods which can be used to determine the relative importance of input epistemic uncertainties on the uncertainty quantified performance estimate. The results from such analyses would then indicate which input uncertainties would merit additional study. The following existing sensitivity analysis methods are examined and described: local sensitivity analysis by finite difference, scatter plot analysis, variance-based analysis, and p-box-based analysis. As none of these methods are ideally suited for analysis of dynamic systems with epistemic uncertainty, an alternate method is proposed. This method uses aspects of both local sensitivity analysis and p-box-based analysis to provide improved computational speed while removing dependence on the assumed nominal model parameters.

scholarly journals Fourth-Order Comprehensive Adjoint Sensitivity Analysis (4th-CASAM) of Response-Coupled Linear Forward/Adjoint Systems: I. Theoretical Framework

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3335
Author(s):  
Dan Gabriel Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Fourth Order ◽  
Model Parameters ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
Adjoint Systems ◽  
Functional Derivatives ◽  
Adjoint State ◽  
State Functions

The most general quantities of interest (called “responses”) produced by the computational model of a linear physical system can depend on both the forward and adjoint state functions that describe the respective system. This work presents the Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (4th-CASAM) for linear systems, which enables the efficient computation of the exact expressions of the 1st-, 2nd-, 3rd- and 4th-order sensitivities of a generic system response, which can depend on both the forward and adjoint state functions, with respect to all of the parameters underlying the respective forward/adjoint systems. Among the best known such system responses are various Lagrangians, including the Schwinger and Roussopoulos functionals, for analyzing ratios of reaction rates, the Rayleigh quotient for analyzing eigenvalues and/or separation constants, etc., which require the simultaneous consideration of both the forward and adjoint systems when computing them and/or their sensitivities (i.e., functional derivatives) with respect to the model parameters. Evidently, such responses encompass, as particular cases, responses that may depend just on the forward or just on the adjoint state functions pertaining to the linear system under consideration. This work also compares the CPU-times needed by the 4th-CASAM versus other deterministic methods (e.g., finite-difference schemes) for computing response sensitivities These comparisons underscore the fact that the 4th-CASAM is the only practically implementable methodology for obtaining and subsequently computing the exact expressions (i.e., free of methodologically-introduced approximations) of the 1st-, 2nd, 3rd- and 4th-order sensitivities (i.e., functional derivatives) of responses to system parameters, for coupled forward/adjoint linear systems. By enabling the practical computation of any and all of the 1st-, 2nd, 3rd- and 4th-order response sensitivities to model parameters, the 4th-CASAM makes it possible to compare the relative values of the sensitivities of various order, in order to assess which sensitivities are important and which may actually be neglected, thus enabling future investigations of the convergence of the (multivariate) Taylor series expansion of the response in terms of parameter variations, as well as investigating the range of validity of other important quantities (e.g., response variances/covariance, skewness, kurtosis, etc.) that are derived from Taylor-expansion of the response as a function of the model’s parameters. The 4th-CASAM presented in this work provides the basis for significant future advances towards overcoming the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling.

scholarly journals TOWARDS OVERCOMING THE CURSE OF DIMENSIONALITY IN PREDICTIVE MODELLING AND UNCERTAINTY QUANTIFICATION

2021 ◽  
Vol 247 ◽  
pp. 20005
Author(s):  
Dan G. Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Predictive Modeling ◽  
Curse Of Dimensionality ◽  
Current Data ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Response Distribution ◽  
Parameter Uncertainties ◽  
Adjoint Sensitivity

This invited presentation summarizes new methodologies developed by the author for performing high-order sensitivity analysis, uncertainty quantification and predictive modeling. The presentation commences by summarizing the newly developed 3rd-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for linear systems, which overcomes the “curse of dimensionality” for sensitivity analysis and uncertainty quantification of a large variety of model responses of interest in reactor physics systems. The use of the exact expressions of the 2nd-, and 3rd-order sensitivities computed using the 3rd-ASAM is subsequently illustrated by presenting 3rd-order formulas for the first three cumulants of the response distribution, for quantifying response uncertainties (covariance, skewness) stemming from model parameter uncertainties. The use of the 1st-, 2nd-, and 3rd-order sensitivities together with the formulas for the first three cumulants of the response distribution are subsequently used in the newly developed 2nd/3rd-BERRU-PM (“Second/Third-Order Best-Estimated Results with Reduced Uncertainties Predictive Modeling”), which aims at overcoming the curse of dimensionality in predictive modeling. The 2nd/3rd-BERRU-PM uses the maximum entropy principle to eliminate the need for introducing a subjective user-defined “cost functional quantifying the discrepancies between measurements and computations.” By utilizing the 1st-, 2nd- and 3rd-order response sensitivities to combine experimental and computational information in the joint phase-space of responses and model parameters, the 2nd/3rd-BERRU-PM generalizes the current data adjustment/assimilation methodologies. Even though all of the 2nd- and 3rd-order are comprised in the mathematical framework of the 2nd/3rd-BERRU-PM formalism, the computations underlying the 2nd/3rd-BERRU-PM require the inversion of a single matrix of dimensions equal to the number of considered responses, thus overcoming the curse of dimensionality which would affect the inversion of hessian and higher-order matrices in the parameter space.

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