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Methodology for model-based uncertainty quantification of the vibrational properties of machining robots
Abstract
In order to increase the efficiency of modern, robot-based machining processes, a precise model of the robot’s vibrational properties is essential. In particular, a reliable estimation of the robot’s eigenfrequencies is crucial to estimate stable process parameters. However, the prediction of the eigenfrequencies is often imprecise, since the model relies on joint compliance parameters, whose identification process itself is prone to errors. The following paper addresses this issue by quantifying the uncertainty of the eigenfrequency prediction based on a novel, probabilistic compliance identification and a subsequent Monte Carlo uncertainty propagation. The uncertainty quantification is completed by a sensitivity analysis.
... Several studies achieved vibration suppression using mechanical modeling given specific vibration properties [11] [12] [17]. The others [13][18]- [24] proposed methods for identifying the vibration properties in mechanical models either through the use of sensors or by experimental exploration using an optimization algorithm. However, as described earlier, an accurate estimation of the vibrational behavior of soft robotic hands is challenging because of the low reproducibility of motion, which limits their adoption in soft robotic hand systems. ...
... This study develops a parameter-tuning method based on the Bayesian optimization algorithm [25]- [29], which is noted for its efficiency in parameter search among various optimization methods. As shown in Table II, various other optimization methods can achieve optimization with a small number of search trials, Table II PSO-based method* [22] ✔Not required SHA-based method* [23] ✔Not required BO-based method* [24] ✔Not required Using mechanical model Mechanical model-based [11][12] [17] ✘Required (assumed to be given) -Using high speed camera [14]- [16] ✘Required (obtained by sensors) Using internal sensors [13] [18] SSA-based method* [19] ✘Required (identified by searching) PSO-based method* [20] BO-based method* [21] Hardware-based method Installing additional structures or mechanisms [7]- [10] ✘Required -* PSO, SHA, BO, and SSA refer to particle swarm optimization, S. Lin's heuristic algorithm, Bayesian optimization, and sparrow search algorithm, respectively. ...
This study proposes a novel motion optimization method for a manipulator equipped with a soft robotic hand for object transportation. The flexibility of the soft robotic hand induces large vibrations. The manipulator must pause until the vibration converges, leading to an increase in the cycle time. The robotic system also has issue with the low motion repeatability in the robotic hand, even under identical operational conditions. In this study, a method based on Bayesian algorithms is developed to optimize the motion of a manipulator. The objective is to minimize the cycle time for object transportation tasks, while considering the challenges of vibration and low repeatability in soft robotic hand systems. The optimization is performed through an exploratory search using actual experiments. To achieve a low-cost and versatile measurement system, this study proposes a method for deriving the cycle time, which is a key metric for optimization, based on the measurement results obtained using a web camera with standard specifications. The proposed optimization method is evaluated through a comparison with existing optimization methods, including the grid-search-based, conventional Bayesian optimization, particle swarm optimization, S. Lin’s heuristic algorithm, and sparrow search algorithm. The proposed method achieves optimization results comparable in accuracy to those obtained using the grid-search-based optimization method, whereas requires 95% fewer searches. Furthermore, it provides more stable optimization results than those obtained using the conventional Bayesian optimization method.
... Occasionally, publications on robot vibrations present resonance curves that show the dependence of the resonance frequencies on the position of the robot arm [31,32]. They are prepared on the basis of modal experiments in which the vibration is excited by an impact hammer pulse. ...
... The tests were carried out in one of the robot positions shown in Figure 6, for β 2 = −120 deg. The excitation described by Equation (32) was used, where the excitation frequency was variable in the range 26-46 Hz in order to excite resonant vibrations in the robot in the two expected resonance zones. The characteristics obtained are shown in Figure 9. ...
This paper deals with the analysis of nonlinear vibration phenomena in the arm system of an industrial robot. The presented mathematical model of the robot takes into account the flexibility of the joints, which results in low-frequency vibrations in the arm. The study of vibration phenomena has been carried out using analytical, numerical and experimental methods. Special attention has been paid to bifurcation phenomena. The influence of two bifurcation parameters on the behaviour of the robot arm was studied. It was shown that the amplitude and frequency of the harmonic excitation create a nonlinear effect on the vibration amplitudes of the links. In bifurcation regions, the vibration amplitudes can even differ several times depending on the direction of changes in the bifurcation parameter. In general, the results indicate that, contrary to common practice, it is worth paying attention to nonlinear phenomena when analysing robot vibrations.
... Modeling complex dynamic systems are inseparable from UQ due to their complexity and sensitivity to uncertainty. Dynamic systems are widely used in diverse engineering applications, such as automotive design, aerospace, and structural engineering, covering topics like dynamical response predictions, dynamical durability, and unwanted vibration mitigation [10][11][12]. Traditional modeling approaches, including analytical and numerical techniques, have been employed to capture dynamic behaviors. While analytical methods provide insights into fundamental physics, they struggle to handle complex geometries and nonlinearities. ...
Uncertainty quantification (UQ) is critical for modeling complex dynamic systems, ensuring robustness and interpretability. This study extends Physics-Guided Bayesian Neural Networks (PG-BNNs) to enhance model robustness by integrating physical laws into Bayesian frameworks. Unlike Artificial Neural Networks (ANNs), which provide deterministic predictions, and Bayesian Neural Networks (BNNs), which handle uncertainty probabilistically but struggle with generalization under sparse and noisy data, PG-BNNs incorporate the laws of physics, such as governing equations and boundary conditions, to enforce physical consistency. This physics-guided approach improves generalization across different noise levels while reducing data dependency. The effectiveness of PG-BNNs is validated through a one-degree-of-freedom vibration system with multiple noise levels, serving as a representative case study to compare the performance of Monte Carlo (MC) dropout ANNs, BNNs, and PG-BNNs across interpolation and extrapolation domains. Model accuracy is assessed using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAE), and Coefficient of Variation of Root Mean Square Error (CVRMSE), while UQ is evaluated through 95% Credible Intervals (CIs), Mean Prediction Interval Width (MPIW), the Quality of Confidence Intervals (QCI), and Coverage Width-based Criterion (CWC). Results demonstrate that PG-BNNs can achieve high accuracy and good adherence to physical laws simultaneously, compared to MC dropout ANNs and BNNs, which confirms the potential of PG-BNNs in engineering applications related to dynamic systems.
... Furthermore, the team's previous work on VRPF has been cited positively by academic peers in terms of the advantages of joint motion assurance [25], posture simultaneously optimization [22,[26][27][28], and milling quality improvement [15]. Along with the increasing demands in milling process on significant metallic parts including large size windy turbine blades, warship propellers, and aerospace cabins, there exist time-varying conditions in the various batches, complicated material properties and uncertain operating environment [29], which motivates our team to further explore the availability in the mentioned challenges. ...
... Tunc and Gonul [24] investigated the stability of robot milling operations, concluding that the vibration response of industrial robots under quasi-static motion conditions differs from that of static conditions, which in turn affects the stability limits at low-frequency chatter conditions. Finally, Busch et al. [25] attempted to quantify the uncertainties imported to the natural frequencies' prediction from the joint parameters used in the machining robot model. ...
The use of industrial robots for machining operations is pursued by industry lately, since they can increase the flexibility of the production system and reduce production costs. However, their industrial adoption is still limited, mainly due to their insufficient structural stiffness and posture-dependent dynamic behavior, leading to limited machining process accuracy. For this purpose, the Digital-Model of a machining robot has been developed, providing a tool for virtual commissioning of the process that can be used during the process planning stage. The Multi-Body Simulation method combined with a Component Mode Synthesis have been adopted, considering flexibility of both the joints and links. On top of that, and motivated from robotic-based machining systems’ flexibility and versatility, two optimization algorithms have been developed, attempting to increase the process accuracy. A workpiece placement optimization algorithm, attempting to maximize the robot stiffness during the process acquiring knowledge from the robot stiffness maps, and a feed-rate scheduling algorithm, attempting to constrain the contour error by regulating the generated cutting forces. The capabilities and functionality of the developed model and optimization algorithms are showcased in two different case studies, with the results proving the improvements on the process accuracy after the application of the optimization algorithms. Finally, an experimental validation of the Digital-Model has been performed, to confirm the consistency between model outputs and real experimental data.
... The second category is force-related, such as joint flexibility [36] and dynamics model misalignment. These sources not only lead to pose errors in robots, but also give rise to uncertainty in the pose errors because these sources usually exhibit nonlinear or spatially dependent properties [37], making it difficult to model and control them accurately. Therefore, when studying robot pose errors, it is essential to quantify the uncertainty of the prediction results in the form of prediction intervals that provide a reasonable range of point predictions for subsequent compensation. ...
Due to their inherent characteristics, robots inevitably suffer from pose errors, and accurate prediction is the key to error compensation, which facilitates the application of robots in high-precision scenarios. Existing studies almost follow the points-view, and the compensation effect depends entirely on the accuracy of the point prediction, which leads to overconfident prediction results. In order to quantify the pose errors uncertainty and achieve more accurate prediction, a method to quantify of uncertainty in robot pose errors and calibration of reliable compensation values is proposed in this paper. In the proposed method, a distribution-free joint prediction model is designed to realize the simultaneous prediction of points and uncertainty intervals. Based on this, the reliable compensation value calibration strategy is innovatively proposed. The proposed method is verified on five tasks including spatial motions, constant load and milling processing, showing accurate joint prediction capability and reliable accuracy improvement. In addition, through online compensation experiments, the pose errors are reduced by 90 %, which promotes the application of robots in higher-precision scenarios.
... From a different perspective, to gauge the model's confidence level in its decisions, ref. [16] employed Bayesian models, particularly for monitoring machine signals in anomalous or unpredictable domains where misdiagnosis might occur in the absence of discernible symptoms. In their efforts to comprehensively model a robot's vibrational attributes, ref. [17] endeavored to quantify the uncertainty linked with eigenfrequency prediction, leveraging the precision of Monte Carlo uncertainty propagation. ...
Condition monitoring (CM) is essential for maintaining operational reliability and safety in complex machinery, particularly in robotic systems. Despite the potential of deep learning (DL) in CM, its ‘black box’ nature restricts its broader adoption, especially in mission-critical applications. Addressing this challenge, our research introduces a robust, four-phase framework explicitly designed for DL-based CM in robotic systems. (1) Feature extraction utilizes advanced Fourier and wavelet transformations to enhance both the model’s accuracy and explainability. (2) Fault diagnosis employs a specialized Convolutional Long Short-Term Memory (CLSTM) model, trained on the features to classify signals effectively. (3) Model refinement uses SHAP (SHapley Additive exPlanation) values for pruning nonessential features, thereby simplifying the model and reducing data dimensionality. (4) CM interpretation develops a system offering insightful explanations of the model’s decision-making process for operators. This framework is rigorously evaluated against five existing fault diagnosis architectures, utilizing two distinct datasets: one involving torque measurements from a robotic arm for safety assessment and another capturing vibration signals from an electric motor with multiple fault types. The results affirm our framework’s superior optimization, reduced training and inference times, and effectiveness in transparently visualizing fault patterns.
... The studies in Ref [2,8] presented an experimental modal analysis for an ABB manipulator. The study in Ref [9] extends the frequency determination problem to include an uncertainty analysis of the determination of resonance zones. The study in Ref [10] allows the determination of modal parameters of robots under static conditions. ...
Vibration analysis of industrial robots is one of the key issues in the context of robotisation of machining processes. Low-frequency vibrations result from flexibility in manipulator joints. Within the scope of the article, a model of a two-link robot manipulator was built. Dynamic equations of motion were formulated to study the influence of the robot arm configuration on vibration effects. Based on numerical simulations, the frequency spectrum of vibrations of the robot’s links was determined, and tests were carried out in a number of configurations, obtaining a map of resonant frequencies depending on the configuration of the manipulator. Experimental studies were then carried out, which confirmed the conclusions from the simulation studies. The results obtained confirm that the positioning of the manipulator’s links has a significant effect on vibration effects. Tests conducted using a vision system with a motion amplification application made it easier to interpret the results. The formulated mathematical model of the manipulator generates results that coincide with the results of experimental studies.
... Among these optimisation methods, the PSO algorithm has the best effect. In addition, in the fields of damage detection [4] , vibration characteristic analysis [5] and groundwater pollution source identification [6][7] , a Bayesian method is often used to study model parameter estimation. The application of this method to valve-controlled cylinder systems has yet to be reported. ...
The accurate estimation of parameters is the premise for establishing a high-fidelity simulation model of a valve-controlled cylinder system. Although bench test data are convenient to obtain in model parameter estimation, there is a need for the load data to conform to the actual working conditions. Although the operating data include the actual load information, it is not easy to collect the control valve operating data. This paper proposes a model parameter estimation method based on bench test and operating data fusion to solve the above problems. The proposed method is based on Bayesian theory, and its core is a pool fusion of prior information from bench test and operating data. First, a system model is established, and the parameters in the model are analysed. Then, the bench test and operating data of the system are collected, and the model parameters and weight coefficients are estimated using the data fusion method. Finally, the estimated effects of the data fusion method, Bayesian method, and PSO algorithm on system model parameters are compared. The research shows that the parameter estimation result based on the data fusion method is accurate. The weight coefficient represents the contribution of different prior information to the parameter estimation result. The effect of parameter estimation based on the data fusion method is better than that of the Bayesian method and the PSO algorithm. The more complex the load is, the worse the model's accuracy, which verifies the influence of the load on the valve-controlled cylinder system model and proves that the data fusion method plays an essential role in parameter estimation studies.
... However, the parameter identification process for the model parameters in M(q), K and C remains an open issue, because conventional parameter identification procedures often result in physically infeasible parameters and, thus, should only be treated as fitting parameters [9]. Based on the popular approach of Dumas et al. [12], Busch et al. [13] presented a methodology to infer physically feasible compliance parameters using a Bayesian regression approach. Additionally, Huynh et al. [9] proposed a methodology to estimate the model's mass and inertia properties. ...
Robotic machining is a promising technology for post-processing large additively manufactured parts. However, the applicability and efficiency of robot-based machining processes are restricted by dynamic instabilities (e.g., due to external excitation or regenerative chatter). To prevent such instabilities, the pose-dependent structural dynamics of the robot must be accurately modeled. To do so, a novel data-driven information fusion approach is proposed: the spatial behavior of the robot’s modal parameters is modeled in a horizontal plane using probabilistic machine learning techniques. A probabilistic formulation allows an estimation of the model uncertainties as well, which increases the model reliability and robustness. To increase the predictive performance, an information fusion scheme is leveraged: information from a rigid body model of the fundamental behavior of the robot’s structural dynamics is fused with a limited number of estimated modal properties from experimental modal analysis. The results indicate that such an approach enables a user-friendly and efficient modeling method and provides reliable predictions of the directional robot dynamics within a large modeling domain.
Because robotic milling has become an important means for machining significant large parts, obtaining the structural frequency response function (FRF) of a milling robot is an important basis for machining process optimization. However, because of its articulated serial structure, a milling robot has an enormous number of operating postures, and its dynamics are affected by the motion state. To accurately obtain the FRF in the operating state of a milling robot, this paper proposes a method based on the structural modification concept. Unlike the traditional excitation method, the proposed method uses robot joint motion excitation instead of hammering excitation to realize automation. To address the problem of the lack of information brought by motion excitation, which leads to inaccurate FRF amplitudes, this paper derives the milling robot regularization theory based on the sensitivity of structural modification, establishes the modal regularization factor, and calibrates the FRF amplitude. Compared to the commonly used manual hammering experiments, the proposed method has high accuracy and reliability when the milling robot is in different postures. Because the measurement can be performed directly and automatically in the operation state, and the problem of inaccurate amplitudes is solved, the proposed method provides a basis for optimizing the machining posture of a milling robot and improving machining efficiency.
Conventional industrial robots are increasingly used for milling applications of large workpieces due to their workspace and their low investment costs in comparison to conventional machine tools. However, static deflections and dynamic instabilities during the milling process limit the efficiency and productivity of such robot-based milling systems. Since the pose-dependent dynamic properties of the industrial robot structures are notoriously difficult to model analytically, machine learning methods are recently gaining more and more popularity to derive system models from experimental data. In this publication, a modeling concept based on a modern information fusion scheme, fusing simulation and experimental data, is proposed. This approach provides a precise model of the robot’s pose-dependent structural dynamics and is validated for a one-dimensional variation of the robot pose. The results of two information fusion algorithms are compared with a conventional, data-driven approach and indicate a superior model accuracy regarding interpolation and extrapolation of the pose-dependent dynamics. The proposed approach enables decreasing the necessary amount of experimental data needed to assess the vibrational properties of the robot for a desired pose. Additionally, the concept is able to predict the robot dynamics at poses where experimental data is very costly to gather.
Industrial robots used in manufacturing processes such as drilling of aerospace structures undergo many rapid positioning motions during each operation. Such aggressive motions excite the structural modes of the robot and cause inertial vibrations at the end-effector, which may damage the part and violate the tolerance requirements. This article presents a vibration avoidance technique based on input shaping combined with a learning-based structural dynamic model. A theoretical dynamic model is first developed for commonly used robotic arms considering the flexibilities of the first three joints of the robot. An artificial neural network is developed and used in conjunction with the dynamic model to predict the natural frequency of the system at any pose in the workspace. Transfer learning techniques are used to extend the trained artificial neural network to account for the mass of the payload with minimal data collection. To reduce the residual vibrations of the robot in rapid motions, zero-vibration derivative shapers are designed and implemented. The effectiveness of the presented methodology has been validated experimentally on a Staubli RX90CR robot with an open-architecture control system developed fully in-house. Experimental results show more than 85% reduction in residual vibrations during aggressive motions of the robot.
Using industrial robots as machine tools is targeted by many industries for their lower cost and larger workspace. Nevertheless, performance of industrial robots is limited due to their mechanical structure involving rotational joints with a lower stiffness. As a consequence, vibration instabilities, known as chatter, are more likely to appear in industrial robots than in conventional machine tools. Commonly, chatter is avoided by using stability lobe diagrams to determine the stable combinations of axial depth of cut and spindle speed. Although the computation of stability lobes in conventional machine tools is a well-studied subject, developing them in ro-botic milling is challenging because of the lack of accurate multi-body dynamics models involving joint compliance able of predicting the posture-dependent dynamics of the robot. In this paper, two multi-body dynamics models of articulated industrial robots suitable for machining applications are presented. The link and rotor inertias along with the joint stiffness and damping parameters of the developed models are identified using a combination of multiple-input multiple-output identification approach, computer-aided design model of the robot, and experimental modal analysis. The performance of the developed models in predicting posture-dependent dynamics of a KUKA KR90 R3100 robotic arm is studied experimentally.
Serial industrial robots tend to have low static stiffness and possess configuration dependent dynamics. The former results in an earlier onset of chatter compared to machine tools whereas the latter introduces robot configuration dependency into the process stability. In this paper, the robot configuration is continuously varied around its functional redundancy to create time varying system dynamics to suppress and/or avoid chatter in a robotic milling operation. It was shown that, at low spindle speeds it is possible to suppress chatter even though the quasi-static stability predictions may indicate instability at different robot configurations for the chosen process parameters.
We present a global sensitivity analysis that quantifies the impact of parameter uncertainty on model outcomes. Specifically, we propose variance-decomposition-based Sobol' indices to establish an importance ranking of parameters and univariate effects to determine the direction of their impact. We employ the state-of-the-art approach of constructing a polynomial chaos expansion of the model, from which Sobol' indices and univariate effects are then obtained analytically, using only a limited number of model evaluations. We apply this analysis to several quantities of interest of a standard real-business-cycle model and compare it to traditional local sensitivity analysis approaches. The results show that local sensitivity analysis can be very misleading, whereas the proposed method accurately and efficiently ranks all parameters according to importance, identifying interactions and nonlinearities.
For the past three decades, robotic machining has attracted a large amount of research interest owning to the benefit of cost efficiency, high flexibility and multi-functionality of industrial robot. Covering articles published on the subjects of robotic machining in the past 30 years or so; this paper aims to provide an up-to-date review of robotic machining research works, a critical analysis of publications that publish the research works, and an understanding of the future directions in the field. The research works are organised into two operation categories, low material removal rate (MRR) and high MRR, according their machining properties, and the research topics are reviewed and highlighted separately. Then, a set of statistical analysis is carried out in terms of published years and countries. Towards an applicable robotic machining, the future trends and key research points are identified at the end of this paper.
During last few decades, industrial robots have been widely used in various applications to develop flexible and efficient manufacturing process such as material handling and welding. However, as a high value-added application, few robotic machining systems have been installed mainly due to the limitation from chatter, which leads to poor product quality and low productivity. Although researchers have been continuously investigating the robotic machining chatter, there is still a lack of understanding due to the complexity of the issue. This paper provides a comprehensive review on chatter related issues during robotic machining tasks, including mechanisms, mitigation strategies and identification methods regarding both regenerative chatter and mode coupling chatter. Due to the low stiffness and couple structure of industrial robots, both regenerate and mode coupling chatter can occur at different cutting conditions. The difference between two chatter mechanism in robotic machining process are compared and a list of guidelines is provided to help distinguish these two types of chatter. Systemic analysis of the mechanisms of chatter identification and suppression is presented providing a research basis for future studies.
Industrial robot provides an optimistic alternative of traditional CNC machine tool due to its advantages of large workspace, low cost and great flexibility. However, the low posture-dependent stiffness deteriorates the machining accuracy in robotic milling tasks. To increase the stiffness, this paper introduces a pose optimization method for the milling robot when converting a five-axis CNC tool path to a commercial six-axis industrial robot trajectory, taking advantage of a redundant degree of freedom. First, considering the displacements of at least three points on the end effector of the robot, a new frame-invariant performance index is proposed to evaluate the stiffness of the robot at a certain posture. Then, by maximizing this index, a one-dimensional posture optimization problem is formulated in consideration of the constraints of joint limits, singularity avoidance and trajectory smoothness. The problem is solved by a simple discretization search algorithm. Finally, the performance index and the robot trajectory optimization algorithm are validated by simulations and experiments on an industrial robot, showing that the machining accuracy can be efficiently improved by the proposed method.
Automated vehicles will increasingly influence our mobility behaviour in near
future. In far future automated vehicles will become a mobility standard in our
lives. When looking at “how to make future automated vehicles safe”, the topic
of trajectory planning plays a key role. How can safe trajectories be found for
autonomous vehicles? Motion planning for automated vehicles moving in usual
traffic situations in general requires decision making based on incomplete and
uncertain knowledge of the situation. The importance of trajectory planning is
most evident for situations with high potential of harming vulnerable road
users. What happens if some assumptions for planning are uncertain? Reactive
re-planning isn't always adequate. It might be cost intensive and
unsecure/unsafe? This article proposes to use methods for uncertainty
quantification in motion planning considering the fact that the environment
cannot be modelled perfectly and predictions are to some degree uncertain.
Especially for situations that include pedestrian movements, there is a lack of
knowledge and evidence (e.g. future intention of the target direction) which
might be critical for safety with standard motion planning strategies taken from
robotics. The presented approach shows how Monte-Carlo Sampling can
efficiently be used for motion planning to get robust trajectories. Finally an
outlook is given for further applications with uncertainty quantification.
SALib contains Python implementations of commonly used global sensitivity analysis
methods, including Sobol (Sobol’ 2001, Andrea Saltelli (2002), Andrea Saltelli et al.
(2010)), Morris (Morris 1991, Campolongo, Cariboni, and Saltelli (2007)), FAST (Cukier
et al. 1973, A. Saltelli, Tarantola, and Chan (1999)), Delta Moment-Independent Measure
(E. Borgonovo 2007, Plischke, Borgonovo, and Smith (2013)) Derivative-based Global
Sensitivity Measure (DGSM) (Sobol’ and Kucherenko 2009) , and Fractional Factorial
Sensitivity Analysis (Andrea Saltelli et al. 2008) methods. SALib is useful in simulation,
optimisation and systems modelling to calculate the influence of model inputs or
exogenous factors on outputs of interest.
SALib exposes a range of global sensitivity analysis techniques to the scientist, researcher
and modeller, making it very easy to easily implement the range of techniques into typical
modelling workflows.
The library facilitates the generation of samples associated with a model’s inputs, and
then provides functions to analyse the outputs from a model and visualise those results.
Probabilistic Programming allows for automatic Bayesian inference on user-defined probabilistic models. Recent advances in Markov chain Monte Carlo (MCMC) sampling allow inference on increasingly complex models. This class of MCMC, known as Hamliltonian Monte Carlo, requires gradient information which is often not readily available. PyMC3 is a new open source Probabilistic Programming framework written in Python that uses Theano to compute gradients via automatic differentiation as well as compile probabilistic programs on-the-fly to C for increased speed. Contrary to other Probabilistic Programming languages, PyMC3 allows model specification directly in Python code. The lack of a domain specific language allows for great flexibility and direct interaction with the model. This paper is a tutorial-style introduction to this software package.
Probabilistic Programming allows for automatic Bayesian inference on user-defined probabilistic models. Recent advances in Markov chain Monte Carlo (MCMC) sampling allow inference on increasingly complex models. This class of MCMC, known as Hamliltonian Monte Carlo, requires gradient information which is often not readily available. PyMC3 is a new open source Probabilistic Programming framework written in Python that uses Theano to compute gradients via automatic differentiation as well as compile probabilistic programs on-the-fly to C for increased speed. Contrary to other Probabilistic Programming languages, PyMC3 allows model specification directly in Python code. The lack of a domain specific language allows for great flexibility and direct interaction with the model. This paper is a tutorial-style introduction to this software package.
In our research we use rigid-body dynamics and optimal control methods to generate 3-D whole-body walking motions. For the dynamics modeling and computation we created RBDL—the Rigid Body Dynamics Library. It is a self-contained free open-source software package that implements state of the art dynamics algorithms including external contacts and collision impacts. It is based on Featherstone’s spatial algebra notation and is implemented in C++ using highly efficient data structures that exploit sparsities in the spatial operators. The library contains various helper methods to compute quantities, such as point velocities, accelerations, Jacobians, angular and linear momentum and others. A concise programming interface and minimal dependencies makes it suitable for integration into existing frameworks. We demonstrate its performance by comparing it with state of the art dynamics libraries both based on recursive evaluations and symbolic code generation.
Nowadays industrial robots are an appropriate technology for developing flexible and reconfigurable manufacturing systems which contribute to perform automatically operation such as milling, cutting, drilling, grinding, deburring and polishing. Machining robots symbolize a cost-saving and flexible alternative compared to conventional CNC machines which are the restricted working area and produced shape limitations. The improvement of individual elements and development of new devices has caused a perception change about the use of industrial robots to perform machining operations. The approach to this research was to analyze technical barriers of individual components that it was broken-down as well as full improving the system. This document is intended to provide technical constraints, current technology and future potential researches about robotic machining.
In this article, a novel method for characterizing the exact solution for interval linear systems is presented. In the proposed method, the entries of the interval coefficient matrix and interval right-hand side vector are formulated as linear functions of two or three parameters. The parameter groups for two- and three-parameter cases are identified. The exact solution is characterized using the solution sets corresponding to the parameter groups. The parametric method is then employed in the motion analysis of planar manipulators considering the uncertainty in kinematic parameters. Example manipulators are used to show the implementation of the method and the effect of uncertainty in the motion performance.
Early studies on robot machining were reported in the 1990s. Even though there are continuous worldwide researches on robot machining ever since, the potential of robot applications in machining has yet to be realized. In this paper, the authors will first look into recent development of robot machining. Such development can be roughly categorized into researches on robot machining system development, robot machining path planning, vibration/chatter analysis including path tracking and compensation, dynamic, or stiffness modeling. These researches will obviously improve the accuracy and efficiency of robot machining and provide useful references for developing robot machining systems for tasks once thought to only be capable by CNC machines. In order to advance the technology of robot machining to the next level so that more practical and competitive systems could be developed, the authors suggest that future researches on robot machining should also focus on robot machining efficiency analysis, stiffness map-based path planning, robotic arm link optimization, planning, and scheduling for a line of machining robots.
The scope of applications for industrial robots is limited in cases with strong forces at the end effector and high positioning and path accuracies required. Thus, their use in machining applications as a cost-saving, flexible alternative for machining tools is restricted due to mechanical compliance. A model-based off-line concept is presented to analyze, predict, and compensate the resulting path deviation of the robot under process force in milling applications. For this purpose a rigid multi-body dynamics model of the robot extended with additional joint elasticities and tilting effects is coupled with a material removal simulation providing the process forces. After systematically adjusting model parameters, an efficient simulation-based path correction strategy shows significant improvements of path accuracy. The general framework is ap- plicable to any tree structured robots and allows for sensitivity analysis with respect to arbitrary model parameters. I. MOTIVATION Major fields of machining applications for industrial robots are automated pre-machining, deburring and fettling of cast parts or trimming of carbon fiber reinforced laminate. Due to a kinematic structure with usually six axes industrial robots can cover a large working space and are able to reach difficult work piece positions, so that they can be applied to perform complex machining operations. Therefore, compared to stan- dard machine tools, industrial robots on the one hand offer an economic machining while they do only reach a limited absolute and repeat accuracy on the other hand; e.g. the repeat accuracy of the industrial robot used for the research presented in this paper is 0:06 mm (11).
Although robots tend to be as competitive as CNC machines for some operations, they are not yet widely used for machining operations. This may be due to the lack of certain technical information that is required for satisfactory machining operation. For instance, it is very difficult to get information about the stiffness of industrial robots from robot manufacturers. As a consequence, this paper introduces a robust and fast procedure that can be used to identify the joint stiffness values of any six-revolute serial robot. This procedure aims to evaluate joint stiffness values considering both translational and rotational displacements of the robot end-effector for a given applied wrench (force and torque). In this paper, the links of the robot are assumed to be much stiffer than its actuated joints. The robustness of the identification method and the sensitivity of the results to measurement errors and the number of experimental tests are also analyzed. Finally, the actual Cartesian stiffness matrix of the robot is obtained from the joint stiffness values and can be used for motion planning and to optimize machining operations.
For robots of increasing complexity such as hu- manoid robots, conventional identification of rigid body dynamics models based on CAD data and actuator models becomes difficult and inaccurate due to the large number of additional nonlinear effects in these systems, e.g., stemming from stiff wires, hydraulic hoses, protective shells, skin, etc. Data driven parameter estimation offers an alternative model identification method, but it is often burdened by various other problems, such as significant noise in all measured or inferred variables of the robot. The danger of physically inconsistent results also exists due to unmodeled nonlinearities or insufficiently rich data. In this paper, we address all these problems by developing a Bayesian parameter identification method that can automatically detect noise in both input and output data for the regression algorithm that performs system identification. A post-processing step ensures physically consistent rigid body parameters by nonlinearly projecting the result of the Bayesian estimation onto constraints given by positive definite inertia matrices and the parallel axis theorem. We demonstrate on synthetic and actual robot data that our technique performs parameter identification with 5 to 20% higher accuracy than traditional methods. Due to the resulting physically consistent parameters, our algorithm enables us to apply advanced control methods that algebraically require physical consistency on robotic platforms.
Stiffness of the robot manipulator plays a crucial role in improving welding accuracy. Due to the relatively low stiffness, the robot can hardly achieve the specified accuracy under the loading condition. Hence, identifying the joint stiffness and compensating the displacement in Cartesian space is an intuitive work to do in welding industry. Although substantial works had been done on stiffness modeling and identification, the uncertainties existed in transmission and manufacturing were neglected which may affect the manipulator's stiffness and accuracy to a certain extent, in practice. In this paper, we propose an uncertain approach to identify the stiffness of a welding manipulator KUKA-KR16. Firstly, the uncertainties of the D-H parameters are considered and simulated by Monte-Carlo method. Then, the Cartesian stiffness is identified through an experiment which is composed of API laser tracker and a cable pulley system with deadweights. Finally, combining the previous enhanced stiffness model, we obtain the distribution of the joint stiffness, based on which the compensation results are proved to be effective in Cartesian space.
This paper presents a new methodology for joint stiffness identification of serial robots. This methodology aims at evaluating all joint stiffness values responsible for both translational and rotational displacements of the robot end-effector subject to an external wrench (force and torque). The links of the robot are supposed to be quite stiffer than the joints and not known as it is usually the case with industrial serial robots. The robustness of the identification method and the sensitivity of the results to measurement errors and number of experimental tests are also analyzed. The Kuka KR240-2 robot is used as an illustrative example through the paper.
Despite widespread industrial applicatzon of harmonic drives, the source of some elastokinetic phenomena and their impact on overall system behavior has not been fully addressed thus far. Some of these phenomena severely influence the behavior of robot arms, both in free and constrained motions, when the end effector is in contact with an environment. The primary goal of this study is to derive an effective, control-oriented model of a harmonic-drive-based robot joint. Systematic observations of an experimental robot with harmonic drives has revealed that the harmonic drive could not entirely transmit the input torque to the output shaft, due to a nonlinear meshing process between the flexible and circular spline teeth. The torque transmitted to the output shaft might saturate at a much lower value than expected (e.g., motor torque multiplied by the gear ratio). This phenomenon may severely influence the system behavior, par ticularly in force/impedance control tasks when full joint-torque capacity and wide bandwidth are needed. To understand the harmonic-drive behavior, as well as to derive a convenient form of its model, we have shown restrained motion experi ments to be much more useful than free-motion experiments.
In this article, we also introduce mathematical models and describe experiments related to other physical phenomena, such as nonlinear stiffness, hysteresis, and soft windup. The goal of our modeling strategy was not to develop a precise and possi bly complicated model, but to generate an appropriate model that could be easily used by control engineers to improve joint behavior To visualize the developed model, equivalent mechan ical and electrical schemes of the joint are introduced. Finally, a simple and reliable estimation procedure has been established for obtaining joint parameters, to ascertain the integrity of the proposed model.
Industrial robots, used for milling processes, have to execute highly dynamic and accurate movements. External static and dynamic process forces lead to static deflections and dynamic excitations. In this paper, we present a coupled offline simulation and planning strategy of the machine-process interaction with online adaptation mechanisms for increased system robustness. The process planning, optimization and milling force prediction are executed offline, while the online compensation and adaptation accounts for static deflections and unmodeled disturbances. The benefits of the combined offline and online approach are demonstrated by stabilizing machining processes and accurate deflection compensation with unmodeled changes in spindle speed and feed rate for the machining of aluminum workpieces.
This paper presents a Gaussian Process Regression (GPR) based approach to model the dynamic properties of a six degree-of-freedom (6-dof) industrial robot within its workspace. Discretely sampled modal parameters (modal frequency, modal stiffness, modal damping coefficient) of the robot structure determined through experimental modal analysis are used to develop the GPR model, which is then evaluated for its ability to accurately predict the modal parameters at different points in the workspace. The validation results show that the model captures the significant trends in the modal parameters within the sampling space but exhibits greater errors in regions further from the robot base. The results of the GPR model are also compared with those derived from an analytical model of the robot tool tip dynamics. The analytical model is found to overestimate the robot's stiffness, especially in extended arm configurations, and to underestimate the natural frequency. The average peak-to-valley vibrations predicted by the GPR model during robotic end milling are compared with experimental results. The model-predicted peak-to-valley vibrations follow the measured values with a maximum error of 0.028 mm in the wall and floor surface directions. The results show that the GPR model presented in this paper can serve as a useful tool for understanding and optimizing the tool tip vibrations produced in robotic milling.
Industrial robots are desired to be used in milling light but large aerospace parts due to easier set-up and portability than large machine tools. However, robots are significantly less stiff than the machine tools, hence they cannot be used in all machining applications. This paper presents dynamics of robotic milling. The structural dynamics of an articulated manipulator with a spindle and a tool are modeled. The dynamic milling forces are applied on the robot structure which has strong cross coupling terms. The stability of the resulting system is analyzed using semi-discrete time and frequency domain methods. The predicted stability charts are experimentally validated in milling of Aluminum and Titanium parts. It is shown that the pose-dependent modes of the robot structure are all at low frequencies, and they are damped out by the machining process at high spindle speeds. Only the pose independent spindle modes cause chatter in high-speed milling, hence high material removal rates can be achieved by selecting analytically predicted stable depth of cuts and spindle speeds in robotic milling of Aluminum parts. In low speed milling of Titanium parts however, the pose dependent low frequency robot modes chatter.
Using robots for machining, implies many advantages. By using the flexibility robots have to offer, workcells with high application versatility can be provided. Nevertheless, there are several challenges to overcome. This paper gives an overview about challenges robotic machining has already met. Besides these challenges, robot-machining still has to encounter obstacles resulting from the fact that robots have been solely handling devices so far. Furthermore, trends in robotic market are outlined by giving particular examples, emphasizing the willingness of industrial robot companies to provide robot-based machining systems.
When calculating the dynamic properties of machine tools by means of the finite-element-analysis, highly correlated component models are needed for the derivation of an accurate model of the assembled machine tool structure. For casted machine tool components this cannot always be ensured due to the significant geometric and material uncertainties inherent in the casting process. In this paper, a stepwise modelling approach for casted machine tool components is proposed that allows the derivation of highly correlated models in a defined frequency range. Based on the assumption of superposition the uncertainties and errors involved in the modelling process are identified and evaluated by means of strain energy considerations. By applying this approach to a casted machine tool column, the initial frequency deviations for the considered first 15 structural modes of up to 15 % from the measured values could be reduced below 3 %. Also deeper insight was gained about the influence of the considered uncertainties and errors on the model correlation, as the deviations could be assigned to their sources.
Currently, the results of a robot calibration procedure are expressed generally in terms of the position and orientation error for a set of locations and orientations, which have been obtained from the previously identified kinematic parameters. In this work, a technique is presented to evaluate the calibration uncertainty for a robot arm calibrated using the circle point analysis method. The method developed is based on the probability distribution propagation calculation recommended by the Guide to the Expression of Uncertainty of Measurement and on the Monte Carlo method. This method makes it possible to calculate the uncertainty in the identification of each single robot parameter, and thus, to estimate the robot positioning uncertainty due to the calibration uncertainty, rather than based on a single set locations and orientations that are previously defined for a unique set of identified parameters. Additionally, this technique allows for the establishment of the best possible conditions for the data capture test, which identifies parameters and determines which of them have the least possible calibration uncertainty. This determination is based on the variables involved in the data capture process by propagating their influence up to the final robot accuracy.
Industrial robots represent a promising, cost-saving and flexible alternative for machining applications. Due to the kinematics
of a vertical articulated robot the system behavior is quite different compared to a conventional machine tool. The robot’s
stiffness is not only much smaller but also position dependent in a non-linear way. This article describes the modeling of
the robot structure and the identification of its parameters with focus on the analysis of the system’s stiffness. Therefore
a method for the calculation of the Cartesian stiffness based on the polar stiffness and the use of the Jacobian matrix is
introduced. Furthermore, so called virtual joints are used. With this method it is possible to model each joint of the robot
with three degrees of freedom. Beside the gear stiffness the method allows the consideration of the tilting rigidity of the
bearing and the link deformations to improve the model accuracy. Based on the results of the parameter identification and
the calculation of the Cartesian stiffness the experimental model validation is done.
This paper presents a novel approach to the modeling and identification of elastic robot joints with hysteresis and backlash. The model captures the dynamic behavior of a rigid robotic manipulator with elastic joints. The model includes electromechanical submodels of the motor and gear from which the relationship between the applied torque and the joint torsion is identified. The friction behavior in both presliding and sliding regimes is captured by generalized Maxwell-slip model. The hysteresis is described by a Preisach operator. The distributed model parameters are identified from experimental data obtained from internal system signals and external angular encoder mounted to the second joint of a 6-DOF industrial robot. The validity of the identified model is confirmed by the agreement of its prediction with independent experimental data not previously used for model identification. The obtained models open an avenue for future advanced high-precision control of robotic manipulator dynamics.
For complex robots such as humanoids, model-based control is highly beneficial for accurate tracking while keeping negative feedback gains low for compliance. However, in such multi degree-of-freedom lightweight systems, conventional identification of rigid body dynamics models using CAD data and actuator models is inaccurate due to unknown nonlinear robot dynamic effects. An alternative method is data-driven parameter estimation, but significant noise in measured and inferred variables affects it adversely. Moreover, standard estimation procedures may give physically inconsistent results due to unmodeled nonlinearities or insufficiently rich data. This paper addresses these problems, proposing a Bayesian system identification technique for linear or piecewise linear systems. Inspired by Factor Analysis regression, we develop a computationally efficient variational Bayesian regression algorithm that is robust to ill-conditioned data, automatically detects relevant features, and identifies input and output noise. We evaluate our approach on rigid body parameter estimation for various robotic systems, achieving an error of up to three times lower than other state-of-the-art machine learning methods.