Statistical analysis of tracking and parametric estimation errors in a 2-link robot based on Lyapunov function

The prediction of human motion is essential for safe human-robot collaboration (HRC). For existing prediction methods based on adaptive neural network (NN) models, estimation errors (EEs) of model parameters are directly coupled with prior EEs of trajectories. This results in poor assessment of the mean square estimation error (MSEE) of model parameters, which is a potential danger to the safety HRC. In this paper, a novel “look-backward-and-forward” method is proposed to assess the EEs of model parameters. This method firstly computes EEs of model parameters in the past few time instants based on the actual error of trajectory predicted in the past. Subsequently, the EEs of model parameters are recursively updated till the current time instant. In this way, the trajectory of a single particle and its MSEE are accurately accessed. The direct coupling between the MSEE of the trajectory and that of model parameters is cut off and the mean estimation errors (MEEs) of parameters are only affected by the EEs of the past trajectory at the recent several time instants, rather than accumulating as the time propagates. This method is further extended to estimate the pose trajectory of a rigid body based on fitting of an ellipsoid’s parameters. The experimental results of predicting 3-D trajectories of human motions show the effectiveness of the proposed method.

In this paper, we propose a genetic algorithm based approach to determine the pose of an object in Automated Visual Inspection having three degrees of freedom. We have investigated the effect of noise at 20 dB SNR and also mismatch resulting from incorrect correspondences between the object space points and the image space points, on the estimation of pose parameters. The maximum error in translation parameters is less than 0.45 cm and rotational error is less than 0.2 degree at 20 dB SNR. The error in parameter estimation is insignificant upto 7 pairs of mismatched points out of 24 points in object space and the results skyrockets when 8 or more pairs of points are mismatched. We have compared our result with that obtained by least square technique and it shows that GA based method outperform the gradient based technique when the number of vertices of the object to be inspected is small. These results have clearly established the robustness of GA in estimating the pose of an object with small number of vertices in automated visual inspection.

Diffusion on graphs is ubiquitous with numerous high-impact applications, ranging from the study of residential segregation in socioeconomics and activation cascading in neuroscience, to the modeling of disease contagion in epidemiology and malware spreading in cybersecurity. In these applications, complete diffusion histories play an essential role in terms of identifying dynamical patterns, reflecting on precaution actions, and forecasting intervention effects. Despite their importance, complete diffusion histories are rarely available and are highly challenging to reconstruct due to ill-posedness, explosive search space, and scarcity of training data. To date, few methods exist for diffusion history reconstruction. They are exclusively based on the maximum likelihood estimation (MLE) formulation and require to know true diffusion parameters. In this paper, we study an even harder problem, namely reconstructing Diffusion history from A single SnapsHot (DASH), where we seek to reconstruct the history from only the final snapshot without knowing true diffusion parameters. We start with theoretical analyses that reveal a fundamental limitation of the MLE formulation. We prove: (a) estimation error of diffusion parameters is unavoidable due to NP-hardness of diffusion parameter estimation, and (b) the MLE formulation is sensitive to estimation error of diffusion parameters. To overcome the inherent limitation of the MLE formulation, we propose a novel barycenter formulation: finding the barycenter of the posterior distribution of histories, which is provably stable against the estimation error of diffusion parameters. We further develop an effective solver named DIffusion hiTting Times with Optimal proposal (DITTO) by reducing the problem to estimating posterior expected hitting times via the Metropolis-Hastings Markov chain Monte Carlo method (M-H MCMC) and employing an unsupervised graph neural network to learn an optimal proposal to accelerate the convergence of M-H MCMC. We conduct extensive experiments to demonstrate the efficacy of the proposed method. Our code is available at https://github.com/q-rz/KDD23-DITTO. The appendix can be found at https://arxiv.org/abs/2306.00488.

Model-based multi-wavelength interdigital dielectrometry parameter estimation algorithms require a good agreement between theory and measurements. Research data indicate that the agreement is high for measurement of the properties of fluid dielectrics or the sensor substrate. However, the non-ideality of the surface contact between the sensor and solid materials creates significant differences between the idealized model and experimental results. One solution to this problem is to evaluate surface contact conditions for every measurement and account for them in software. Two alternative sensor designs are compared in this paper in their ability to provide reliable measurement data that can be used by parameter estimation algorithms. Measurement of dielectric and conduction properties of both fluids and solid dielectrics are considered. It is shown that the distribution of the electric field excitation over the entire multi-wavelength sensor head, as opposed to using separate electrode wavelengths, leads to reduction of errors in parameter estimation.

Direct investigations are required for future missions to small planetary bodies, in addition to obtain terrain maps and collecting samples from the surface. Rovers, mobile robots on surface of a planetary body, are effective in investigating into several specific points. We proposed a method of localization for navigating rovers to specific features. The proposed method measures two-way range between the rover and the mother spacecraft orbiting around the investigating planetary body using radio waves. The proposed method can be applied with reasonable accuracy on large and small planetary bodies and it can particularly be used with sub-hundred-meter-sized bodies, which conventional methods cannot be applied to. Sensitivity analysis of the proposed method is summarized in this paper, according with estimation errors in rotation parameters of the planetary body. A method of estimation is described here, which takes into account errors of rotational parameters.

Trajectory following control of robot manipulators requires the online evaluation of the robot dynamic model. It is known that the continuous (analog) implementation of model-based (also called inverse dynamics or computed-torque) control can provide perfect tracking under perfect knowledge of the robot dynamic model. The model describing the robot dynamic behavior is highly nonlinear and computationally complex. Its complexity necessitates online evaluation of the robot dynamic model digitally either via VLSI/hardware implementation or under computer (software) control. Digital implementations require sampling of robot states and zero-order-hold (ZOH) actuations which introduce trajectory tracking errors. Modeling errors further add tracking errors due to inexact cancellation of robot dynamics resulting in a still-coupled and nonlinear system. Modeling errors come from parameter errors as well as unmodeled dynamics.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We have calculated the estimation error of parameters of echo power spectra observed by mesosphere‐stratosphere‐troposphere (MST) radars by means of computer simulations for least squares fitting and moment methods. The least squares fitting method is shown to be better than the moment method in the region with low signal‐to‐noise ratio (snr), especially for narrow spectra. However, the estimation error of the fitting method at infinite snr is approximately twice that of the moment method. This has been attributed to the nature of the statistical fluctuation of the power spectral density, which shows a χ2 distribution. For both methods at infinite snr we have derived equations which show the accuracy of the estimates versus observation period and spectral width. When we use the fitting method for the data observed with the MU radar (46.5 MHz), the typical errors of the radial wind velocities are 0.7 and 2.0 m s−1 in the stratosphere and in the mesosphere, respectively. By calculating the logarithm of the spectrum with inifite snr and fitting a parabolic curve to it, the error of the Doppler shift has become approximately 20 times smaller than that of the moment method. It has been shown that this is one technique to achieve the theoretical lower bound of the estimates.

Chapter 8 - Robust adaptive parameter estimation and control for vehicle active suspension systems

The objective of this paper is a redefinition of the robot control problem, based on realistic (1) models for the industrial robot as a controlled plant, (2) end effector trajectories consistent with manufacturing applications, and (3) the need for end-effector sensing to compensate for uncertainties inherent to most robotic manufacturing applications. Based on extensive analytical and experimental studies, realistic robot dynamic models are presented that have been validated over the frequency range 0 to 50 Hz. These models exhibit a strong influence of drive system flexibility, producing lightly damped poles in the neighborhood of 8 Hz, 14 Hz, and 40 Hz, all unmodeled by the conventional rigid body multiple link robot dynamic approach. The models presented also quantify the significance of nonlinearities in the drive system, in addition to those well-known in the linkage itself. Realistic simulations of robot dynamics and motion controls demonstrate that existing controls coupled with effective path planning produce dynamic path errors that are acceptable for most manufacturing applications. Major benefits are projected, with examples cited, for use of end-effector sensors for position, force, and process control that compensate for uncertainties encountered on the factory floor.

This paper discusses how National Statistical Institutes (NSI’s) can use hidden Markov models (HMMs) to produce consistent official statistics for categorical, longitudinal variables using inconsistent sources. Two main challenges are addressed: first, the reconciliation of inconsistent sources with multi-indicator HMMs requires linking the sources on the micro level. Such linkage might lead to bias due to linkage error. Second, applying and estimating HMMs regularly is a complicated and expensive procedure. Therefore, it is preferable to use the error parameter estimates as a correction factor for a number of years. However, this might lead to biased structural estimates if measurement error changes over time or if the data collection process changes. Our results on these issues are highly encouraging and imply that the suggested method is appropriate for NSI’s. Specifically, linkage error only leads to (substantial) bias in very extreme scenarios. Moreover, measurement error parameters are largely stable over time if no major changes in the data collection process occur. However, when a substantial change in the data collection process occurs, such as a switch from dependent (DI) to independent (INDI) interviewing, re-using measurement error estimates is not advisable.

The flexible robots are widely used in space applications due to their quick response, lower energy consumption, lower overall mass and operation at high speed compared to conventional industrial rigid link robots. These robots are inherently flexible, so that the kinematics of flexible robots can't be solved with rigid body assumptions. The flexibility in links and joints affects end-point positioning accuracy of the robot. It is important to model the link kinematics with precision which in turn simplifies modelling of dynamics of flexible robots. The main objective of this paper is to evaluate the effect of link flexibility on a tip position of a single link robotic arm for a given motion. The joint is assumed to be rigid and only link flexibility is considered. The kinematics of flexible link problem is evaluated by Assumed Modes Method (AMM) using MAT LAB Programming. To evaluate the effect of link flexibility (with and without payload) of robotic arm, the normalized tip deviation is found for flexible link with respect to a rigid link. Finally, the limiting inertia for payload mass is found if the allowable tip deviation is 5%.

A simple and robust position controller is proposed for a small planar three- degree-of-freedom robot arm actuated by two shape memory alloy (SMA) actuators and a servomotor. A simple model of the robot is used for controller development. The model combines robot kinematics and dynamics with crude models of SMA wire heat convection, constitutive law, and phase transformation. It is then used to estimate ‘optimal’ parameters for the position controllers. The controllers are based on variable structure control approach and their development is of an evolutionary nature starting with a simple switching surface of position tracking errors and followed by the addition of velocity and integral tracking errors, respectively. The final controller is shown to be particularly fast since it heats the SMA wires with maximum available voltage, but avoids overshoot thereby avoiding the slow natural cooling process compared. Several experiments have been performed with a desktop prototype of the robot. The experimental results verify the effective and robust performance of the controllers despite significant modeling inaccuracies during the controller parameter development process. An additional advantage of the controller is that it can be implemented on a controller board with very limited computation capacity.

: Two studies were carried out to evaluate the quality of multidimensional item response theory (MIRT) model parameter estimates obtained from the computer program NOHARM. The purpose of the first study was to compute empirical estimates of the standard errors of the parameters. In addition, the parameter estimates were evaluated for bias and the effects of using different starting values and anchor items. The second study was included to compare the performance of NOHARM with the findings of an earlier simulation study which evaluated other MIRT estimation programs. Results were generally good, with fairly small standard errors for most parameter estimates and little indication of bias. Although the estimation procedure appeared to be robust under different starting values, the specific choice of items used to anchor the solution appears to have important effects on the magnitude of the estimated standard errors. The comparison of NOHARM with other programs was very favorable and supports the use of NORHARM for practical MIRT applications.

Considering parametric uncertainties and unmodeled disturbances in hydraulic systems, this paper presents an asymptotic adaptive motion control scheme by adopting full state feedback. To accomplish this study, a novel parameter adaptive law based on both parametric estimation errors and tracking errors is developed to deal with parametric uncertainties of hydraulic systems, which can attenuate the major of parametric uncertainties and enhance the tracking performance. Then a composite robust integral of the sign of the error (RISE) feedback controller is employed to restrain the rest of parametric uncertainties and unmodeled disturbances. The developed continuous RISE-based controller is free of chattering, which is beneficial to practical implementation. Stability analysis indicates that the proposed method guarantees an excellent asymptotic tracking performance even in facing with time-variant disturbances and parametric uncertainties. Comparative simulation results are obtained to verify the high-performance nature of the proposed control strategy as well.

The selected simulation results of the angular velocity estimator, whose operation algorithm has been elaborated basing on the inductance frequency characteristic of the considered induction motor (IM), have been presented in the paper. The simulations have been conducted at specified operating frequencies of the scalar-controlled induction motor drive with a modulator employing the space vector pulse width modulation technique. This allowed for the indication of the influence of the IM current distortion on the accuracy of the IM angular velocity estimation process and thereby the efficiency of the considered IM drive. The impact of the estimator input signals filtering on the level of angular velocity estimation and tracking errors has been also investigated in the paper. The analysis has been conducted for the mathematical model of the four-pole induction motor of Sg 132S-4 type with a solid rotor manufactured from the magnetic material S235JR.