Unknown Motion Parameters Research Articles

Kinematics Analysis of 6-Degrees-of-Freedom Parallel + Serial Type Hybrid Mechanisms Containing Parallel Mechanism With High Coupling Motions

AbstractThe existing displacement of parallel + serial type hybrid mechanisms is mainly solved by the equivalent serial mechanism (SM) method. However, a large number of lower mobility parallel mechanisms (PMs) that have high coupled motions at the end-effector cannot be equivalent to SMs. Thus, the displacement problem especially for the inverse displacement of this type of hybrid mechanisms has not been well solved. On the basis of this situation, this article takes a 6-degrees-of-freedom (DOFs) 3-UPU + 3R hybrid mechanism as an example to give a general method to solve the displacement problem. First, based on the inverse displacement and pose coupling relationship of the 3-UPU PM, its forward displacement is solved by Sylvester’s dialytic elimination method, and then the forward displacement of the 3-UPU + 3R hybrid mechanism is obtained by the superposition method. Second, by skillfully dealing with the relationship between coupling motions of the 3-UPU PM and the motion of hybrid mechanism, three nonlinear equations containing three unknown motion parameters are obtained, and the inverse displacement problem is solved using Sylvester’s dialytic elimination. The research in this article is valuable in the kinematics modeling of hybrid mechanisms.

Iterative Fine Point-Set Matching of a Free-Form Surface Based on the Point-to-Sphere Distance

Three-dimensional point-set matching that aligns the moving point set with the fixed design model is an increasingly popular technique in manufacturing automation, which also increases the demand for matching performance. In this article, an iterative fine matching algorithm based on point-to-sphere distance is proposed to balance convergence accuracy, stability, and speed. By considering the neighborhood of a fixed point as a spherical surface, a point-to-sphere distance from a moving point to the design model is derived to improve the distance calculation accuracy with respect to unknown motion parameters. A point-to-sphere iterative closest point (ICP) matching method is presented, which translates the matching into a nonlinear optimization problem. Using the Newton method, a second-order Taylor expansion is applied to iteratively solve the motion parameters. Theoretical analysis verifies the advantages in convergence performance. It is proven that the proposed method can show faster convergence speed than point-to-point ICP and better convergence stability than point-to-plane ICP in large initial poses. Experiments implementing five models verify the feasibility of the point-to-sphere distance and the corresponding matching method.

Adaptive nonlinear motion parameters estimation algorithm for digital twin of multi-link mechanism motion trajectory synthesis

Monitoring systems of automated production lines requires high accuracy and processing speed of acquired data. Nowadays digital twin technologies are rapidly developing as part of Industry 4.0. Digital twin is a virtual representation of a physical system that mimics the behaviour of a real object, and is used in real-time control, monitoring and disturbance prediction, without influence on a real object. Digital twin is being used in many fields of application such as: healthcare, manufacturing, education, city development, etc. Nonetheless, despite the rising popularity of digital twin researches, there is no basic approach to digital twin synthesis. Mostly, in state of the art articles, systems with known parameters are considered. In this paper, approach to development of digital twin, based on internal model for multi-link mechanisms with unknown motion parameters, is presented. Described approach intended to ease the task of production line monitoring and extend digital twin technology application field. In this article adaptive controller design, based on internal model, is presented, theoretical explanations of design process are provided, and application of the control algorithm in the task of multi-link mechanism motion trajectory parameters estimation is described. In this work the experimental synthesis of digital twin for Kuka youBot manipulator based on presented approach in real time is described. Adaptive motion parameters estimation was made for two links of the manipulator for the sake of confirmation of presented approach usage in the task of digital twin for systems with unknown parameters. Motion trajectory parameters of the robot links were defined manually with the use of chaotic generators to estimate the accuracy of the adaptive control system. This approach was used in order to calculate the error of reference tracking by comparing the control signal for digital twin with the reference exogenous input for manipulator links. As the results of the experiment, the graphs of the error reference tracking for both links are presented. As the goal of the experiment, the convergence of reference tracking error to the field [–0.005, 0.005] radian was set, and as can be seen from graphs this goal was achieved. There is a small disturbance of the error convergence on the graphs within the desired field which was caused by noised measurements and delays of the chosen modelling environment real-time simulations. In the conclusion of this paper, further work to reduce the influence of mentioned causes is described. The results of this paper can be used in further digital twin technology researches. Presented approach can be implemented in robots remote control tasks, production lines technical condition monitoring and in general motion trajectory parameters estimation tasks for multi-link mechanisms

Omega-KA-Net: A SAR Ground Moving Target Imaging Network Based on Trainable Omega-K Algorithm and Sparse Optimization

The ground moving target (GMT) is defocused due to unknown motion parameters in synthetic aperture radar (SAR) imaging. Although the conventional Omega-K algorithm (Omega-KA) has been proven to be applicable for GMT imaging, its disadvantages are slow imaging speed, obvious sidelobe interference, and high computational complexity. To solve the above problems, a SAR-GMT imaging network is proposed based on trainable Omega-KA and sparse optimization. Specifically, we propose a two-dimensional (2-D) sparse imaging model deducted from the Omega-KA focusing process. Then, a recurrent neural network (RNN) based on an iterative optimization algorithm is built to learn the trainable parameters of Omega-KA by an off-line supervised training method, and the solving process of the sparse imaging model is mapped to each layer of the RNN. The proposed trainable Omega-KA network (Omega-KA-net) forms a new GMT imaging method that can be applied to high-quality imaging under down-sampling and a low signal to noise ratio (SNR) while saving the imaging time substantially. The experiments of simulation data and measured data demonstrate that the Omega-KA-net is superior to the conventional algorithms in terms of GMT imaging quality and time.

Unambiguous velocity estimation method based on intra‐pulse cross‐correlation

In this study, by employing the intra-pulse cross-correlation (IPCC) operation, an unambiguous velocity estimation method is proposed for narrow-band long-range radars with high carrier frequency and low pulse repetition frequency. This estimation algorithm is simple and could be easily implemented in existing radar systems without changing the radar hardware or the pulse transmitting scheme. Comparing with the slow time dimension correlation algorithm, the accuracy of the proposed intra-pulse frequency domain method is greatly improved, and the brute-force search for the unknown motion parameters is also unnecessary. By first setting a small frequency offset of the IPCC operation, the unambiguous velocity region could be significantly enlarged. Using the relatively coarse but unambiguous estimates and increasing the frequency offset step by step, the IPCC is repeatedly applied to obtain more accurate estimates. Note that the estimation results of the IPCC algorithm could be used in the maximum-likelihood estimator for ambiguity resolution. The Cramer-Rao bound for the proposed algorithm is derived, and the optimal frequency offset in the sense of estimation accuracy is also analysed. Through numerical simulations for both synthetic and real radar data, the effectiveness of the proposed estimation algorithm is verified.

Refocusing of Ground Moving Target in Circular Synthetic Aperture Radar

Due to the non-cooperative motion of ground moving targets, they appear smeared and dislocated in circular synthetic aperture radar (CSAR) imagery. Refocusing of ground moving target in CSAR is a challenging problem because of the circular trajectory of the radar platform and unknown motion parameters of ground moving targets. In this paper, an inverse SAR (ISAR) technique-based method with Legendre polynomial approximation for ground moving target refocusing in CSAR is proposed. Different from the conventional ISAR-based method, the method extracts range migration of the moving target in the range-frequency domain directly, which can avoid the range alignment procedure in conventional ISAR techniques. Furthermore, the Legendre polynomial approximation is applied to fit the extracted range migration, which can be carried out iteratively to fulfill the requirement of accuracy. The experimental CSAR data processing results show that the proposed method can achieve satisfied imaging quality of ground moving targets.

Efficient Algorithm for SAR Refocusing of Ground Fast-Maneuvering Targets

The synthetic aperture radar (SAR) image of moving targets will defocus due to the unknown motion parameters. For fast-maneuvering targets, the range cell migration (RCM), Doppler frequency migration and Doppler ambiguity are complex problems. As a result, focusing of fast-maneuvering targets is difficult. In this work, an efficient SAR refocusing algorithm is proposed for fast-maneuvering targets. The proposed algorithm mainly contains three steps. Firstly, the RCM is corrected using sequence reversing, matrix complex multiplication and an improved second-order RCM correction function. Secondly, a 1D scaled Fourier transform is introduced to estimate the remaining chirp rate. Thirdly, a matched filter based on the estimated chirp rate is proposed to focus the maneuvering target in the range–azimuth time domain. The proposed method is computationally efficient because it can be implemented by the fast Fourier transform (FFT), inverse FFT and non-uniform FFT. A new deramp function is proposed to further address the serious problem of Doppler ambiguity. A spurious peak recognition procedure is proposed on the basis of the cross-term analysis. Simulated and real data processing results demonstrate the validity of the proposed target focusing algorithm and spurious peak recognition procedure.

Deep CNNs as a method to classify rotating objects based on monostatic RCS

Radar systems emit a time-varying signal and measure the response of a radar-reflecting surface. In the case of narrowband, monostatic radar signal domain, all spatial information is projected into a radar cross-section (RCS) scalar. The authors address the challenging problem of determining shape class using monostatic RCS estimates collected as a time series from a rotating object tumbling with unknown motion parameters under detectability limitations and signal noise. Previous shape classification methods have relied on image-like synthetic aperture radar or multistatic (multiview) radar configurations with known geometry. Convolutional neural networks (CNNs) have revolutionised learning tasks in the computer vision domain by leveraging images and video rich with high-resolution two-dimensional (2D) or 3D spatial information. They show that a feed-forward CNN can be trained to successfully classify object shape using only noisy monostatic RCS signals with unknown motion. They construct datasets containing over 100,000 simulated RCS signals belonging to different shape classes. They introduce deep neural network architectures that produce 2% classification error on testing data. They also introduce a refinement network that transforms simulated signals to appear more realistic and improve training utility. The results are a pioneering step toward the recognition of more complex targets using narrowband, monostatic radar.

Background-Free Ground Moving Target Imaging for Multi-PRF Airborne SAR

Synthetic aperture radar (SAR) is an advanced imaging sensor that can image side-looking terrain. Until now, SAR schemes and imaging theories have been researched for stationary scenes. Unlike a stationary scene, due to unknown motion parameters, a ground moving target (GMT) is shifted and defocused in a background image, which causes difficulties in their use for further applications. This paper proposes a multiple pulse repetition frequency (PRF) airborne SAR scheme for background-free GMT imaging. In the proposed scheme, pulses are transmitted by a nonuniform pulse repetition time, and echoes are divided into groups with different PRFs. For spectra with different PRFs, due to their diverse respective spectra extending periods, periodical extending GMT spectra will not appear at the same location except for the original spectra. A theorem is proposed to prove that the spectra can be extracted intact, undistorted, and unpolluted. In light of the divergence of the GMT spectra location from that of the clutter, filter banks are designed to locate, extract, and reconstruct the GMT spectra out of the mixed spectra that contain the GMT and clutter. For GMT SAR imaging, a moving target is regarded as a steady target under an equivalent geometry with a new equivalent squint angle and a new SAR platform velocity. The SAR image is obtained with the range-Doppler algorithm with equivalent geometry parameters that are estimated from the Doppler parameters. Experimental results obtained from using extensive numerical simulated data validate our proposed approach.

Short-Time Velocity Identification and Coherent-Like Detection of Ultrahigh Speed Targets

Finding a balance between observation duration and detection rates is the ultimate goal of the detection of ultrahigh speed targets. However, short observation durations, both across range unit, and Doppler frequency migration, may severely limit the detection performance of ultrahigh speed targets. Although, traditional coherent integration methods can efficiently accumulate signal energy to produce a high signal-to-noise-ratio measurement, they often need to search for unknown motion parameters. This search is time consuming and unacceptable for the real-time detection of ultrahigh speed targets. In this paper, a coherent-like detection method is designed based on the finite-dimension theory of Wigner matrices along with velocity identification. The proposed method can efficiently integrate signal energy without rendering motion parameters. We use the distribution and mean of the eigenvalues of the constructed matrix, i.e., an additive Wigner matrix, to identify velocities and detect ultrahigh speed targets, respectively. Simulation results validate the theoretical derivation, superiority and operability of the proposed method.

Visual servoing tracking control of uncalibrated manipulators with a moving feature point

ABSTRACTThe paper is concerned with the problem of uncalibrated visual servoing robots tracking a dynamic feature point along with the desired trajectory. A nonlinear observer and a nonlinear controller are proposed, which allow the considered uncalibrated visual servoing robotic system to fulfil the desired tracking task. Based on this novel control method, a dynamic feature point with unknown motion parameters can be tracked effectively along with the desired trajectory, even with multiple uncertainties existing in the camera, the kinematics and the manipulator dynamics. By the Lyapunov theory, asymptotic convergence of the image errors to zero with the proposed control scheme is rigorously proven. Simulations have been conducted to verify the performance of the proposed control scheme. The results demonstrated good convergence of the image errors.

Fast non-searching method for ground moving target refocusing and motion parameters estimation

Ground moving targets may be smeared in a synthetic aperture radar (SAR) image due to the range migration, Doppler ambiguity and azimuth spectrum split caused by target unknown motion parameters. To handle these problems, we propose a fast non-searching method for maneuvering target refocusing and motion parameters estimation in this paper. First, the azimuth-deramp is conducted, which is capable of eliminating the azimuth spectrum splitting. In the sequel, the second-order keystone transform (SOKT) based on the scaling principle is applied to further correct the residual range curvature. Then, the phase difference (PD) is performed to eliminate the range walk and estimate the motion parameters, which does not require the prior knowledge of Doppler ambiguity number. Finally, the moving target can be well focused with the estimated parameters. This method has high computational efficiency and improved parameter estimation accuracy. Both simulated and real data are processed to demonstrate the effectiveness of the proposed method.

Ground Moving Target Imaging Based on Keystone Transform and Coherently Integrated CPF With a Single-Channel SAR

It is well known that ground moving targets may be smeared in a synthetic aperture radar (SAR) image due to the range migration, Doppler phase broadening, and velocity ambiguity caused by target unknown motion parameters, especially for the accelerating targets within a long observation time. To deal with these problems, a maneuvering target refocusing method based on keystone transform (KT) and coherently integrated cubic phase function (CICPF) is proposed in this paper. First, an azimuth deramp function is constructed along the slow-time dimension at each range-frequency gate to reduce the order of envelope migration and phase response over the slow-time. Then, the residual range walk and the time-varying Doppler phase are eliminated by the KT and the CICPF, respectively. With the estimated motion parameters, moving targets can be finely refocused. Both simulated and real SAR data processing results are presented to validate the proposed algorithm.

Refocusing of Moving Targets in SAR Images via Parametric Sparse Representation

In this paper, a parametric sparse representation (PSR) method is proposed for refocusing of moving targets in synthetic aperture radar (SAR) images. In regular SAR images, moving targets are defocused due to unknown motion parameters. Refocusing of moving targets requires accurate phase compensation of echo data. In the proposed method, the region of interest (ROI) data containing the moving targets are extracted from the complex SAR image and represented in a sparse fashion through a parametric transform, which is related to the phase compensation parameter. By updating the reflectivities of moving target scatterers and the parametric transform in an iterative fashion, the phase compensation parameter can be accurately estimated and the SAR images of moving targets can be refocused well. The proposed method directly operates on small-size defocused ROI data, which helps to reduce the computational burden and suppress the clutter. Compared to other existing ROI-based methods, the proposed method can suppress asymmetric side-lobes and improve the image quality. Both simulated data and real SAR data collected by GF-3 satellite are used to validate the effectiveness of the proposed method.

Structure‐independent motion recovery from a monocular image sequence with low fill fraction

SummaryReal‐world image sequences are usually characterized by frequent loss and replacement of tracked feature data, and the key to accurate motion recovery from such image sequences lies in the synthesis of a structure‐independent dynamic filter that enables the replacement of lost point features with newly acquired points in a seamless manner. In this note, a novel nonlinear observer is proposed that relies on filtered estimates of optical flow to accomplish structure‐independent motion recovery from monocular image sequences with a low fill fraction. With a single component of linear velocity assumed known, the proposed scheme relies on the perspective observation of at least five points to yield exponentially convergent estimates of the unknown motion parameters that converge to a uniform, ultimate bound in the presence of model error. The unknown linear and angular velocities are assumed to be generated using an imperfectly known model that incorporates a bounded uncertainty, and optical flow estimation is accomplished using a robust differentiator that is based on the sliding‐mode technique. Numerical results are used to validate and demonstrate superior observer performance compared to a leading alternative design on a real‐world–like image sequence that is characterized by significant measurement noise and high feature turnover rate.

A Method for Determination of the Extrinsic Camera Parameters from a Pair of Images with the Use of Dual Quaternions

Real-world problems associated with the use of the moving vehicles present a problem for estimation of the unknown motion parameters on the basis of the data obtained from a static camera set on the surface of those vehicles. The initial data (in absence of information about the vehicle motion) are the images obtained from different viewpoints. The traditional approach to estimation of the rotation and translation parameters, which consists in determination of the so-called fundamental matrix and the subsequent calculation of the required matrices has several drawbacks. In particular, if the largest portion of the predefined points in the images is located on the same plane, the fundamental matrix estimation involves serious errors, which, in turn, lead to errors in estimation of the camera parameters. Unlike in the traditional approach, in this paper the corresponding points are used to estimate not the fundamental matrix, but the internal and external camera parameters directly. Besides, this paper presents a multiple view geometry model, based on three-dimensional images and camera parameters in the form of dual quaternions. The proposed approach to the problem is a new method of estimation of the unknown camera parameters, which is more accurate and reliable compared with the traditional one. This method was implemented as a program in C + +. Using the developed program, the authors carried out an experiment to establish a correlation between the errors in the input data (points of coordinates on the planes of the camera) and the errors in the estimated rotation and translation parameters. As the result, it was confirmed that the accuracy of the parameters' estimation in most cases surpasses the quality of the results obtained by using the fundamental matrix.

Robust structure and motion recovery for monocular vision systems with noisy measurements

ABSTRACTThis study proposes a novel complete-order nonlinear structure and motion observer for monocular vision systems subjected to significant measurement noise. In contrast with previous studies that assume noise-free measurements, and require prior knowledge of either the relative motion of the camera or scene geometry, the proposed scheme assumes a single component of linear velocity as known. Under a persistency of excitation condition, the observer then relies on filtered estimates of optical flow to yield exponentially convergent estimates of the unknown motion parameters and feature depth that converge to a uniform, ultimate bound in the presence of measurement noise. The unknown linear and angular velocities are assumed to be generated using an imperfectly known model that incorporates a bounded uncertainty, and optical flow estimation is accomplished using a robust differentiator that is based on the sliding-mode technique. Numerical results are used to validate and demonstrate superior observer performance compared to an alternative leading design in the presence of model uncertainty and measurement noise.

An Analytically Stable Structure and Motion Observer Based on Monocular Vision

This paper presents a novel nonlinear sliding-mode differentiator-based complete-order observer for structure and motion identification with a calibrated monocular camera. In comparison with earlier work that requires prior knowledge of either the Euclidean geometry of the observed object or the linear acceleration of the camera and is restricted to establishing stability and convergence from image-plane measurements of a single tracked feature, the proposed scheme assumes partial velocity state feedback to asymptotically identify the true-scale Euclidean coordinates of numerous observed object features and the unknown motion parameters. The dynamics of the motion parameters are assumed to be described by a model with unknown parameters that incorporates a bounded uncertainty, and a Lyapunov analysis is provided to prove that the observer yields exponentially convergent estimates that converge to a uniform ultimate bound under a generic persistency of excitation condition. Numerical and experimental results are obtained that demonstrate the robust performance of the current scheme in the presence of model error and measurement noise.

SU‐F‐J‐77: Variations in the Displacement Vector Fields Calculated by Different Deformable Image Registration Algorithms Used in Helical, Axial and Cone‐Beam CT Images of a Mobile

Purpose:To investigate quantitatively the displacement‐vector‐fields (DVF) obtained from different deformable image registration algorithms (DIR) in helical (HCT), axial (ACT) and cone‐beam CT (CBCT) to register CT images of a mobile phantom and its correlation with motion amplitudes and frequencies.Methods:HCT, ACT and CBCT are used to image a mobile phantom which includes three targets with different sizes that are manufactured from water‐equivalent material and embedded in low density foam. The phantom is moved with controlled motion patterns where a range of motion amplitudes (0–40mm) and frequencies (0.125–0.5Hz) are used. The CT images obtained from scanning of the mobile phantom are registered with the stationary CT‐images using four deformable image registration algorithms including demons, fast‐demons, Horn‐Schunk and Locas‐Kanade from DIRART software.Results:The DVF calculated by the different algorithms correlate well with the motion amplitudes that are applied on the mobile phantom where maximal DVF increase linearly with the motion amplitudes of the mobile phantom in CBCT. Similarly in HCT, DVF increase linearly with motion amplitude, however, its correlation is weaker than CBCT. In ACT, the DVF's do not correlate well with the motion amplitudes where motion induces strong image artifacts and DIR algorithms are not able to deform the ACT image of the mobile targets to the stationary targets. Three DIR‐algorithms produce comparable values and patterns of the DVF for certain CT imaging modality. However, DVF from fast‐demons deviated strongly from other algorithms at large motion amplitudes.Conclusion:In CBCT and HCT, the DVF correlate well with the motion amplitude of the mobile phantom. However, in ACT, DVF do not correlate with motion amplitudes. Correlations of DVF with motion amplitude as in CBCT and HCT imaging techniques can provide information about unknown motion parameters of the mobile organs in real patients as demonstrated in this phantom visibility study.

Radar High-Speed Target Detection Based on the Scaled Inverse Fourier Transform

In this paper, by employing the symmetric autocorrelation function and the scaled inverse Fourier transform (SCIFT), a coherent detection algorithm is proposed for high-speed targets. This coherent detection algorithm is simple and can be easily implemented by using complex multiplications, the fast Fourier transform (FFT) and the inverse FFT (IFFT). Compared to the Hough transform and the keystone transform, this coherent detection algorithm can detect high-speed targets without the brute-force searching of unknown motion parameters and achieve a good balance between the computational cost and the antinoise performance. Through simulations and analyses for synthetic models and the real data, we verify the effectiveness of the proposed coherent detection algorithm.