Pseudo-inverse Calculation Research Articles

A Convolutional Neural Network-Based Broad Incremental Learning Filter for Attenuating Physiological Tremors in Telerobot Systems

While master-slave teleoperated robotic systems have extensive applications in practice, the physiological tremors can easily affect the control accuracy and even destroy the stability of the closed-loop control systems during operation. Hence, the development of some effective approaches for counteracting physiological tremors is of both theoretical and practical importance. In this paper, a broad learning network-based filter integrating a deep learning network and modified incremental learning algorithms is proposed to reconstruct and compensate for tremor signals. To strengthen the recognition of correlations between different moments, the lateral connectivity structure is adopted to obtain multi-scale feature maps. Each feature window is obtained from multi-scale feature maps generated by the convolutional neural network, which has an advantage that makes the feature nodes fuse the feature information of long time series and short time series by the lateral connection. The broad learning network is a unique construction, which only needs to obtain the input and the output to conveniently calculate the connection weights by the pseudo-inverse without involving backpropagation. It is known that the relation between the data X and the label Y can be represented as XW=Y, and the solution W can be obtained by the pseudo-inverse W=X+Y. In addition, to guarantee the ill-posed problem, a ridge regression algorithm is used for the pseudo-inverse calculation. The effectiveness of our raised network architecture is illustrated by comparative simulation and experiment results.

Comparative studies and performance analysis on neural-dynamics-driven control of redundant robot manipulators with unknown models

This paper proposes an inverse-free and model-free control scheme based on gradient neural dynamics (GND), which avoids the calculation of pseudo-inverse, to achieve the tracking control of redundant robot manipulators without knowing their kinematic models. Specifically, two GND models are deployed to solve the inverse kinematics problem and to estimate the unknown Jacobian matrix of manipulators respectively. We prove that the residual tracking error associated with the proposed scheme theoretically converges to an arbitrarily small upper bound in finite-time. Besides, combining GND and zeroing neural dynamics (ZND), this paper also proposes two control schemes based on hybrid neural dynamics to further achieve better performance. Moreover, the proposed continuous-time control schemes are improved to discrete-time algorithms to facilitate the deployment. Finally, the feasibility and merits of the proposed control schemes are revealed by experiments and comparisons.

Iterative Hard Thresholding Algorithm-Based Detector for Compressed OFDM-IM Systems

A low-complexity iterative hard thresholding (IHT) algorithm-based detector is proposed for the compressed orthogonal frequency division multiplexing with index modulation (OFDM-IM) system. To improve recovery accuracy and reduce the number of iterations, detection is embedded into the iterations of the IHT algorithm, and the block energy information is used to identify subblocks that are more likely to be error-recovered. Compared with the existing methods for improving spectral efficiency, the new method does not expand the detection search space and not need extra pseudo-inverse calculations during iterations. Theoretical and simulation results show that the proposed scheme can considerably reduce computational complexity while improving spectral efficiency and preserving significant BER performance gain.

A Reduced-Complexity Direct Learning Architecture for Digital Predistortion Through Iterative Pseudoinverse Calculation

In this letter, a novel approach is proposed for digital predistortion (DPD) with direct learning architecture (DLA). Regression of a Volterra behavioral model requires the pseudoinverse of a matrix, which needs many resources due to the inverse operation when the Moore–Penrose pseudoinverse is used. This work substitutes the pseudoinverse calculation by a polynomial expansion (PE) method to obtain a polynomial expansion direct learning architecture (PE-DLA), which attains a pseudoinverse in an iterative fashion avoiding the inverse operation and consequently reducing the algorithm computational complexity. Experimental results show that the number of iterations in the PE-DLA affects the convergence speed. The proposal is benchmarked against other state-of-the-art approaches such as the classic DLA and the covariance matrix DLA (CM-DLA) in the DPD of a commercial class AB power amplifier, concluding that the linearization performance of the current proposal is equivalent to others while featuring simple operations.

A real-time inverse kinematics solution based on joint perturbation for redundant manipulators

Abstract. Aiming at the problem that the calculation of the inverse kinematics solution of redundant manipulators is very time-consuming, this paper presents a real-time method based on joint perturbation and joint motion priority. The method first seeks the pose nearest to the target pose in the manipulator's pose set through fine-tuning all the joints with different angle deviations at the same time and then regards this pose as the starting one to perform iterative calculations until the error between the current pose and the target pose is less than the predetermined error, thus obtaining the inverse kinematics solution corresponding to the target pose. This method can avoid the pseudo-inverse calculations of the Jacobian matrix and significantly reduce the solving complexity. Two types of manipulators are taken as examples to validate the proposed method. Under the premise that the manipulator motion trajectory is satisfied, the Jacobian pseudo-inverse method and the proposed method are both adopted to solve the inverse kinematics. Simulations and comparisons show that the proposed method has better real-time performance, and the joint motions can be flexibly controlled by setting different joint motion priorities. This method can make the work cycle faster and improve the production efficiency of redundant manipulators in real applications.

Analytical and numerical methods for the stiffness modeling of cable-Driven serpentine manipulators

Cable-driven serpentine manipulators have advantages in compact structure, light weight and superior dexterity. They are suitable for applications in unstructured environments. However, the flexibility of the driving cables reduces the manipulator’s stiffness and brings concerns on system performances. Therefore, stiffness is a key problem. This paper aims to establish a general framework for studying the stiffness of cable-driven serpentine manipulators. We firstly established the kinematic and static models, and then proposed the analytical and numerical methods to calculate the stiffness matrix. Simulation validations show that the relative difference of the stiffness matrices by the two methods is negligible. But traditional stiffness models that neglect Jocobian matrix’s variations and/or use pseudo-inverse calculations could cause large error. Further comparisons show that the analytical method has advantages in accuracy, calculating speed and real-time performance, but requires complex formula derivation. Based on these results, suggestions are given on how to choose the proper method. Lastly, discussions are made on the numerical model’s accuracy and the cable control model selection. The proposed methods are useful for the stiffness analyses of cable-driven serpentine manipulators, and could further provide a theoretical tool for structural optimization, deformation compensation, variable stiffness control, compliance control, etc.

Teleoperation Control Design with Virtual Force Feedback for the Cable-Driven Hyper-Redundant Continuum Manipulator

Hyper-redundant continuum manipulators present dexterous kinematic skills in complicated tasks and demonstrate promising potential in underground exploration, intra-cavity inspection, surgery, etc. However, the hyper-redundancy, which endows much dexterity and flexibility, brings a huge challenge to the kinematics solution and control of the continuum manipulators. Due to the pseudoinverse calculation of high-order Jacobian matrix or iteration, many inverse kinematic solution approaches of continuum manipulators are very time-consuming, which extremely limit their applicability in real-time control. Additionally, it is often difficult for the manipulators to perform the tasks well in complex scenarios due to lack of human intervention. Therefore, in this paper, a simplified kinematics model of a typical hyper-redundant manipulator is proposed based on its unique geometry relationships, where the mapping relationships between the actuators’ rotation and the end-effector’s position are derived through the analysis of its driving subsystem and motion subsystem, in particular the joint modules. To perform the tasks of manipulators with the help of operators, a teleoperation control scheme with modified wave transmission structure is designed to achieve the guaranteed stability and improved transparency, and the leader’s trajectory and generated force feedback are the transmitted signals in the communication channel. Specifically, a virtual force feedback generation algorithm is developed in the teleoperation control scheme via the processing tracking errors, which can improve the operators’ assistance and perception during the teleoperation process. The practical experiments with comparative wave variable structures in two different sets are implemented to verify the effectiveness of proposed kinematics model and control scheme.

Efficient Kalman Filter-Based Precoder Tracking for Time-Varying Massive MIMO-OFDM Systems

The inaccuracy of channel state information (CSI) and high computational complexity for pseudo-inverse calculation in time-varying massive multiple-input multiple-output (MIMO) systems can hinder the widespread utility of regularized zero-forcing (RZF) precoding. In this letter, a novel framework is proposed for directly tracking the RZF coefficients using a Kalman filter to improve the underlying precoding performance. Specifically, a temporal autocorrelation function (ACF) of RZF coefficients is derived for the proposed tracking. Simulation results show that our proposed algorithm can almost reach the performance of the existing benchmark involving pseudo-inverse computation and thus, significantly reduces the underlying complexity by more than 32%.

Using Social Behavior of Beetles to Establish a Computational Model for Operational Management

In this article, we computationally model the social behavior of beetles and apply it to the tracking control of manipulators. The beetles demonstrate excellent skills to forage food in a previously unknown environment by merely using their olfactory senses. The goal of the beetle is to search the region with the maximum smell. Therefore, the actions of the beetle can be characterized as an optimization algorithm. This article mathematically models this behavior in the form of a recurrent neural network (RNN) with a temporal-feedback connection. We apply the formulated RNN controller for the redundancy resolution and tracking control of the redundant manipulators with an unknown kinematic model. Most of the industrial robots have redundant manipulators, and kinematic trajectory tracking is a fundamental problem for any industrial task. The behavior of the beetle allows us to formulate a position-level controller without relying on the manipulation of the Jacobian matrix. It is in contrast with the conventional velocity-level controllers, which require an accurate kinematic model of the manipulator and calculation of pseudoinverse of Jacobian, a computationally expensive task. The proposed algorithm, called Beetle Antennae Olfactory Recurrent Neural Network (BAORNN) algorithm, is capable of driving the manipulator by only using the feedback from the position and orientation sensors. The stability and convergence of the proposed algorithm are theoretically proved, and the simulations results using a seven-degree-of-freedom (DOF) industrial robotic arm, KUKA LBR IIWA14, are presented to demonstrate the performance of the proposed algorithm.

Dynamic neural networks based adaptive admittance control for redundant manipulators with model uncertainties

Force control is of great significance in the field of robotic control, for example, in tasks which requires precise control of contact force between robot and the environment, traditional path-tracking based methods may hardly achieve expected performance. However, it remains challenging for redundant manipulators with bounded constraints and model uncertainties. In this paper, we propose a novel adaptive admittance controller based on the idea of quadratic programming(QP). The control problem is transferred into an optimization one, in which the objective function is defined to make advantage of redundant DOFs, and the desired motion-force task is rebuilt as an equality constraints using admittance control strategy. Simultaneously, the bounded physical restrictions are regarded as inequality constraints. The uncertainties of both interaction model and physical parameters are also taken into consideration, which inspires us to use adaptive technology to identify those parameters online. Then an adaptive recurrent neural network is established to solve the QP problem online. This control scheme generalizes recurrent neural network based kinematic control of manipulators to that of position-force control, which opens a new avenue to shift position-force control of manipulators from pure control perspective to cross design with both convergence and optimality consideration. Besides, this method could deal with model uncertainties, and the calculation of pseudo-inverse of Jacobian matrix is no longer required. Numerical results on a 7-DOF manipulator iiwa and comparisons with existing methods show the validity of the proposed control method.

Efficient Implementation of Least Squares Sine Fitting Algorithms

In this paper, three- and four-parameter least squares (LS) sine fitting algorithms are investigated. It is pointed out that the three-parameter fitting is well conditioned in its standard form, both for short and long records. Then, the conditioning of the four-parameter fitting (4PF) is investigated. A scaling factor is derived in order to ensure good conditioning of the equations. A Monte Carlo analysis is carried out to demonstrate that in practical cases, using this scaling factor ensures good conditioning for the four-parameter system. It is also shown that parameters can be determined precisely using direct pseudoinverse calculation for both methods. Hence, in this case, there is no need to use the computationally more demanding decomposition methods, although these are generally recommended for the solution of LS problems. In addition, data centering for time instants is introduced in order to further improve the numerical properties of the 4PF. It is shown that with this method, the four-parameter problem can be approximated with a diagonal matrix. Finally, an evaluation method is presented to significantly decrease roundoff errors of the widely used LS methods.

Efficient construction of a reduced system in multi-domain system with free subdomains

Approximate techniques have been developed to calculate eigenvalues of structural system in a reduced manner. However, the construction of a reduced system is problematic with regard to localized selection of the important degrees of freedom and excessive computing time. Recently, a scheme that combines a subdomain method and a reduced system has been proposed as a means of overcoming these problems. Although the combined method is more efficient than previous reduction methods, we still suffer from one aspect: namely, it tends to produce a number of subdomains without any boundary constraints when partitioning the global domain. The Ritz vector estimation is required to be extracted in the selection process of the primary degrees of freedom. The Ritz vector of each subdomain can be easily obtained through a general static analysis of a subdomain with a boundary constraint. In contrast, a pseudo-inverse calculation takes considerable computing time to obtain the reduced system of a floating subdomain without any boundary constraints. This problem can be overcome by using the reduced pseudo-inverse method based on static condensation, which is not related to the selection of the primary degrees of freedom for eigenvalue analysis of given structure. Numerical examples demonstrate that the proposed scheme effectively reduces the computational cost in the process of primary degree-of-freedom selection. In addition, the reduced system based on the proposed scheme can accurately predict the eigenvalues of a global system as well as the time response under dynamic loads.

Force Compensating Trajectories for Redundant Robots: Experimental Results

We proposed a new approach for redundant robots trajectories planning, based on the Null space (or Kernel) features. The Null space (Kernel) exists only in the case of redundant robots and it describes these joints motion which do not affect the robot end-effector motion in the sense of both position and orientation. Based on this “hidden motion” realized in the configuration space, which does not affect the motion in the working zone, we can control independently the robot end-effector position and orientation motions, or just maintain its state while some external force is applied to it. The proposed control strategy is simple, no additional penalty functions are used to restraint the end-effector motion as in the case of the conventional methods. No pseudo inverse kinematics calculations are required; the desired trajectories are generated directly in the configuration space. No complicated control schemes are introduced, the proposed method is based on solving algebraic systems of equations and finding eigenvectors and eigenvalues. In the paper the results from simulations and experiments based on the proposed method are presented and discussed.

Impact of nonlinearities and model error on pseudo-inverse calculations

Pseudo-inverse calculations have been made within the operational and research meteorological communities to identify components of the error in the initial state that are responsible for a significant portion of the forecast error. These calculations are based on the assumptions of a perfect model and linear perturbation growth, conditions not realizable in operational forecasting. In this study, the impact of nonlinearities and model error on pseudo-inverse calculations is investigated within an idealized framework using a simple atmospheric model. Forecasts are run within the perfect and imperfect model frameworks, with initial errors of varying sizes. Model error is introduced by changing the model dissipation terms. It is found that for pseudo-inverses composed of a small subset of the leading singular vectors (SVs), the nonlinear forecast correction is often better than the expected theoretical correction, indicating the suppression of error growth both inside and outside the linear pseudo-inverse subspace. As the size of the pseudo-inverse is increased, the nonlinear forecast correction starts to degrade. This forecast degradation coincides with a degradation in the analysis correction. It is possible to improve the forecast by degrading the analysis in the presence of model error, especially when the initial error is very small. However, for initial errors of reasonable magnitude, this is unlikely to happen in instances when the nonlinear forecast correction is better than the theoretical correction. Just as improving the initial state may suppress errors outside of the linear SV subspace, degrading it may likewise increase errors outside the SV subspace. This suggests that the size of the nonlinear correction relative to the expected theoretical correction may be useful in determining when pseudo-inverse perturbations are likely to have improved the analyses.

Design optimization studies for large-scale contoured beam deployable satellite antennas

Satellite communications systems over the past two decades have become more sophisticated and evolved new applications that require much higher flux densities. These new requirements to provide high data rate services to very small user terminals have in turn led to the need for large aperture space antenna systems with higher gain. Conventional parabolic reflectors constructed of metal have become, over time, too massive to support these new missions in a cost effective manner and also have posed problems of fitting within the constrained volume of launch vehicles. Designers of new space antenna systems have thus begun to explore new design options. These design options for advanced space communications networks include such alternatives as inflatable antennas using polyimide materials, antennas constructed of piezo-electric materials, phased array antenna systems (especially in the EHF bands) and deployable antenna systems constructed of wire mesh or cabling systems. This article updates studies being conducted in Japan of such deployable space antenna systems [H. Tanaka, M.C. Natori, Shape control of space antennas consisting of cable networks, Acta Astronautica 55 (2004) 519–527]. In particular, this study shows how the design of such large-scale deployable antenna systems can be optimized based on various factors including the frequency bands to be employed with such innovative reflector design. In particular, this study investigates how contoured beam space antennas can be effective by constructed out of so-called cable networks or mesh-like reflectors. This design can be accomplished via “plane wave synthesis” and by the “force density method” and then to iterate the design to achieve the optimum solution. We have concluded that the best design is achieved by plane wave synthesis. Further, we demonstrate that the nodes on the reflector are best determined by a pseudo-inverse calculation of the matrix that can be interpolated so as to achieve the minimum deviation from the reflectors’ ideal shape. The RMS characteristics of the “cable network” in any deployable space antenna are constrained from exactly achieving the ideal contour because they ultimately contain very small plane facets. The effect of these plane facets on the characteristics of the contoured beams can be identified, however, by numerical simulations. Then these characteristics can be improved with the node locations being optimized as these simulations are undertaken. This process, however, must take into account a non-dimensional parameter. This parameter is based on the frequencies being employed, the plane facet size, and the angle of plane wave from the z-axis. When this optimization process is undertaken, the optimum location of the nodes in the “cable network” that compose the space antenna reflector can be precisely identified.

Iterative Error-based Nonlinear PLS Method for Nonlinear Chemical Process Modeling.

A novel nonlinear Partial Least Square (PLS) method is proposed to enhance modeling capability for nonlinear chemical processes. The proposed method incorporates a modified back-propagation algorithm for artificial neural network within Nonlinear Iterative Partial Least Square (NIPALS) algorithm for PLS methods, without deteriorating the robustness of PLS methods. The modified back-propagation algorithm iteratively updates the weights within the networks. The proposed method circumvents the pseudo-inverse calculation of the error-based neural network PLS proposed by Baffi et al. (1999b), and thus makes the weight updating procedure more stable and the solutions more accurate. The modeling capability of the proposed method was investigated through three case studies: 1) a pH neutralization process, 2) cosmetic data, and 3) an industrial crude column process. Simulation results showed that the proposed method represented more stable convergence and enhanced prediction power than those of the linear PLS, the neural network PLS, and the error-based neural network PLS.

Reconstruction of MR images from data acquired on a general nonregular grid by pseudoinverse calculation

A minimum-norm least-squares image-reconstruction method for the reconstruction of magnetic resonance images from non-Cartesian sampled data is proposed. The method is based on a general formalism for continuous-to-discrete mapping and pseudoinverse calculation. It does not involve any regridding or interpolation of the data and therefore the methodology differs fundamentally from existing regridding-based methods. Moreover, the method uses a continuous representation of objects in the image domain instead of a discretized representation. Simulations and experiments show the possibilities of the method in both radial and spiral imaging. Simulations revealed that minimum-norm least-squares image reconstruction can result in a drastic decrease of artifacts compared with regridding-based reconstruction. Besides, both in vivo and phantom experiments showed that minimum-norm least-squares image reconstruction leads to contrast improvement and increased signal-to-noise ratio compared with image reconstruction based on regridding. As an appendix, an analytical calculation of the raw data corresponding to the well-known Shepp and Logan software head phantom is presented.

Redundancy resolution of robotic manipulators with neural computation

This letter presents a neural-network-based computational scheme for redundancy resolution of manipulators. The Tank-Hopfield (TH) network is adopted for pseudoinverse and inverse kinematics calculations and it can provide joint velocity and joint acceleration solutions within a time frame of the order of hundreds of nanoseconds. Incorporating the TH network into the redundancy resolution scheme allows planning algorithms to be implemented in real time. Simulation results for a three-link planar manipulator are presented to demonstrate that the proposed approach is efficient and practical.

A bidirectional associative memory based on optimal linear associative memory

A bidirectional associative memory is presented. Unlike many existing BAM algorithms, the presented BAM uses an optimal associative memory matrix in place of the standard Hebbian or quasi correlation matrix. The optimal associative memory matrix is determined by using only simple correlation learning, requiring no pseudoinverse calculation. Guaranteed recall of all training pairs is ensured by the present BAM. The designs of a linear BAM (LBAM) and a nonlinear BAM (NBAM) are given, and the stability and other performances of the BAMs are analyzed. The introduction of a nonlinear characteristic enhances considerably the ability of the BAM to suppress the noises occurring in the output pattern, and reduces largely the spurious memories, and therefore improves greatly the recall performance of the BAM. Due to the nonsymmetry of the connection matrix of the network, the capacities of the present BAMs are far higher than that of the existing BAMs. Excellent performances of the present BAMs are shown by simulation results.

A novel model of autoassociative memory and its self-organization

A network is presented which embodies the orthogonal type of association. A remarkable point of the network is that the weights of the connections between neurons can be determined directly from the correlation matrix derived from the prototype patterns, requiring no pseudoinverse calculation. As a result, the connection weights can also be obtained by an unsupervised, local learning procedure based on the conventional Hebbian principle.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>