Inverse Solution Research Articles

Model-Free Intelligent Control for Space Soft Robotic Manipulators

Given the advantages of softness, lightness, low cost, and interaction safety, inverse kinematic modeling and control of soft actuators has caused a research boom. However, in realizing dexterous manipulation of space large soft manipulators, it is much more difficult to achieve precise control not only because of the greater accumulation of errors in the multiple degrees of freedom and nonlinear properties of soft materials at large scales but also because of the inability of directly solving the inverse kinematics in the cases of singular pure elongation. In this work, a model-free intelligent kinematic control strategy is proposed for these problems that exhibit a mapping relationship between the output end-effector position and the input pressure. For multiple-degree-of-freedom robots, especially pneumatic soft manipulators, traditional inverse kinematic modeling methods are complex and inverse Jacobian matrix solution often encounters geometric singularities. To address this issue, this paper proposes an inverse kinematics–multilayer perceptron (IK-MLP) method for soft manipulators. In this strategy, the trained intelligent controller can be applied to control pneumatic manipulators without establishing a traditional inverse kinematic model. The control algorithm is experimentally tested based on the ground experiment system of the space soft manipulator. Simulations and experiments are carried out to validate the given model-free intelligent controller, proving that the IK-MLP method can effectively solve the singularity of inverse kinematics.

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning

β-FGJO: A General Metaheuristic Method for Inverse Kinematics Solution of Multi-DOF Robotic Manipulators

<i>β</i>-FGJO: A General Metaheuristic Method for Inverse Kinematics Solution of Multi-DOF Robotic Manipulators

Combining closed-form and numerical solutions for the inverse kinematics of six-degrees-of-freedom collaborative handling robot

In the process of solving the inverse kinematics of six-degrees-of-freedom collaborative robots, the numerical solution has problems such as low accuracy and singular configurations. Moreover, due to the high coupling of its position and attitude, the direct closed-form solution fails. To address these problems, an inverse kinematics algorithm that combines closed-form and numerical solutions was proposed. The Jacobian matrix was established based on the forward kinematics equation of the six-degrees-of-freedom collaborative robot. Its inverse matrix was obtained by a singular value decomposition of the matrix using the Manocha elimination method to avoid the singularities of the Jacobian matrix. The optimal inverse kinematics solution was obtained using the Newton–Raphson iterative method. A computer simulation implemented in MATLAB and Visual C++ was used to evaluate the accuracy and speed of the proposed algorithm. The results of the trajectory planning experiments demonstrate that the algorithm satisfies the requirements for real-time smooth motion. This study of inverse kinematics lays the theoretical foundation for solutions to the inverse problem and real-time control of collaborative robots.

Sequential estimation of high temperatures of liquid metals by using particle filter methods

This work follows up our previous studies dedicated to the estimation of the transient temperature of niobium and 100c6 steel samples, in ranges that include solid and liquid phases, as well as phase changes. In the experimental setup, a metallic sample of few millimeters is aerodynamically levitated and then heated by a powerful laser, while a collimator focused on the sample collects the radiative flux that is split towards five pyrometers of different wavelengths. The measured spectral fluxes are used in an inverse analysis to estimate the sample temperature. Difficulties in the inverse problem solution related to the dependence of the sample emittance with temperature and wavelength could be overcome by reducing the number of model parameters using a simple linear variation of the emittance with respect to the wavelength. In this work the transient temperature of the sample is estimated sequentially by solving a state estimation problem with two algorithms of the particle filter method, namely: the Sampling Importance Resampling (SIR) and Auxiliary Sampling Importance Resampling (ASIR) algorithms. Results obtained with these algorithms and the radiative spectral fluxes exhibited small discrepancies with respect to the temperature measurements of a reference bichromatic pyrometer.

A method of fluorescence molecular tomographic reconstruction via the second-order sensitivity matrix

Fluorescence molecular tomographic (FMT) reconstruction is commonly solved based on the Jacobian matrix, which is a first-order sensitivity matrix. Basically, using the second-order derivatives for iterative reconstruction can help improve the performance of convergence. In this paper, a reconstruction method of FMT based on the reduction of the second-order sensitivity matrix is proposed. In addition, the strategy of detectors rotation is combined into the inverse reconstruction to further improve the reconstruction quality. The reconstructed results demonstrate that the proposed method accelerates the reconstruction with high precision of inverse solutions.

A variable future-time-steps method for solving nonlinear unsteady inverse heat conduction problems

In some non-linear unsteady inverse problems, the inverse solution will oscillate violently in the whole time domain due to the sharp change of the sensitivity coefficients. To deal with this problem, a new sequential function specification method with variable future time steps is proposed in this paper. The future time steps are adjusted by the error amplification coefficients which are defined as the reciprocal of the square sum of the sensitivity coefficients. When the error amplification coefficients are small, a small number of future time steps is used to reduce the deterministic error. While in the period with large error amplification coefficient, a large number of future time steps is used to reduce stochastic error. Finally, the total error of estimated heat flux is reduced. Avoid the sharp fluctuation of estimated heat flux in time domain due to the sharp change of sensitivity coefficients. The variable future-time-steps method is applied to the estimation of 1-D non-linear unsteady heat flux without and with ablation through numerical experiments. Numerical experiments show that the proposed method can not only estimate various forms of heat flux, but also its inversion results are significantly better than those of the fixed future time steps method based on the discrepancy principle, and also better than those of the fixed future time step method based on the minimum relative error of heat flux.

Application of conjugate gradient least squares method in solving magnetic moments of magnetic targets based on magnetic dipole array model

In order to solve the problem of magnetic targets magnetic field modeling, a magnetic dipole array model was established, a modeling inversion equation system was constructed, and the degree of sickness of the solved equation system under different numbers of magnetic dipoles was quantitatively analyzed based on the coefficient matrix condition number. In order to solve the problem of the pathological system of magnetic field modeling equations, a regularization method based on the conjugate gradient least squares method was designed to invert the magnetic moment parameters of the magnetic dipole. In order to analyze the applicability of the regularization method in magnetic field modeling inversion, the magnetic moment solving accuracy, the magnetic moment solving robustness, calculation time, and other metrics are defined. A detailed test of the ship model was designed, and the magnetic field passing characteristics of the two types of ship models at different positive and horizontal conditions at two depths were measured. Under the condition of no interference and interference, the conjugate gradient least squares method is used to invert the magnetic field model, and the numerical test analysis shows that the conjugate gradient least squares method has higher applicability than the generalized inverse solution method and the stepwise regression method. Under the condition of interference, the relative error of magnetic field fitting of the array model with 15 magnetic dipoles is 0.1537, and the relative error of magnetic field extrapolation is 0.0868. The method proposed has the advantages of high accuracy and strong robustness in solving the magnetic moment of the magnetic dipole array model.

Methane gas spectral imaging method based on dual wedge scanning mirrors

With the increase in the number of oil and gas pipelines laid in China, more attention needs to be paid to pipeline maintenance work. At present, the main methods of detecting natural gas leaks in oil and gas transmission stations include manual inspections, opposing natural gas detection equipment, and cloud desktop natural gas detection equipment. Hand held natural gas detection equipment is used for manual inspection, which requires regular manual inspection. However, the response speed is poor and gas leaks cannot be detected in a timely manner. The opposed laser gas detection method can only detect the presence of gas on the beam path. If a larger area of leakage detection is desired, more equipment needs to be installed, resulting in a greatly increase in hardware costs. The existing cloud desktop laser gas detection method controls the deflection of the laser beam through the cloud platform to achieve leak detection at various points in the area to be tested. However, the rotation speed of the cloud platform is slow, and a complete detection cycle takes dozens of minutes, and only the presence of gas can be detected. For accurate leak location, manual on-site survey is also required to further determine the leak location. In order to meet the needs of the real-time monitoring and rapid positioning of oil and gas pipeline leaks, in this work, a fast and accurately controlled dual wedge scanning mirror system is designed, which combines tunable semiconductor laser absorption spectroscopy technology to convert the gas measurement laser beam from point measurement to surface measurement, thereby obtaining the two-dimensional distribution of gas, which is conducive to subsequent analysis and positioning of gas leakage sources. By using the inverse solution iterative optimization algorithm, the angle of the wedge mirror is controlled to obtain an efficient and uniform beam scanning trajectory. The deflection direction and detection position of the laser beam are fused with the corresponding methane concentration information, and a methane concentration data containing position information is constructed. In order to quantitatively verify the measurement accuracy and spatial resolution in the experiment, a standard air bag is used to simulate the methane leakage distribution. The results show that the minimum detection limit of the system can be lower than 5×10&lt;sup&gt;–4&lt;/sup&gt; m, and the spatial resolution can be less than 6 cm. At the same time, this method can adjust the scanning step node based on the measurement distance of the oil from gas station, thereby achieving adjustable imaging resolution. This imaging method provides a new idea for accurately positioning and detecting the methane leakage location and amount.

Identification Localization and Gathering of Pepper Based on Depth Camera and Inverse Kinematics

Highlights The spatial coordinate position of peppers is obtained by YOLOv5 algorithm fused with localization technique. The inverse kinematics for gathering arm is solved by disassembly and Euler-angle method. Pentadic polynomials are applied to realize the motion planning and control of robotic arm. The proposed method achieves an average gathering success rate about 60%. Abstract. To avoid mutation and interference with intelligent gathering, an autonomous gathering method is proposed in this paper. An improved YOLOv5 target detection algorithm is used to recognize peppers. The kinematics solution of the robotic arm is realized by using the disassembly method and the Euler-angle method. Simulating and modeling robotic arms is conducted by the Robotic Toolbox in Matlab. The robotic arm's spatial motion planning is controlled by the pentadic polynomial interpolation method. The feasibility of the inverse solution and planning is verified in Matlab. Different conditions’ gathering experiments are conducted on the gathering platform. Experiments show that this method is smooth and interference-free, with a high gathering success rate, realizing the accurate gathering of single, small fruits in complex environments. Keywords: Robot gathering, Robotic arm inverse kinematics, Target detection, Trajectory planning

A Novel Method for Selecting Inverse Kinematic Solutions Based on Configuration Space Partition for 6R Noncuspidal Manipulators

A Novel Method for Selecting Inverse Kinematic Solutions Based on Configuration Space Partition for 6R Noncuspidal Manipulators

Hybrid Deep Learning and Sensitivity Operator-Based Algorithm for Identification of Localized Emission Sources

Hybrid approaches combining machine learning with traditional inverse problem solution methods represent a promising direction for the further development of inverse modeling algorithms. The paper proposes an approach to emission source identification from measurement data for advection–diffusion–reaction models. The approach combines general-type source identification and post-processing refinement: first, emission source identification by measurement data is carried out by a sensitivity operator-based algorithm, and then refinement is done by incorporating a priori information about unknown sources. A general-type distributed emission source identified at the first stage is transformed into a localized source consisting of multiple point-wise sources. The second, refinement stage consists of two steps: point-wise source localization and emission rate estimation. Emission source localization is carried out using deep learning with convolutional neural networks. Training samples are generated using a sensitivity operator obtained at the source identification stage. The algorithm was tested in regional remote sensing emission source identification scenarios for the Lake Baikal region and was able to refine the emission source reconstruction results. Hence, the aggregates used in traditional inverse problem solution algorithms can be successfully applied within machine learning frameworks to produce hybrid algorithms.

Physics-informed machine learning method with space-time Karhunen-Loève expansions for forward and inverse partial differential equations

We propose a physics-informed machine-learning method based on space-time-dependent Karhunen-Loève expansions (KLEs) of the state variables and the residual least-square formulation of the solution of partial differential equations. This method, which we name dPICKLE, results in a reduced-order model for solving forward and inverse time-dependent partial differential equations. By conditioning KLEs on data, dPICKLE seamlessly assimilates data in forward and inverse solutions. KLEs are linear in unknown parameters. Because of this, and unlike physics-informed deep-learning methods based on the residual least-square formulation, for well-posed partial differential equation (PDE) problems, dPICKLE leads to linear least-square problems (directly for linear PDEs and after linearization for nonlinear PDEs), which guarantees a unique solution. The efficiency and accuracy of dPICKLE are demonstrated for linear and nonlinear forward and inverse problems via comparison with analytical, finite difference, and physics-informed neural network (PINN) solutions.

Kinematics and Workspace Analysis of 5-DOF Hybrid Redundantly Driven Mechanism

A novel 5-DOF (5-SPS)+5R2U hybrid redun-dantly driven mechanism (HRDM for short) is proposed, which can realize 3 translations and 2 rotations (3T2R) movements. (5-SPS)+5R2U parallel mechanism is composed of six driving limbs. Of which 5-SPS (S represents spherical pair, P represents prismatic pair) limbs are symmetrically distributed at the center point of static and moving platform have no restriction on the degrees of freedom of the mechanism. The middle limb (7R)U (R represents revolute pair, U represents Hooke joint) is connected to the static platform and the center point of the moving platform. It is jointly driven by constant velocity motor and servo motor, and plays a role of restraining the freedom of the whole mechanism. It is called hybrid redundantly driven limb (HRDL for short). Hybrid-driven mechanism and redundantly actuated mechanism can be integrated into one mechanism by HRDL, which can give full play to the advantages of both. The inverse position solution model of the mechanism is established, and the velocity Jacobian matrix and acceleration expression are derived to obtain the velocity and acceleration variation laws of the me-chanism. On this basis, the factors affecting the workspace are analyzed, and the workspace atlas under different orientation angles is obtained. The results provide theoretical model for the realization planning trajectory of (5-SPS)+5R2U HRDM.

A method to calculate inverse solutions for steady open channel free-surface flow

The inverse problem of steady two-dimensional open channel free-surface flow is considered, with the focus on determining two types of disturbances: a surface pressure distribution and solid channel bottom topography. A closed-form expression for the inverse surface pressure is derived, and a linear Fredholm equation of the first kind is shown to describe the inverse topography problem, which then needs to be descretised and solved numerically. However, the equation for the channel bottom is prone to instability, so the truncated singular value decomposition (TSVD) method is proposed as a way to stabilise the associated discrete solution. The effectiveness of the TSVD method is demonstrated through several numerical examples, and its performance in the presence of error-contaminated input data is also examined. The results show that the TSVD method can recover the topography accurately from the forward free-surface problem, and provide good approximations even with noisy input data.

A Novel Inverse Algorithm To Solve the Integrated Optimization of Dose, Dose Rate, and Linear Energy Transfer of Proton FLASH Therapy With Sparse Filters

Purpose:The recently proposed Integrated Physical Optimization Intensity Modulated Proton Therapy (IPO-IMPT) framework allows simultaneous optimization of dose, dose rate, and linear energy transfer (LET) for FLASH treatment planning. Finding solutions to IPO-IMPT is difficult due to computational intensiveness. Nevertheless, an inverse solution that simultaneously specifies the geometry of a sparse filter and weights of a proton intensity map is desirable for both clinical and preclinical applications. Such solutions can reduce effective biological dose to organs at risk in cancer patients as well as reduce the number of animal irradiations needed to derive extra biological dose models in preclinical studies. Methods:Unlike the initial forward heuristic, this inverse IPO-IMPT solution includes simultaneous optimization of sparse range compensation, sparse range modulation, and spot intensity. The daunting computational tasks vital to this endeavor were resolved iteratively with a distributed computing framework to enable Simultaneous Intensity and Energy Modulation and Compensation (SIEMAC). SIEMAC was demonstrated on a human central lung cancer patient and a minipig. Results:SIEMAC simultaneously improves maps of spot intensities and patient-field-specific sparse range compensators and range modulators. For the lung cancer patient, at our maximum nozzle current of 300 nA, dose rate coverage above 100 Gy/s increased from 57% to 96% in the lung and from 93% to 100% in the heart, and LET coverage above 4 keV/μm dropped from 68% to 9% in the lung and from 26% to <1% in the heart. For a simple minipig plan, the full-width-half-maximum of the dose, dose rate, and LET distributions decreased by 30%, 1.6%, and 57%, respectively, again with similar target dose coverage, thus reducing uncertainty in these quantities for preclinical studies. Conclusion:The inverse solution to IPO-IMPT demonstrated the capability to simultaneously modulate sub-spot proton energy and intensity distributions for clinical and preclinical studies.

Fast Convergent Ali Baba and Forty Thieves Algorithm for Inverse Kinematic Solution of 7-DOF Robotic Manipulator

Inverse kinematics is a crucial topic in robotics, enabling robots to calculate the joint angles required to achieve the desired end effector position and orientation. Solving the inverse kinematics problem quickly with high accuracy is vital for robot manipulators. If sufficient speed is provided, the real-time motion planning task of robot manipulators can be achieved. Real-time motion planning of complex robot manipulators is not possible with classical mathematical methods. Overcoming this problem will provide many benefits in the design and control of robot manipulators. In contemporary research, metaheuristic approaches have become widely employed for addressing the inverse kinematics problem. This investigation utilizes the efficient and simple Ali Baba and the Forty Thieves (AFT) algorithm to resolve the inverse kinematics problem. To increase convergence speed of AFT, a parameter has been used in early iterations of the algorithm to prevent thieves from randomly searching within the search area to find Ali Baba when they realized they had been deceived. Additionally, an approach has been proposed regarding the accuracy of the information brought by the Marjaneh. Finally, the inverse kinematics solution of the 7-DOF robot manipulator was carried out comparatively.

Basis and applicability of noninvasive inverse electrocardiography: a comparison between cardiac source models.

The body surface electrocardiogram (ECG) is a direct result of electrical activity generated by the myocardium. Using the body surface ECGs to reconstruct cardiac electrical activity is called the inverse problem of electrocardiography. The method to solve the inverse problem depends on the chosen cardiac source model to describe cardiac electrical activity. In this paper, we describe the theoretical basis of two inverse methods based on the most commonly used cardiac source models: the epicardial potential model and the equivalent dipole layer model. We discuss similarities and differences in applicability, strengths and weaknesses and sketch a road towards improved inverse solutions by targeted use, sequential application or a combination of the two methods.

Localization of brain signals by alternating projection

A popular approach for modeling brain activity in MEG and EEG is based on a small set of current dipoles, where each dipole represents the combined activation of a local area of the brain. Here, we address the problem of multiple dipole localization with a novel solution called Alternating Projection (AP). The AP solution is based on minimizing the least-squares (LS) criterion by transforming the multi-dimensional optimization required for direct LS solution, to a sequential and iterative solution in which one source at a time is localized, while keeping the other sources fixed. Results from simulated, phantom, and human MEG data demonstrated the high accuracy of the AP method, with superior localization results than popular scanning methods from the multiple-signal classification (MUSIC) and beamformer families. In addition, the AP method was more robust to forward model errors resulting from head rotations and translations, as well as different cortex tessellation grids for the forward and inverse solutions, with consistently higher localization accuracy in low SNR and highly correlated sources.

Error compensation of a 2TPR&amp;2TPS parallel mechanism based on particle swarm optimization

This paper solves the problem of the precise compensation of the pose error of a 2TPR&amp;2TPS parallel mechanism. First, the inverse solution of the mechanism is solved, the error source of the mechanism is analyzed, and a closed-loop vector method error model based on the inverse solution is established. Then, the ball screw commutation gap is measured with a high-precision grating ruler, and a laser tracker is used to measure the comprehensive position error of the mechanism under the set trajectory (circle). Finally, an error compensation algorithm based on the particle swarm algorithm is constructed, the measured trajectory data are substituted into the compensation algorithm, the position accuracy of the mechanism is significantly improved, and the compensation effect is remarkable. The compensation algorithm has good versatility, is simple and feasible, and can be applied to the error compensation of various mechanisms.