Product Of Exponentials Research Articles

Industrial robot calibration optimization method based on R-optimal criterion and improved IOOPS algorithm

Abstract In this paper, a novel kinematic parameter calibration method based on the R-optimal criterion and the improved iterative one-by-one pose search (IOOPS) algorithm is proposed to improve the end-effector positioning accuracy of industrial robots. First, a novel industrial robot error calibration model based on the product of exponential model and generalized error model is established, and the ideal pose transformation matrix from the robot base coordinate system to the laser tracker measurement coordinate system is obtained using the least-squares method, thereby obtaining the initial parameter vector of the robot calibration system. Second, various joint angle values at different positions within the robot’s workspace and the corresponding end-effector coordinate data, namely calibration sampling point data, are collected. Subsequently, the improved IOOPS algorithm combined with the observability index O R proposed by the R-optimal criterion is used to select the optimized calibration sampling points. Finally, the optimized sampling point data are combined with the Levenberg–Marquardt algorithm to optimize the parameters and obtain the optimal kinematic parameters. The experimental results show that the average end-effector error of the robot decreases from 0.5822 to 0.2492 mm after calibration using this method, demonstrating the effectiveness of the optimized sampling points in the calibration process achieved through the improved algorithm and the new observability index.

Enhancing protein signal detection in asexual and viviparous pea aphids: A guided protocol for tissue dissection and proteinase K treatment

Aphids, as hemipteran insects, reproduce via parthenogenesis and viviparity, resulting in rapid and exponential offspring production. To investigate the molecular mechanisms underlying parthenogenetic viviparity in asexual aphids, precise protein detection through immunostaining is essential. Our previous research demonstrated the need for proteinase K (PK) treatment to improve tissue permeability, enabling antibodies targeting the germ-cell marker Ap-Vas1 to access gastrulating and later-stage embryos. However, optimal PK digestion protocols have not been thoroughly explored. In this study, we propose strategies to optimize PK digestion conditions for early, middle, and late-stage pea aphid embryos, which have varying tissue thicknesses. Additionally, we extend the application of PK treatment to salivary glands, a representative somatic tissue, by optimizing conditions for antibody penetration against the salivary gland marker C002. To enhance spatial precision in signal detection, we provide a detailed protocol for tissue dissection specific to pea aphids, focusing on the preservation of tissue integrity. These comprehensive guidelines, covering tissue dissection and PK titration, are expected to improve the specificity and intensity of protein signals in pea aphids and other aphid species.•Provide aphid-specific dissection methods to obtain intact embryos and salivary glands.•Present strategies for optimizing PK treatment conditions across different tissue types.

Robot Calibration Sampling Data Optimization Method Based on Improved Robot Observability Metrics and Binary Simulated Annealing Algorithm

As the societal demand for precision in industrial robot operations increases, calibration can enhance the end-effector positioning accuracy of robots. Sampling data optimization plays an important role in improving the calibration effect. In this study, a robot calibration sampling point optimization method based on improved robot observability metrics and a Binary Simulated Annealing Algorithm is proposed. Initially, a robot kinematic model based on the Product of Exponentials (POE) model and a generalized error model is established. By utilizing the least squares method, the ideal pose transformation relationship between the robot’s base coordinate system and the laser tracker measurement coordinate system is derived, resulting in an error calibration model based on spatial single points. An improved robot observability metric combined with the Binary Simulated Annealing Algorithm (BSAA) is introduced to optimize the selection of calibration sampling data. Finally, the robot’s parameter errors are obtained using a nonlinear least squares method. Experimental results demonstrate that the average end-effector positioning error of the robot after calibration can be reduced from 0.356 mm to 0.254 mm using this method.

Growth, profitability, nutritional, and anti-nutritional properties of seven Manihot esculenta Crantz (cassava) varieties as affected by arbuscular mycorrhizal fungi

Despite a range of methods used to promote modern agriculture with several outcomes, food quality and availability problems remain. This work aims to evaluate the effect of AM fungi inoculation on the growth, yield, nutritional, and antinutritional properties of 7 varieties of cassava. Growth characteristics, yields, rentability, nutritional, and antinutritional of tubers of each treatment were determined at harvest. All the cassava varieties used form a symbiosis with AM fungi at various frequencies, with the I090590 variety being the best (61.66 %). The best amount of chlorophyll, carotenoid, and height of plants were recorded at 9 months old. The 96/1414, TME/693 and MD varieties respectively show the best amount of chlorophyll, size, and carotenoids at 9 months old. Following AM fungi inoculation, an increase in the content of chlorophyll, size, and carotenoids was recorded for all the varieties with the best rate attributed respectively to 92/0326, MD, and 92/0326. Tuber yields vary significantly depending on the cassava varieties, with the best (56.16 t/ha) recorded for the I090590 variety. Following inoculation with AM fungi, a significant increase in yields was recorded, with the best ratio (2.7) obtained with the AE variety. The I090590 variety shows the best yield and by then the most profitable. Inoculation with AM fungi leads to a significant increase in the sugar, protein, fibre, and phosphorus content of all cassava varieties, with the best ratios obtained in 96/1414, 01/1797, and I090590 varieties respectively. Similarly, the inoculation of cassava varieties with AM fungi leads to a significant reduction in the content of cyanides, oxalates, and phytates. The best ratio of reduction for cyanide was 1.91 for the MD variety. AM fungi inoculation is an important way to ensure safe, exponential production and high economic profitability of foodstuffs.

Hip joint motion amplitude control based on exponential product formula

Background: Handball is a team sport, and during a game, there is a lot of direct squabbling and close contact between the players. Objective: The goal of the research is to determine how handball training affected several aspects of physical fitness. The study also investigates the relationship between playing handball, passive hip range of motion (ROM), and the development of radiologically detectable hip osteoarthritis (OA) in formerly elite handball players. The research employed the exponential product algorithm for evaluating bilateral radiographs to classify and diagnose hip OA. This technique most likely evaluated subchondral sclerosis, osteophyte formation, joint space narrowing, and other radiological signs of OA in the individuals’ hip joints. Methods: The relationship among the risk of hip OA in long-term top handball players is explored, as well as the connections among hip ROM, OA, and pain. The research was conducted using a sample size of 20 ex-professional handball players and 39 control subjects. Information on demographics, loading patterns during exercise, and history of lower limb joint injury were gathered via a questionnaire. The inclusion criteria for individuals consisted former professional handball players with significant elite-level competitive experience, as well as control subjects with no background of high-impact sports. Confounding characteristics such as age, gender, and previous lower limb joint injuries were carefully controlled for using extensive demographic and injury history evaluations. To identify and categorize hip OA, bilateral radiographs were analyzed using the exponential product algorithm. The goniometer was used to assess the bilateral passive hip ROM. Long-term participation in elite handball at a high level was found to have a strong correlation with the hip development of osteoarthritis (OA). Sixty percent of handball players had been identified with OA in at least one hip joint, compared to only thirteen percent of control patients. Results: Hip flexion and medial rotation in the handball players were significantly decreased, whereas abduction, extension, and lateral rotation were increased considerably compared to the control values. When doing daily activities, the hip joints of the handball players with OA were less painful than those of the OA-afflicted control participants. Retired handball players seem to be at a much higher risk than the general population for developing early hip OA. Conclusion: The repetitive nature of handball-specific movements may result in anomalies that are seldom seen in the general population, which makes diagnosing pain and discomfort a challenging diagnostic challenge for sports physicians.

Room Temperature Efficient Regeneration of Spent LiFePO4 by Direct Chemical Lithiation

The exponential production of lithium-ion batteries for electric vehicles (EVs) and electronic applications leads to the creation of a huge stock of batteries at the end of life. Considering the current economic, geopolitical and environmental context, the recycling of these spent batteries is becoming an urgent need in order to mitigate environmental pollution and limit the waste of valuable and critical resources1.In this work, we report a rewarding direct recycling process of spent LiFePO4 cathode material by direct chemical lithiation in solution2. After safe opening of the spent commercial battery, a structural, morphological, spectroscopic and electrochemical characterization of the spent LFP cathode was carried out to identify the reason(s) of battery failure. The results obtained by XRD (Fig 1a) and Mössbauer spectroscopy (Fig 1b) show that the loss of lithium in the cathode (up to 50%) consumed during formation and growth of the SEI during cycling, is the major reason of the end of life of these batteries, in total agreement with the literature3.To address the lithium shortage problem, a recycling process via direct chemical lithiation in organic solution at room temperature of the LFP cathode has been implemented. Lithium iodide (LiI) dissolved in several solvents such as acetonitrile, cyclohexane, ethanol, DMSO, methanol and propan-1,2-diol was used as both the reductant and the lithiation agent. The best results were obtained with the cathode regenerated in ethanol, which is also the most captivating and environmentally friendly solvent. The different characterizations of this regenerated cathode allow evaluating the efficiency of the regeneration process. Mössbauer spectroscopy (Fig. 2a) confirms the total reduction of FeIIIPO4 to LiFeIIPO4, while electrochemical characterization (Fig. 2b) shows encouraging properties with a reversible capacity of ~168 mAh/g for the regenerated LFP.

Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond

A thermal interpretation of the stochastic formalism of a slow-rolling scalar field in de Sitter (dS) is given. We construct a correspondence between Hubble patches of dS and particles living in another space called an abstract space. By assuming a dual description of scalar fields and classical mechanics in the abstract space, we show that the stochastic evolution of the infrared part of the field is equivalent to the Brownian motion in the abstract space filled with a heat bath of massless particles. The 1st slow-roll condition and the Hubble expansion are also reinterpreted in the abstract space as the speed of light and a transfer of conserved energy, respectively. Inspired by this, we sketch quantum emergent particles, which may realize the Hubble expansion by an exponential particle production. This gives another meaning of dS entropy as entropy per Hubble volume.

The energy-critical metals: technologies with a human face

The importance of energy-transition issues was poignantly summarised in 1973, by economist Ernst Schumacher (Schumacher 1973, p. 99): ‘ energy is for the mechanical world what consciousness is for the human world. If energy fails, everything fails .’ Schumacher's words have ever greater societal relevance since his cautionary predictions are now manifested, after half a century of the Great Acceleration (Steffen et al. 2015) in energy use, population increase and global warming. Schumacher (1973) regarded natural resources as valuable Earth materials, pivotal to the transition from coal to natural gas and uranium fuel productions. The World Economic Forum promotes energy transitions and their associated technological innovation clusters as part of the Fourth Industrial Revolution (Prisecaru 2016; Philbeck and Davis 2018). But if we take Schumacher's approach of putting valuable Earth materials at the heart of debates about economy, there is scant evidence of revolution. Instead, we see graphs of exponential production of an increasing array of raw materials, whether they are described as bulk metals or critical raw materials, and geoscientists are repeatedly required to identify the geological capacity for raw materials production (Konnunaho et al. 2023; Moore et al. 2023; Savinova et al. 2023; Valenta et al. 2023; Gardiner et al. 2024).

A multi-stage exponential production model for the assessment of China’s regional electric power supply chain efficiency: Does digital innovation matter?

A multi-stage exponential production model for the assessment of China’s regional electric power supply chain efficiency: Does digital innovation matter?

POE-Based Error Modeling and Multiple Plane Constraint-Based Parameter Identification for the Kinematic Calibration of a 4-UPS/SPR Parallel External Fixator

Limb deformity is a common complaint in orthopedic surgery. Currently, gradual treatment using parallel external fixator (PEF) has become the preferred option for deformity correction. As the key medical apparatus with the special application properties of temporary assembly and direct utilization, the geometric errors generated during the manufacturing and assembly process of the PEF contribute to the post-correction residual and iatrogenic deformities. However, considering the complexity of clinical scenarios, there is a lack of an applicable solution to reduce the effect of the above error source of PEF. To overcome these problems, taking a 4-UPS/SPR PEF as the research object, this paper proposes a novel kinematic calibration method. First, the error model with the features of completeness, continuity, and minimality is first established based on the product of exponentials (POE) formula. Then, the identifiability analysis is conducted to eliminate the redundant error parameters and ensure the stability and accuracy of the iterative calculation in the process of parameter identification. Furthermore, a multiple plane constraint (MPC)-based parameter identification approach is introduced to the calibration task of the PEF to effectively reduce the difficulty of the pose information measurement in the current cost-effective constraint calibration method. Finally, the simulation and prototype experiments validate that the proposed calibration method (i.e., the combination of the POE-based error model and the MPC-based parameter identification approach) can accomplish the calibration tasks in clinical applications and meet the cost-effectiveness and efficiency requirements.

Phosphorylations and Acetylations of Cytochrome c Control Mitochondrial Respiration, Mitochondrial Membrane Potential, Energy, ROS, and Apoptosis.

Cytochrome c (Cytc) has both life-sustaining and cellular death-related functions, depending on subcellular localization. Within mitochondria, Cytc acts as a single electron carrier as part of the electron transport chain (ETC). When released into the cytosol after cellular insult, Cytc triggers the assembly of the apoptosome, committing the cell to intrinsic apoptosis. Due to these dual natures, Cytc requires strong regulation by the cell, including post-translational modifications, such as phosphorylation and acetylation. Six phosphorylation sites and three acetylation sites have been detected on Cytc in vivo. Phosphorylations at T28, S47, Y48, T49, T58, and Y97 tend to be present under basal conditions in a tissue-specific manner. In contrast, the acetylations at K8, K39, and K53 tend to be present in specific pathophysiological conditions. All of the phosphorylation sites and two of the three acetylation sites partially inhibit respiration, which we propose serves to maintain an optimal, intermediate mitochondrial membrane potential (ΔΨm) to minimize reactive oxygen species (ROS) production. Cytc phosphorylations are lost during ischemia, which drives ETC hyperactivity and ΔΨm hyperpolarization, resulting in exponential ROS production thus causing reperfusion injury following ischemia. One of the acetylation sites, K39, shows a unique behavior in that it is gained during ischemia, stimulating respiration while blocking apoptosis, demonstrating that skeletal muscle, which is particularly resilient to ischemia-reperfusion injury compared to other organs, possesses a different metabolic strategy to handle ischemic stress. The regulation of Cytc by these post-translational modifications underscores the importance of Cytc for the ETC, ΔΨm, ROS production, apoptosis, and the cell as a whole.

Estimation of heterogeneous population variance using memory-type estimators based on EWMA statistic in the presence of measurement error for time-scaled surveys

In this present article, we have suggested memory-type ratio, exponential ratio, product and exponential product estimators based on exponentially weighted moving average statistic for the estimation of heterogeneous population variance using stratified sampling design in presence of measurement error for time-scaled surveys. Mathematical expressions of approximate mean square error are derived using Taylor and exponential expansions for the proposed memory-type estimators. We have also discussed the situations in which the memory-type estimators would perform efficiently than the conventional estimators. The results of extensive simulation study revealed that the proposed memory-type estimators based exponentially weighted moving average statistic would perform better than the conventional estimators in the presence measurement error for time-scaled surveys under certain condition.

High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach

This paper proposes a framework for constructing high-order linearly implicit exponential integrators that conserve a quadratic invariant. This is then applied to the scalar auxiliary variable (SAV) approach. Quadratic invariants are significant objects that are present in various physical equations and also in computationally efficient conservative schemes for general invariants. For instance, the SAV approach converts the invariant into a quadratic form by introducing scalar auxiliary variables, which have been intensively studied in recent years. In this vein, Sato et al. (Appl. Numer. Math. 187, 71-88 2023) proposed high-order linearly implicit schemes that conserve a quadratic invariant. In this study, it is shown that their method can be effectively merged with the Lawson transformation, a technique commonly utilized in the construction of exponential integrators. It is also demonstrated that combining the constructed exponential integrators and the SAV approach yields schemes that are computationally less expensive. Specifically, the main part of the computational cost is the product of several matrix exponentials and vectors, which are parallelizable. Moreover, we conduct some mathematical analyses on the proposed schemes.

Kinematic Calibration of an Industrial Manipulator without External Measurement Devices

This paper presents a practical approach to fully automated kinematic calibration of an industrial manipulator. The approach is based on the principle of plane constraint. The electrical signal is used to fix the moment of contact between the conductive tool and the flat surface. The measurement data are manipulator configurations (joint angles) at the moment of contact. A modification of the algorithm to deal with the scaling problem is also proposed. This approach provides both high calibration accuracy and lower cost of the experimental setup compared to coordinate measuring machines (CMMs), laser trackers, and vision systems. The article examines the impact of various methods of kinematic parameterization of manipulators: the Denavit – Hartenberg agreement (DH), product of exponentials (POE), as well as the complete and parametrically continuous model (CPC) on the calibration accuracy. A comparison is made of the open-loop and the proposed closed-loop calibration methods on the Puma 560 model known in the literature. POE parameters were converted to DH and CPC to compare accuracy after calibration based on these parameterizations. The method of computing POE-CPC transformation as a solution to a certain optimization problem is proposed. The problem of identifying geometric parameters in the presence of restrictions is solved by gradient optimization methods. Experiments have been carried out on an ABB IRB 1600 industrial manipulator with an installed conductive probe and an ABB IRBP A-500 robotic positioner with a conductive metal flat surface. A technique for indirectly checking the accuracy of calibration of kinematic parameters is proposed based on a study of the accuracy of manipulation when using these parameters.

Validity and error analysis of calculating matrix exponential function and vector product

Validity and error analysis of calculating matrix exponential function and vector product

EFR Empirical Brilliance in Employment Strategies: Orchestrating Firm Stature, Exquisite Labor Proficiency, and Exponential Productivity in Confluence with Discerning Leverage and Enriched FDI Share

This study endeavors to scrutinize the veracity of Gibrat's law pertaining to the expansion of firms at the micro-level and explores the determinants of firms’ growth by employing datasets from emerging nations from 2004 to 2021. The study used panel unit root tests to scrutinize stationarity and system GMM to tackle endogeneity and unobserved heterogeneity. Overall, the findings of this study provide empirical support for Gibrat's law in the context of privatized banks in developing nations. Furthermore, the outcomes indicate that globalization and integration have posed considerable challenges for firms seeking to grow in developing countries that have implemented privatization policies. These conclusions suggest that certain elements, apart from size and sector growth, play a significant role in the evolution of a firm's growth trajectory. Nonetheless, the scope of this study is restricted to the evaluation of privatized banks in developing countries, and it does not delve into the specific methods of privatization utilized. Future research should explore diverse cohort sizes and expand the literature to address micro-level intricacies.

Trends in Production of Pulses and Oilseeds Over Last Two Decades in Eastern India

"India is a major producer and consumer of a wide variety of pulses and oilseeds but still struggles to achieve self-sufficiency due to the growing disparity between demand and supply. The present study has made an attempt to compare and disseminate trends in acreage, production, and productivity of pulses and oilseeds over the last two decades (1999-2000 to 2018-2019). Regarding the computation of growth and instability, a modified exponential production function is fitted, and to judge the overall change in production, a decomposition of the trend in area and yield over two decades has been performed. Bihar and West Bengal stand out as the primary producers of pulses, while rapeseed and mustard take the lead among oilseed crops, followed by sesame. Odisha uniquely contributes to groundnut production, while linseed has become integral to West Bengal’s overall oilseeds output. To enhance production in these states, implementing HYV seeds, proper land preparation techniques, and adopting paira cropping in rice-fallow situations can significantly boost the current status of pulses and oilseeds in the eastern India."

Efficient Kinematic Calibration for Articulated Robot Based on Unit Dual Quaternion

Removing the parameter redundancy in the kinematic error model does improve the robustness of parameter identification. However, this does not help much on saving the calculation time on the error compensation process, which is closely related to the data structure used for representing rigid-body motion. Compared with the homogenous transformation matrix (HTM), the unit dual quaternion (UDQ) can describe the rigid-body motion in term of an array with eight entries, thus it is a conducive data structure for efficient kinematic computation. In this work, the exponential and logarithm mappings of a UDQ are defined explicitly, so that the relationship between finite and instantaneous motions is set up under the exponential coordinate. Thereafter, by defining the adjoint operator of UDQ to transform the twist under different frames, the linearized kinematic error models are built with local product-of-exponentials (POE) formula. This facilitates the upcoming parameter identification and error compensation processes. Specially, the counts of elementary operations are evaluated throughout the compensation processes, which shows the number of arithmetic operations are greatly reduced compared with using POE formula based on HTM. Additionally, the simple data structure in term of 1-D arrays saves the data dispatch time when performing adjoint operations. These make the developed model suitable for calibration of articulated robot with a long sequence of trajectories. Experiments on a 6-degree-of-freedom industrial robot validate the effectiveness of proposed approach.

Construction of acceptance sampling schemes for exponential lifetime products with progressive type II right censoring

Ensuring product quality is crucial for enhancing a company's competitiveness, and product lifetime serves as a vital metric, particularly in the context of electronic goods, for evaluating product quality. To meet quality requirements and mitigate risks for both producers and consumers, thorough examinations of components and final products are necessary. Acceptance sampling plans are commonly employed to achieve these objectives. When assessing product lifetime under non-normal distributions, the lifetime performance index emerges as a valuable and frequently utilized metric. In practical scenarios, lifetime tests may encounter challenges such as the absence of experimenters to observe all product lifetimes and the possibility of accidental product breakage. To address these issues, this study introduces two sampling schemes: a single sampling plan and a repetitive group sampling plan. These plans are specifically designed for exponential lifetime products, utilizing the progressively type II right censored sample as the data type for lifetime testing. The study provides tabulated plan parameters for practical implementation and presents a comparative analysis between the two proposed plans. Furthermore, a practical example is presented to demonstrate the efficacy of the developed sampling plans.

Applying Screw Theory to Design the Turmell-Bot: A Cable-Driven, Reconfigurable Ankle Rehabilitation Parallel Robot

The ankle is a complex joint with a high injury incidence. Rehabilitation Robotics applied to the ankle is a very active research field. We present the kinematics and statics of a cable-driven reconfigurable ankle rehabilitation robot. First, we studied how the tendons pull mid-foot bones around the talocrural and subtalar axes. We proposed a hybrid serial-parallel mechanism analogous to the ankle. Then, using screw theory, we synthesized a cable-driven robot with the human ankle in the closed-loop kinematics. We incorporated a draw-wire sensor to measure the axes’ pose and compute the product of exponentials. We also reconfigured the cables to balance the tension and pressure forces using the axis projection on the base and platform planes. Furthermore, we computed the workspace to show that the reconfigurable design fits several sizes. The data used are from anthropometry and statistics. Finally, we validated the robot’s statics with MuJoCo for various cable length groups corresponding to the axes’ range of motion. We suggested a platform adjusting system and an alignment method. The design is lightweight, and the cable-driven robot has advantages over rigid parallel robots, such as Stewart platforms. We will use compliant actuators for enhancing human–robot interaction.