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Simultaneous Localization and Mapping (SLAM) is the foundation of autonomous navigation for unmanned systems. The existing SLAM solutions are mainly divided into the visual SLAM(vSLAM) equipped with camera and the lidar SLAM equipped with lidar. However, pure visual SLAM have shortcomings such as low positioning accuracy, the paper proposes a visual-inertial information fusion SLAM based on Runge-Kutta improved pre-integration. First, the Inertial Measurement Unit (IMU) information between two adjacent keyframes is pre-integrated at the front-end to provide IMU constraints for visual-inertial information fusion. In particular, to improve the accuracy in pre-integration, the paper uses the Runge-Kutta algorithm instead of Euler integral to calculate the pre-integration value at the next moment. Then, the IMU pre-integration value is used as the initial value of the system state at the current frame time. We combine the visual reprojection error and imu pre-integration error to optimize the state variables such as speed and pose, and restore map points' three-dimensional coordinates. Finally, we set a sliding window to optimize map points' coordinates and state variables. The experimental part is divided into dataset experiment and complex indoor-environment experiment. The results show that compared with pure visual SLAM and the existing visual-inertial fusion SLAM, our method has higher positioning accuracy.

Laboratory experiments were performed to study the impact of the relative particle protrusion P/D (P is the protrusion height and D is the diameter of the target particle) on the mechanism of entra...

Localisation is an important part of many applications. Our motivating scenarios are short-term construction work and emergency rescue. These scenarios also require rapid setup and robustness to environmental conditions additional to localisation accuracy. These requirements preclude the use of many traditional high-performance methods, e.g. vision-based, laser-based, Ultra-wide band (UWB) and Global Positioning System (GPS)-based localisation systems. To overcome these challenges, we introduce iMag+, an accurate and rapidly deployable inertial magneto-inductive (MI) mapping and localisation system, which only requires monitored workers to carry a single MI transmitter and an inertial measurement unit in order to localise themselves with minimal setup effort. However, one major challenge is to use distorted and ambiguous MI location estimates for localisation. To solve this challenge, we propose a novel method to use MI devices for sensing environmental distortions for accurate closing inertial loops. We also suggest a robust and efficient first quadrant estimator to sanitise the ambiguous MI estimates. By applying robust simultaneous localisation and mapping (SLAM), our proposed localisation method achieves excellent tracking accuracy and can improve performance significantly compared with only using a Magneto-inductive device or inertial measurement unit (IMU) for localisation.

For the considered reaction-diffusion inertial memristive neural networks (IMNNs), this article proposes a novel gain-scheduled generalized pinning control scheme, where three pinning control strategies are involved and 2ⁿ controller gains can be scheduled for different system parameters. Moreover, a time delay is considered in the controller to make it has a memory function. With the designed controller, drive-and-response systems can be synchronized within a finite-time interval. Note that the final finite-time synchronization criterion is obtained in the forms of linear matrix inequalities (LMIs) by introducing a memristor-dependent sign function into the controller and constructing a new Lyapunov-Krasovskii functional (LKF). Furthermore, by utilizing some improved integral inequality methods, the conservatism of the main results can be greatly reduced. Finally, three numerical examples are provided to illustrate the feasibility, superiority, and practicability of this article.

This paper presents a non-smooth multibody dynamic formulation and error analysis of an antenna pointing mechanism including frictional spatial revolute joints (FSRJs) with small clearance in the framework of the special Euclidian group SE(3). The formulation leads to an inertial frame-invariant, a compact and unified description for rigid bodies and spatial revolute joints (SRJs). The geometric constraint of the bearing is covered by four open semi-cylinders, which can be treated as bilateral constraints assuming that the impact effects are negligible. The frictional contact problem is formulated as a horizontal linear complementary problem (HLCP), which is embedded in the Lie-group integration scheme. Error of the antenna pointing mechanism is modeled by means of the adjoint transformation and POE-based formula. The evolution of errors is obtained through the solution of non-smooth dynamics. The obtained numerical results illustrate the influences of FSRJs in dynamics modeling and error analysis of the antenna pointing mechanism.

This article explores the exponential stabilization issue of a class of state-based switched inertial complex-valued neural networks with multiple delays via event-triggered control. First, the state-based switched inertial complex-valued neural networks with multiple delays are modeled. Second, by separating the real and imaginary parts of complex values, the state-based switched inertial complex-valued neural networks are transformed into two state-based switched inertial real-valued neural networks. Through the variable substitution method, the model of the second-order inertial neural networks is transformed into a model of the first-order neural networks. Third, an event-triggered controller with the transmission sequence is designed to study the exponential stabilization issue of neural networks constructed above. Then, by constructing the Lyapunov functions and based on some inequalities, we obtain sufficient conditions for exponential stabilization of the proposed neural networks. Furthermore, it is proved that the Zeno phenomenon cannot happen under the designed event-triggered controller. Finally, a simulation example is given to illustrate the correctness of the results.

It is difficult to obtain linear output displacements for stepping piezoelectric platform due to their discontinuous outputs. Inspired by the theory that the maximum static friction force is greater than the sliding friction force, this letter proposed a bipedal alternating inertial actuation mode (BAIAM) to improve the displacement linearity of stepping platform. The output displacements are measured, the linear fitting is carried out by the least square method, the correlation coefficient and linear fitting function are used to evaluate the displacement linearity, the correlation coefficients of the forward and backward motions are calculated as 0.9998 and 0.9999 in BAIAM, respectively, which verifies the effectiveness of the proposed method. Closed-loop experiments in BAIAM are also carried out, the steady state errors for target position of 40 m within 0.2 m in the point-to-point positioning control experiments are achieved. The experiment results confirm that the developed platform can be applied in precision fields requiring large travel range, planar two-DOF motion and linear outputs.

The force-generation mechanism of a dovelike flapping-wing micro air vehicle was studied by numerical simulation and experiment. To obtain the real deformation pattern of the flapping wing, the digital image correlation technology was used to measure the dynamic deformation of the wing. The dynamic deformation data were subsequently interpolated and embedded into the CFD solver to account for the aeroelastic effects. The dynamic deformation data were further used to calculate the inertial forces by regarding the wing as a system of particles to take into account the wing flexibility. The temporal variation of the forces produced by the flapping wing was measured by a miniature load cell. The numerical results provide more flow details of the unsteady aerodynamics of the flapping wing in terms of vortex formation and evolution. The calculated results of the inertial forces are analyzed and compared with the CFD results which represent the aerodynamic forces. In addition, the total forces, i.e., the sum of the CFD result and inertial result, are compared with the experimental results, and an overall good agreement is obtained.

Foot-mounted inertial navigation with zero velocity update (ZUPT) is commonly used in pedestrian positioning.To suppress the accumulating position error owing to the low-cost inertial sensor,classical dual-foot pedestrian navigation method provides the compensation using the two feet's relative step length,whose values can be set an upper bound constraint or measured by ranging sensors.However,it suffers from low improvement and poor wearability.In this study,the two sensors are distributed on the toe and ankle of the same leg.The sensor-to-sensor position is unchangeable with the lower limb segments.This makes the uncoupled two subsystems be related.Through gait analysis,the step is divided into the stance and swing phases.For each phase,positions,velocities,and the related characteristics of the toe and the ankle are analyzed and modeled,respectively.A Kalman filter is constructed to fuse the position and velocity observations according to the geometric constraints and the foot vector.The Mahony filter by fusing the inertial sensor and magnetometer is adopted for the attitude improvement.Several experiments at low and high walking velocities on the plane and upstairs are carried out to verify the proposed method.The results show that compared with the conventional single-IMU ZUPT and dual-IMU two-foot constraint methods,the position and heading errors have been well suppressed.

This paper proposes to use a newly-derived transformed inertial navigation system (INS) mechanization to fuse INS with other complementary navigation systems. Through formulating the attitude, velocity and position as one group state of group of double direct spatial isometries SE2(3), the transformed INS mechanization has proven to be group affine, which means that the corresponding vector error state model will be trajectory-independent. In order to make use of the transformed INS mechanization in inertial based integration, both the right and left vector error state models are derived. The INS/GPS and INS/Odometer integration are investigated as two representatives of inertial based integration. Some application aspects of the derived error state models in the two applications are presented, which include how to select the error state model, initialization of the SE2(3) based error state covariance and feedback correction corresponding to the error state definitions. Extensive Monte Carlo simulations and land vehicle experiments are conducted to evaluate the performance of the derived error state models. It is shown that the most striking superiority of using the derived error state models is their ability to handle the large initial attitude misalignments, which is just the result of log-linearity property of the derived error state models. Therefore, the derived error state models can be used in the so-called attitude alignment for the two applications. Moreover, the derived right error state-space model is also very preferred for long-endurance INS/Odometer integration due to the filtering consistency caused by its less dependence on the global state estimate.

The H∞ state estimation issue for switched delayed inertial neural networks is addressed in this work. A more universal switching law, persistent dwell-time (DT) switching law, is considered here rather than average DT one of which switching frequency among subsystems is strictly limited, or DT one. Concurrently, time delays are inevitable when transmitting information, then taking the time-varying delays into account makes the constructed systems conform well with the actual situations. The main goal in the work is devoted to designing a state estimator to ensure that the state estimation error system is globally uniformly exponentially stable and satisfies a prescribed H∞ noise attenuation level. A mixed time/mode-dependent Lyapunov-Krasovskii functional matched with the foregoing switching law is introduced. Through utilizing some reasonable inequalities and common matrix operations, some sufficient criteria which guarantee the aforesaid stability and the solvability of the addressed issue are presented. Finally, an illustrative example is provided to present the potentiality and validity of the developed results.

Inertial Navigation System/Celestial Navigation System (INS/CNS) integration, especially for the tightly-coupled mode, provides a promising autonomous tactics for Hypersonic Vehicle (HV) in military demands. However, INS/CNS integration is a challenging research task due to its special characteristics such as strong nonlinearity, non-additive noise and dynamic complexity. This paper presents a novel nonlinear filtering method for INS/CNS integration by adopting the emerging Cubature Kalman Filter (CKF) to handle the strong INS error model nonlinearity caused by HV’s high dynamics. It combines the state-augmentation technique into the nonlinear CKF to decrease the negative effect of non-additive noise in inertial measurements. Subsequently, a technique for the detection of dynamic model uncertainty is developed, and the augmented CKF is modified with fading memory to tackle dynamic model uncertainty by rigorously deriving the fading factor via the theory of Mahalanobis distance without artificial empiricism. Simulation results and comparison analysis prove that the proposed method can effectively curb the adverse impacts of non-additive noise and dynamic model uncertainty for inertial measurements, leading to improved performance for HV navigation with tightly-coupled INS/CNS integration.

This article tackles the global exponential stability for a class of delayed complex-valued inertial neural networks in a discrete-time form. It is assumed that the activation function can be separated explicitly into the real part and imaginary part. Two methods are employed to deal with the stability issue. One is based on the reduced-order method. Two exponential stability criteria are obtained for the equivalent reduced-order network with the generalized matrix-measure concept. The other is directly based on the original second-order system. The main theoretical results complement each other. Some comparisons with the existing works show that the results in this article are less conservative. Two numerical examples are given to illustrate the validity of the main results.

This article focuses on the solution to the coordinated formation problem of heterogeneous vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) in the presence of parametric uncertainties. In particular, their inertial parameters are distinct and unavailable. For the sake of the accomplishment of the coordinated formation objective of multiple underactuated VTOL UAVs through local information exchange, an adaptive distributed control algorithm is developed under a cascaded structure. Specifically, by introducing an immersion and invariance (I&I) adaption strategy for the exponential mass estimation, a distributed command force is first synthesized in the position loop. Next, an applied torque with adaption is synthesized for the attitude tracking to a command attitude. This command attitude, as well as the applied thrust, is extracted from the synthesized command force without singularity. It is shown in terms of the Lyapunov theory that driven by the proposed adaptive distributed control algorithm, the concerned coordinated formation control of multiple VTOL UAVs is achieved asymptotically. Finally, an illustrative example is simulated to validate the effectiveness of the proposed control algorithm.

This paper deals with the simultaneous estimation of the attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on $SO(3)\times \mathbb{R}^{15}$ relying on body-frame acceleration, angular velocity and (stereo or monocular) bearing measurements of some landmarks that are constant and known in the inertial frame. Unlike the existing local Kalman-type observers, our proposed nonlinear observer guarantees almost global asymptotic stability and local exponential stability. A detailed uniform observability analysis has been conducted and sufficient conditions are derived. Moreover, a hybrid version of the proposed observer is provided to handle the intermittent nature of the measurements in practical applications. Simulation and experimental results are provided to illustrate the effectiveness of the proposed state observer., Accepted for publication in IEEE Transaction on Automatic Control. 16 pages, 6 figures

Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the gyroscope signal but is subject to a fundamentally numerical stability problem due to the Runge effect on equispaced samples. This paper reviews the theoretical results of Runge phenomenon in related areas and proposes a straightforward borrowing-and-cutting (BAC) strategy to depress it. It employs the neighboring samples for higher-order polynomial interpolation but only uses the middle polynomial segment in the actual time interval. The BAC strategy has been incorporated into attitude computation by functional iteration, leading to accuracy benefit of several orders of magnitude under the classical coning motion. It would potentially bring significant benefits to the inertial navigation computation under sustained dynamic motions., 9 pages, 8 figures

Insertion into delicate tissue, such as retina vein occlusion, cell manipulation and vitreoretinal injection, poses challenges to surgeons and biomedical researchers due to the high resolution, large movement range, compact structure and multi-DOF output requirements. In order to meet these requirements, a 2-DOF arched needle insertion device driven by inertial piezoelectric actuator was proposed in this work. This device could perform theoretical unlimited translational movement and full rotation with high step resolution. A prototype was fabricated with compact structure, the length and diameter were 230 mm and 32 mm, respectively. The experimental tests were carried out, the insertion device output 2.47 m and 0.56 mrad step distance with maximum velocity of 382 m/s and 200.9 mrad/s under 120 V driving signals, the maximum insertion force of 32 mN was measured. Additionally, a handheld controller with friendly user interface was also developed for open-loop control utilization, which could automatically calculate and generate the required control signals according to the motion command. This device explores the biomedical application of inertial piezoelectric actuator within a compact size, providing a new choice for numerous innovative treatment and biological research involving precision operation.

A piezoelectric stick slip actuator with the inertial block structure is presented in an attempt to achieve smooth motion. Under asymmetric excitation, the inertial block produces different inertia, which can dynamically change the normal pressure between the stator and rotor to adjust the friction. During the slip stage, the driving arm produces a deflection away from the rotor, the normal pressure between the stator and rotor can be eliminated, and the angular impulse of the moment of friction force on the rotor can be almost reduced to zero. To verify the feasibility of the prototype, finite element method (FEM) simulation is performed. On the basis of the experimental system, the output characteristics of the prototype are systematically studied. The experimental results indicate that the prototype can achieve smooth motion under large pre-tightening displacement. The displacement curve under the load of 2.0 kg still shows good smoothness, and the resolution is 1.56 rad. This work proposes a new design concept of dynamic control of the normal pressure to achieve smooth motion for piezoelectric stick slip actuators, even under heavy-load conditions, using the inertial block structure.

In this article a global method for master-slave synchronization of nonlinear systems is provided. Based on a diffeomorphic transformation of the original dynamics, a reduced observer is designed such that the nonlinear state feedback law is independent of the inertial frame. Generally, the method requires non trivial computations but leads to global convergence results for the invariant tracking error. We illustrate the design procedure in detail for a master-slave synchronization of a bacterial growth model, which may escape to infinity in finite time.

Resumo O Princípio da Relatividade de Galileu (PRG) estabelece que as leis da mecânica são as mesmas em qualquer referencial inercial. Ao determinar que todos os referenciais inerciais são equivalentes, esse princípio implica em uma relatividade do movimento. Por outro lado, mesmo considerando o PRG como basilar para a mecânica, Isaac Newton introduz os conceitos de tempo e espaço absolutos e apresenta argumentos, de natureza dinâmica, em defesa do movimento absoluto, justificado na diferenciação entre referenciais inerciais e não-inerciais. A Teoria da Relatividade Restrita (TRR) critica as noções de tempo e espaço absolutos, mas preserva o papel privilegiado dos referenciais inerciais na descrição das leis da natureza. Apenas com a Teoria da Relatividade Geral (TRG) é estabelecida a equivalência entre todos os referenciais, independentemente do seu estado de movimento e, assim, é derrubada a noção de movimento absoluto. Este trabalho tem por objetivo discutir as principais dúvidas e questões que surgem ao se estudar os conceitos supramencionados, bem como investigar a aparente dubiedade entre o PRG e o movimento absoluto. Abstract Galileo’s Principle of Relativity (GPR) states that the laws of mechanics are the same in any inertial frame of reference. By determining that all inertial reference frames are equivalent, this principle implies a relativity of motion. On the other hand, even considering the GPR as fundamental for mechanics, Isaac Newton introduces the concepts of absolute time and space and presents arguments, of a dynamic nature, in defense of absolute motion, justified by the differentiation between inertial and non-inertial reference frames. The Special Relativity Theory (SRT) criticizes the notions of absolute time and space, but preserves the privileged role of inertial reference frames in the description of the laws of nature. Only with the General Relativity Theory (GRT) is equivalence established between all references, regardless of their state of motion and, thus, the notion of absolute motion is overthrown. This work aims to discuss the main doubts and issues that arise when studying the aforementioned concepts, as well as to investigate the apparent dubiousness between the PRG and the absolutemovement.

With the improvement of the accuracy of the inertial system, the influence of the disturbing gravity field on the accuracy of long-range rocket has become increasingly prominent. However, in actual engineering, there are problems of low accuracy and being time-consuming for disturbing gravity field compensation. In view of this, this paper proposes a set of online comprehensive solutions combining disturbing gravity reconstruction and stellar correction. According to the pre-launch binding parameters, the net function assignment method is used in the navigation system to calculate disturbing gravity in the boost phase online. In the guidance system, a closed-loop guidance online compensation method is proposed based on the state-space perturbation method for the disturbing gravity in the coast phase. At the same time, the vertical deflection can also be corrected by stellar guidance. The calculation results are simulated and verified under different circumstances. Simulation results show that the proposed online compensation algorithm has an accuracy improvement compared with the element compensation algorithm on ground. And the stellar guidance algorithm can further correct the impact deviation. The impact deviation after comprehensive compensation does not exceed 50 m, and the compensation percentage is greater than 65%.

In this article, we consider the exponential consensus of coupled inertial (double-integrator) agents, particularly with the general setting of the damping and stiffness control gains. Each agent has one damping gain and one stiffness gain. Here, the damping and stiffness control gains of all agents can be both fully heterogeneous (FH) and fully variable (FV), which are called the FH-FV gains for convenience of reference. Specifically, the FH gains are defined as follows: 1) the damping gains of all agents are heterogeneous; 2) the stiffness gains of all agents are heterogeneous; and 3) the set of the damping gains and the set of the stiffness gains are distinct without dependence. Otherwise, the control gains are said partially heterogeneous (PH). The FV or partially variable (PV) aspect of control gains is defined similarly. The FH-FV gains setting is novel and generalizes the specially PH settings of constant gains in previous papers. We also consider the general FH-PV gains and the PH-PV gains. Then, we provide the series of conditions that ensure exponential convergence to consensus, for the agents with the FH-FV gains, the general FH-PV gains, and the PH-PV gains, respectively. The series of the conditions for each type of control gains has particular meaning for characterizing heterogeneity of the gains, especially, when the digraph of the agents is far-from-balanced.

A three-dimensional low-order modeling technique is described for modeling both wing inertial and aerodynamic forces of animals and robots flapping heavy and morphing wings. The model is applied to...

This paper investigates global dynamics in fractional-order dual inertial neural networks with time lags. Firstly, according to some crucial features of Mittag-Leffler functions and Banach contracting mapping principle, the existence and uniqueness of $ S $-asymptotically $ \omega $-periodic oscillation of the model are gained. Secondly, by using the comparison principle and the stability criteria of delayed Caputo fractional-order differential equations, global asymptotical stability of the model is studied. In the end, the feasibility and effectiveness of the obtained conclusions are supported by two numerical examples. There are few papers focus on $ S $-asymptotically $ \omega $-periodic dynamics in fractional-order dual inertial neural networks with time-varying lags, apparently, the works in this paper fill some of the gaps.

This article is concentrated on the stabilization problem of inertial memristive neural networks (IMNNs) with time-varying delay. Here, removing the reduced order method, the stabilization of delayed IMNNs is directly studied under the framework of the second-order system. To decrease control cost, the aperiodically intermittent control strategy is adopted. This strategy implies that work time (with control input) alternates with rest time (without control input), and every work or rest width may be different. By constructing a suitable Lyapunov functional, some algebraic criteria are achieved to guarantee the stabilization of the considered system. Note that the obtained control gains are often larger than practical needs due to the conservatism deriving from inevitable inequality scaling. For further saving control resources, an intermittent adaptive control strategy is applied to stabilize the delayed IMNNs. Finally, a numerical example is exhibited to confirm the availability of the developed theoretical outcomes.

In this paper we discuss the model of fractional oscillator where the inertial and restoring force terms maintains their usual expression but the damping term involves a fractional derivative of Caputo type, the so called fractional Kelvin-Voigt oscillator. The transient solution of this model is given in terms of the so called bivariate Mittag-Leffler function, while the steady-state solution in response to a sinusoidal force involves a 4-variate Mittag-Leffler function. We give numerical examples comparing the solutions for different values of the order α of the fractional derivative (0

The aim of this study was to investigate the effect of four different inertial loads (0.025, 0.050, 0.075, and 0.100 kg· m²) on concentric (CON) power, eccentric (ECC) power, and ECC overload in the flywheel Romanian deadlift (RDL). Fourteen recreationally trained males (27.9 ± 6.4 years, 90 ± 10.7 kg, 180.7 ± 5.5 cm) volunteered for the study. They had a minimum of two years of resistance training experience, although none had experience in flywheel inertia training (FIT). All participants performed the flywheel RDL on a flywheel device (kBox 3, Exxentric, AB TM, Bromma, Sweden). Each set was performed using different inertial loads, those being 0.025, 0.050, 0.075, and 0.100 kg·m². For CON, ECC power, and ECC overload, there was a significant difference (p0.001) between inertial loadings. In conclusion, results highlight that lower inertial load leads to higher peak CON and ECC power values, precisely 0.025 kg· m². Regarding ECC overload, medium to higher loads (0.050, 0.075, and 0.100 kg·m²) will lead to higher values.

This study investigates the weak convergence of the sequences generated by the inertial technique combining the parallel monotone hybrid method for finding a common fixed point of a finite family of $ G $-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. Some numerical examples are also presented, providing applications to signal recovery under situations without knowing the type of noises. Besides, numerical experiments of the proposed algorithms, defined by different types of blurred matrices and noises on the algorithm, are able to show the efficiency and the implementation for LASSO problem in signal recovery.

Foot-mounted inertial sensors become popular in many indoor or GPS-denied applications, including but not limited to medical monitoring, gait analysis, soldier, and first responder positioning. However, the foot-mounted inertial navigation relies largely on the aid of zero velocity update (ZUPT) and has encountered inherent problems, such as heading drift. This article implements a pedestrian navigation system based on dual foot-mounted low-cost inertial measurement units (IMUs) and interfoot ultrasonic ranging. The observability analysis of the system is performed to investigate the roles of the ZUPT measurement and the foot-to-foot ranging measurement in improving the state estimability. A Kalman-based estimation algorithm is mechanized in the Earth frame, rather than in the common navigation frame, which is found to be effective in depressing the linearization error in Kalman filtering. An ellipsoid constraint in the Earth frame is also proposed to further restrict the height drift. Simulation and real field experiments show that the proposed method has better robustness and positioning accuracy (about 0.1%-0.2% traveled distance) than the traditional pedestrian navigation schemes do.

Redundant inertial sensor systems improve navigation performance and guarantee fault detection or fault isolation functions. However, they may cause unexpected side effects owing to their enlarged size. The misalignment between the center of gravity of the sensor system and the rotational origin of the vehicle results in the lever arm effect inducing significant acceleration errors. To minimize the lever arm effect error, the configuration of redundant sensors should be carefully considered, as their performance is highly dependent on its configuration. Thus, the figure-of-merit (FOM), which is considered a performance index or cost function, is proposed to obtain the optimal configuration for minimizing the lever arm effect error. Further, to define an FOM the angular velocity and angular acceleration are considered as random variables and to quantify them, they were replaced as variances. The lever arm effect error was found to be completely eliminated when a redundant inertial measurement unit (RIMU) with more than eight single-axis inertial sensors was configured using the proposed FOM. Further, a case study and simulation were conducted to verify the proposed FOM and configuration, and it was found that the proposed FOM can be used to obtain the optimal configuration of the RIMU and as an indicator of the lever arm effect error.

In this paper, we introduce an inertial parallel CQ subgradient extragradient method for finding a common solutions of variational inequality problems. The novelty of this paper is using linesearch methods to find unknown L constant of L-Lipschitz continuous mappings. Strong convergence theorem has been proved under some suitable conditions in Hilbert spaces. Finally, we show applications to signal and image recovery, and show the good efficiency of our proposed algorithm when the number of subproblems is increasing.

Inertial impactors are an important part of aerosol science where they are used to obtain particle size distributions in a wide range of practical and scientific applications. A shortcoming of thes...

Purpose This paper aims to present a pipeline to progressively deal with the online external parameter calibration and estimator initialization of the Stereo-inertial measurement unit (IMU) system, which does not require any prior information and is suitable for system initialization in a variety of environments. Design/methodology/approach Before calibration and initialization, a modified stereo tracking method is adopted to obtain a motion pose, which provides prerequisites for the next three steps. Firstly, the authors align the pose obtained with the IMU measurements and linearly calculate the rough external parameters and gravity vector to provide initial values for the next optimization. Secondly, the authors fix the pose obtained by the vision and restore the external and inertial parameters of the system by optimizing the pre-integration of the IMU. Thirdly, the result of the previous step is used to perform visual-inertial joint optimization to further refine the external and inertial parameters. Findings The results of public data set experiments and actual experiments show that this method has better accuracy and robustness compared with the state of-the-art. Originality/value This method improves the accuracy of external parameters calibration and initialization and prevents the system from falling into a local minimum. Different from the traditional method of solving inertial navigation parameters separately, in this paper, all inertial navigation parameters are solved at one time, and the results of the previous step are used as the seed for the next optimization, and gradually solve the external inertial navigation parameters from coarse to fine, which avoids falling into a local minimum, reduces the number of iterations during optimization and improves the efficiency of the system.

This article proposes a predictive end-effector control method for manipulators operating on mobile platforms subjected to unwanted base motion. Time series is used to forecast the base motion using historical state information. Then, a trajectory specified in the inertial frame is transformed to a predicted trajectory with respect to the manipulator. By tracking this transformed trajectory, the manipulator negates the base motion. A model-predictive control problem is formulated via quadratic programming (QP) to track said trajectory over the prediction horizon. Only the first control action in the control sequence is constrained by kinematic feasibility. In this manner, QP can be swiftly solved with linear inequality constraints. It is shown that the actual joint trajectory executed by the manipulator is always kinematically feasible. Moreover, tracking error can still be reduced despite future predicted control actions being infeasible. The method is validated through both simulation and experiment. The proposed method can reduce pose error by over 60% compared to a proportional-integral feedback controller.

There is currently an increase in inertial flywheel application in strength training; thus, it must be monitored by an accurate and reliable device. The present study tested: (1) the accuracy of an inertial measurement device (IMU) to correctly measure angular velocity and (2) its inter-unit reliability for the measurement of external load. The analysis was performed using Pearson Correlation and Intraclass Correlation Coefficient (ICC). The IMU accuracy was tested using Bland-Altman and the reliability with the coefficient of variation (CV). Ten elite-level football players performed ten series of 5 repetitions in a one-hand standing row exercise (5 series with each arm). A nearly perfect accuracy (ICC=.999) and a very good between-device reliability (Bias=-.010; CV=.017%) was found. IMU is a reliable and valid device to assess angular velocity in inertial flywheel workout objectively. Resumen Actualmente, hay un aumento en la utilización de la polea cónica en el entrenamiento de fuerza; por lo tanto, es necesario monitorearlo con un dispositivo preciso y confiable. El presente estudio probó: (1) la precisión de un dispositivo de medición inercial (IMU), para medir correctamente la velocidad angular y (2) su confiabilidad entre unidades para la medición de carga externa. El análisis se realizó utilizando la correlación de Pearson y el Coeficiente de Correlación Intra-clase (CCI). La precisión de la IMU se probó usando Bland-Altman y la confiabilidad con el Coeficiente de Variación (CV). Diez jugadores de fútbol de nivel élite realizaron 10 series de 5 repeticiones en un ejercicio de fila de pie con una mano (5 series con cada brazo). Se encontró una precisión casi perfecta (ICC = .999) y una muy buena confiabilidad entre dispositivos (Sesgo = -. 010; CV = .017%). IMU´s es un dispositivo confiable y válido para evaluar objetivamente la velocidad angular en el entrenamiento inercial de la polea cónica. Resumo Atualmente, há um aumento na utilização da polia cônica no treinamento de força; portanto, é necessário monitorá-lo com um dispositivo preciso e confiável. O presente estudo testou: (1) a precisão de um dispositivo de medição inercial (IMU), para medir corretamente a velocidade angular e (2) sua confiabilidade interunidades para medição de carga externa. A análise foi realizada por meio da correlação de Pearson e do Coeficiente de Correlação Intraclasse (ICC). A precisão do IMU foi testada usando Bland-Altman e a confiabilidade com o Coeficiente de Variação (CV). Dez jogadores de futebol de elite realizaram 10 séries de 5 repetições em um exercício de linha em pé com uma mão (5 séries com cada braço). Foi encontrado uma precisão quase perfeita (ICC = 0,999) e confiabilidade entre dispositivos muito boa (Bias = - 0,010; CV = 0,017%). IMU's é um dispositivo confiável e válido para avaliar objetivamente a velocidade angular no treinamento inercial da polia cônica.

The complex marine environment and the high energy consumption of shipboard equipment pose challenges to the long-term navigation of autonomous unmanned ships. In wave-induced motion, inertial gyro antirolling technology is used to offset the energy transmitted by waves, but the massive consumption of energy is not conducive to long-term navigation of the unmanned ships. This paper attempts to exploit the wave energy transmitted by the gyro to improve the power supply of the unmanned ship. Firstly, a nonlinear coupling model of the gyro antirolling device and the unmanned ship is established. Secondly, considering various model constraints and physical constraints of the equipment, the energy evaluation objective function of nonlinear model predictive control (NMPC) is designed. In the simulation, the proposed control method can effectively extract electric energy from different waves.

This paper studies a class of inertial neural networks with leakages and varying delays on timescales: $$\begin{aligned} x_{i}^{\bigtriangleup \bigtriangleup }(t)&=-a_{i}(t)x_{i}^{\bigtriangleup }(t-\eta _{i} (t))- b_{i}(t)x_{i}(t-\xi _{i} (t)) +\sum \limits _{j=1}^{n} c_{ij}(t)f_{j}(x_{j}(t))\\&\quad +\sum \limits _{j=1}^{n} d_{ij}(t)g_{j}(x_{j}(t- q_{ij}(t)))+S_{i}(t). \end{aligned}$$ The problems of the existence, the uniqueness and the exponential stability of almost anti-periodic solution on timescales are investigated. We establish some sufficient conditions to guarantee the main results, by constructing the Lyapunov functions and using some classical inequalities. A numerical example is given for illustration.

In this paper, we investigate the monotone variational inequality in Hilbert spaces. Based on Censor’s subgradient extragradient method, we propose two modified subgradient extragradient algorithms with self-adaptive and inertial techniques for finding the solution of the monotone variational inequality in real Hilbert spaces. Strong convergence analysis of the proposed algorithms have been obtained under some mild conditions.

In this paper, the stability for a class fractional-order inertial neural networks with time-delay are investigated. Moreover, some sufficient conditions for the Mittag-Leffler stability and the asymptotical ω -periodicity are obtained, by the appropriate transformation, using the property of the Riemann-Liouville fractional integral and derivative. In the end, results of the theoretical derivation are verified by virtue of two numerical simulation examples.

In this paper, we consider a new class of quasi-variational inequalities, which is called the general quasi-variational inequality. Using the projection operator technique, we establish the equivalence between the general quasi-variational inequalities and the fixed point problems. We use this alternate formulation to propose some new inertial iterative schemes for solving the general quasi-variational inequalities. The convergence criteria of the new inertial projection methods under some appropriate conditions is investigated. Since the general quasi-variational inequalities include the quasi-variational inequalities, variational inequalities, complementarity problems and the related optimization problems as special cases, our results continue to hold for these problems. It is an interesting problem to compare the efficiency of the proposed methods with other known methods.

In this article, we propose a novel optimization-based tightly coupled Direct Visual-Inertial Odometry (DVIO), which fuses the visual and inertial measurements to provide real-time full state estimation. Different from existing frameworks, the key novelty of the proposed method is to integrate the data association, state estimation, and outlier detection into a nonlinear optimization framework in a tightly coupled way. Specifically, by jointly minimizing the preintegration error of the inertial measurement unit and the photometric error of the camera, the data association is tightly coupled with the process of state estimation. Then, an iterative selection strategy is design to reject outliers during the data association and establish more visual constraints in the optimization. In addition, a hybrid weighting method is proposed to tightly integrate the iterative selection into the optimization by dynamically weighting residual terms. As a consequence, the proposed method aligns the image patches, estimates the motion and removes the outliers synchronously. Comparative experiments on the public dataset and extensive real-world experiments show that DVIO outperforms state-of-the-art visual-inertial odometries in terms of both the accuracy and the robustness. Thus, DVIO is highly applicable to the navigation or the simultaneous localization and mapping of mobile devices or agile robots like micro air vehicles.

The disturbance propagation mechanism is crucial for the preventive, corrective, and in-extremis control of power grids. This paper proposes a novel non-uniform frame structure model for power system disturbance propagation analysis. A general state transition model of the power grid is derived from the electromechanical wave propagation process. This is further used together with the Gaussian function to derive the non-uniform heterogeneous inertial continuum model, where the non-uniform parameters of the inertia are estimated using the state transition model. The proposed non-uniform frame structure model can be integrated with the electromechanical wave equation to study the disturbance propagation process. These novel developments allow us to tackle the inertial loss and uniform homogenous assumption in existing models. Extensive comparison results carried out on both the chain grid and the IEEE 118-bus system demonstrate that the proposed model can achieve 5- and 3-times accuracy improvements of the state-of-the-art SHU-FSM and ISHU-FSM models, respectively.

In this paper, we introduce a new iterative forward-backward splitting method with an error for solving the variational inclusion problem of the sum of two monotone operators in real Hilbert spaces. We suggest and analyze this method under some mild appropriate conditions imposed on the parameters such that another strong convergence theorem for these problem is obtained. We also apply our main result to improve the fast iterative shrinkage thresholding algorithm (IFISTA) with an error for solving the image deblurring problem. Finally, we provide numerical experiments to illustrate the convergence behavior and show the effectiveness of the sequence constructed by the inertial technique to the fast processing with high performance and the fast convergence with good performance of IFISTA.

Human motion is often tracked using three-dimensional video motion tracking systems, which have demonstrated high levels of validity. More recently, inertial measurement units (IMUs) have been used to measure human movement due to their ease of access and application. The purpose of this study was to systematically review the literature regarding the validity of inertial sensor systems when being used to track human motion. Four electronic databases were used for the search, and eleven studies were included in the final review. IMUs have a high level of agreement with motion capture systems in the frontal and sagittal planes, measured with root mean square error (RMSE), intraclass correlation coefficient, and Pearson's correlation. However, the transverse or rotational planes began to show large discrepancies in joint angles between systems. Furthermore, as the intensity of the task being measured increased, the RMSE values began to get much larger. Currently, the use of accelerometers and inertial sensor systems has limited application in the assessment of human motion, but if the precision and processing of IMU devices improves further, it could provide researchers an opportunity to collect data in less synthetic environments, as well as improve ease of access to biomechanically analyse human movement.

Among other variables, smart tyre systems are capable of determining tyre contact forces. Combining this information with the signals obtained from conventional vehicle sensors, e.g. inertial measu...