Arbitrary Motion Research Articles

О рекуррентных движениях динамических систем в полуметрическом пространстве

The present paper is devoted to studying the properties of recurrent motions of a dynamical system g^t defined in a Hausdorff semi-metric space Γ. Based on the definitions of a minimal set and recurrent motion introduced by G. Birkhoff at the beginning of the last century, a new sufficient condition for the recurrence of motions of the system g^t in Γ is obtained. This condition establishes a new property of motions, which rigidly connects arbitrary and recurrent motions. Based on this property, it is shown that if in the space Γ positively (negatively) semi-trajectory of some motion is relatively sequentially compact, then the ω-limit (α-limit) set of this motion is a sequentially compact minimal set. As one of the applications of the results obtained, the behavior of motions of the dynamical system g^t given on a topological manifold V is studied. This study made it possible to significantly simplify the classical concept of interrelation of motions on V which was actually stated by G. Birkhoff in 1922 and has not changed since then.

Informed Circular Fields for Global Reactive Obstacle Avoidance of Robotic Manipulators

In this paper a global reactive motion planning framework for robotic manipulators in complex dynamic environments is presented. In particular, the circular field predictions (CFP) planner from Becker et al. (2021) is extended to ensure obstacle avoidance of the whole structure of a robotic manipulator. Towards this end, a motion planning framework is developed that leverages global information about promising avoidance directions from arbitrary configuration space motion planners, resulting in improved global trajectories while reactively avoiding dynamic obstacles and decreasing the required computational power. The resulting motion planning framework is tested in multiple simulations with complex and dynamic obstacles and demonstrates great potential compared to existing motion planning approaches.

3D Mapping for a Large Crane Using Rotating 2D-Lidar and IMU Attached to the Crane Boom

This paper describes a novel method for large-scale 3D mapping for construction cranes with an arbitrary motion of the sensor system (2D lidar and IMU) attached to the crane boom. A heavy lidar with a slowly rotating base is needed to make a large-scale map both vertically and horizontally for cranes. This sensor configuration and mapping conditions entail handling each 2D scan separately, making it difficult to adopt existing rotating 2D lidar-based methods that construct a virtual 3D scan from a set of 2D scans. In the proposed method, we introduce a complementary filter with moving average filtering for lidar pose estimation, which is more robust to severe vibration than Kalman filter-based methods. As there are only a small amount of overlaps between 2D lidar scans, we propose a map correction method based on a pose graph optimization with planar environmental constraints. We evaluate the proposed method in a simulation and a small-sized real environment and compare it with one of the state-of-the-art methods. The evaluation results reveal that the proposed method can accurately estimate the sensor poses, thereby generating a high-quality, large-scale 3D point cloud map.

Spatiotemporal Edges for Arbitrarily Moving Video Classification in Protected and Sensitive Scenes

Classification of arbitrary moving objects including vehicles and human beings in a real environment (such as protected and sensitive areas) is challenging due to arbitrary deformation and directions caused by shaky camera and wind. This work aims at adopting a spatio-temporal approach for classifying arbitrarily moving objects. The intuition to propose the approach is that the behavior of the arbitrary moving objects caused by wind and shaky camera are inconsistent and unstable while for static objects, the behavior is consistent and stable. The proposed method segments foreground objects from background using the frame difference between median frame and individual frame. This step outputs several different foreground information. The method finds static and dynamic edges by subtracting Canny of foreground information from the Canny edges of respective input frames. The ratio of the number of static and dynamic edges of each frame is considered as features. The features are normalized to avoid the problems of imbalanced feature size and irrelevant features. For classification, the work uses 10-fold cross-validation to choose the number of training and testing samples and the random forest classifier is used for the final classification of frames with static objects and arbitrary movement objects. For evaluating the proposed method, we construct our own dataset, which contains video of static and arbitrarily moving objects caused by shaky camera and wind. The results on the video dataset show that the proposed method achieves the state-of-the-art performance (76% classification rate) which is 14% better than the best existing method.

An Improved Data-Driven Calibration Method with High Efficiency for a 6-DOF Hybrid Robot

This paper proposes an improved data-driven calibration method for a six degrees of freedom (DOF) hybrid robot. It focuses mainly on improving the measurement efficiency and practicability of existing data-driven calibration methods through the following approaches. (1) The arbitrary motion of the hybrid robot is equivalently decomposed into three independent sub-motions by motion decomposition. Sequentially, the sub-motions are combined according to specific motion rules. Then, a large number of robot poses can be acquired in the whole workspace via a limited number of measurements, effectively solving the curse of dimensionality in measurement. (2) A mapping between the nominal joint variables and joint compensation values is established using a back propagation neural network (BPNN), which is trained directly using the measurement data through a unique algorithm involving inverse kinematics. Thus, the practicability of data-driven calibration is significantly improved. The validation experiments are carried out on a TriMule-200 robot. The results show that the robot’s maximal position/orientation errors are reduced by 91.16%/88.17% to 0.085 mm/0.022 deg, respectively, after calibration.

Self-Calibrating Magnetometer-Free Inertial Motion Tracking of 2-DoF Joints.

Human motion analysis using inertial measurement units (IMUs) has recently been shown to provide accuracy similar to the gold standard, optical motion capture, but at lower costs and while being less restrictive and time-consuming. However, IMU-based motion analysis requires precise knowledge of the orientations in which the sensors are attached to the body segments. This knowledge is commonly obtained via time-consuming and error-prone anatomical calibration based on precisely defined poses or motions. In the present work, we propose a self-calibrating approach for magnetometer-free joint angle tracking that is suitable for joints with two degrees of freedom (DoF), such as the elbow, ankle, and metacarpophalangeal finger joints. The proposed methods exploit kinematic constraints in the angular rates and the relative orientations to simultaneously identify the joint axes and the heading offset. The experimental evaluation shows that the proposed methods are able to estimate plausible and consistent joint axes from just ten seconds of arbitrary elbow joint motion. Comparison with optical motion capture shows that the proposed methods yield joint angles with similar accuracy as a conventional IMU-based method while being much less restrictive. Therefore, the proposed methods improve the practical usability of IMU-based motion tracking in many clinical and biomedical applications.

Comparative Analysis of ANN-Based Mobility Prediction Performance in an Ad-Hoc Network

The facility of arbitrary node movement one side has advantages on application on the other side very difficult to manage the network because random node mobility directly effects on network connectivity and interrupt on the performance, obtained challenges like routing overhead, packet losses, increases energy consumption, wasted bandwidth for reconnection, decreases throughput etc. Thus an accurate mobility prediction of a node before leaving one position to another or subsequence position can be improve network performance which is effects by node mobility. Now day’s artificial neural networks (ANNs) is very common and trending for approximation and prediction application and also popular for node trajectory prediction. In this paper we explore the architectures of some static (like MLP and RBF) and dynamic (like FTDNN, DTDNN, NARX and LSTM) neural network and search best ANN model by obtaining optimal model parameters to predict node mobility and compared the performance using mobility model (Gauss Markov model) dataset as well as real-world dataset collected from Crawdad to highlight generalization capabilities. Mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and average coordinates distance error (DE) between observed and estimated positions are used to evaluate their performance. The empirical results show that LSTM is the best artificial neural network (ANN) model for mobility prediction in both model based and real-world dataset(testing sets).

Combining beams in different locations for aerospace defense in a turbulent atmosphere

A fixed high-power laser system used as an aerospace defense weapon has limitations such as the transmitter size, serious thermal blooming during propagation, rapid motion, and the variation of the location of the target. In the present paper, we propose a method by arranging many high-power systems with adequate distance in a defense area. The intensity distribution and the energy irradiated on the target are studied and compared with a fixed laser system. Results show that adequate arrangement of many high-power laser systems can reply to the arbitrary and rapid motion of the target.

Hierarchical refinement in isogeometric analysis for flexible multibody impact simulations

Detailed impact simulations in flexible multibody systems can be simulated based on reduced isogeometric analysis (IGA) models. However, a precise simulation of an impact requires a high element resolution in the contact area. Usually in IGA, global refinement methods are used, which are easy to implement. However, in the literature, also the use of hierarchical local refinement is proposed. The local refinement generates fewer countable degrees of freedom compared to an equivalent global refinement. Numerous application areas can be found in the literature, such as contact simulations, where the computational effort is reduced by local refinement. In this work, we introduce the inclusion of hierarchically refined IGA models within the floating frame of reference formulation. Thereby, the hierarchically refined IGA model is reduced and applied in impact simulations. In two application examples, we simulate the impact of two- and three-dimensional spheres and compare with an analytical solution. The focus here is on the comparison of calculation times and accuracy of globally and locally refined reference models. The third application example consists of two flexible double pendulums and is devoted to systems in which the bodies undergo both arbitrary rigid body motions and small elastic deformations.

The Finite Segment Method—A Numerical Rolling Contact Fatigue Life Model for Bearings Subjected to Stochastic Operating Conditions

Abstract Fatigue life calculation in bearings is an issue that has been the focus of decades of research culminating in national and international standards that are easily applicable to a wide variety of applications. However, almost all research has focused on simple, repetitive operating conditions. This paper explains why these approaches are not completely applicable to bearings under certain conditions, particularly not to those with a change in the load position over time undergoing inconstant movement. Based on existing standards, namely ISO 281, the paper then proposes a numerical approach to calculate the life of a bearing under stochastic operating conditions. The bearing life for any arbitrary load history and movement patterns can be calculated using the presented approach. The approach is presented and some example applications are given, notably including the life calculation of a rotor blade bearing in a wind turbine.

A Fine Property of Sets at Points of Lebesgue Density

Consider an integer n≥2, m∈[n,+∞) and put α‾:=m−1n−1. Moreover: ∙ Let γx:(0,+∞)→Rn be the line through x=(x1,…,xn)∈Rn defined as γx(t):=(tx1,tα‾x2,…,tα‾xn); ∙ If T is any motion of Rn, then let γx(T) be the line through x=(x1,…,xn)∈Rn defined as γx(T):=T∘γT−1(x); ∙ Let H1 denote the one-dimensional Hausdorff measure in Rn. The main goal of this paper is to prove the following property: If x0 is an m-density point of a Lebesgue measurable set E and T is an arbitrary motion of Rn mapping the origin to x0, then we have lim supt→0+ H1(E∩γx(T)((0,t])) H1(γx(T)((0,t]))=1 for almost every x∈T({1}×Rn−1). An application of this result to locally finite perimeter sets is provided.

A neural mechanism underlying predictive visual motion processing in patients with schizophrenia

Psychotic symptoms may be traced back to sensory sensitivity. Thereby, visual motion (VM) processing particularly has been suggested to be impaired in schizophrenia (SCZ). In healthy brains, VM underlies predictive processing within hierarchically structured systems. However, less is known about predictive VM processing in SCZ. Therefore, we performed fMRI during a VM paradigm with three conditions of varying predictability, i.e., Predictable-, Random-, and Arbitrary motion. The study sample comprised 17 SCZ patients and 23 healthy controls. We calculated general linear model (GLM) analysis to assess group differences in VM processing across motion conditions. Here, we identified significantly lower activity in right temporoparietal junction (TPJ) for SCZ patients. Therefore, right TPJ was set as seed for connectivity analyses. For patients, across conditions we identified increased connections to higher regions, namely medial prefrontal cortex, or paracingulate gyrus. Healthy subjects activated sensory regions as area V5, or superior parietal lobule. Reduced TPJ activity may reflect both a failure in the bottom-up flow of visual information and a decrease of signal processing as consequence of increased top-down input from frontal areas. In sum, these altered neural patterns provide a framework for future studies focusing on predictive VM processing to identify potential biomarkers of psychosis.

ANALYSIS OF SCIENTIFIC RESEARCH ON THE SENSIMOTOR DEVELOPMENT OF CHILDREN WITH DISORDERS OF INTELLECTUAL DEVELOPMENT

The article provides a theoretical analysis of research on the problem of sensorimotor development with children with violation of intellectual development. Theoretical aspects of sensorimotor development of children with intellectual disabilities in the following areas are considered: vestibular-postural reactions and bilateral coordination. Motor mechanisms affect the general development of the child, his ability to work and master the curriculum. Studies have shown the effect of physical activity on mental activity and academic performance. Imperfections of the motor sphere of children with PIR are revealed. Children's gait is unstable, movements are chaotic, poorly coordinated, poorly regulated muscular effort, impaired visual-motor coordination, inability to imitate, underdevelopment of differentiated finger movements. The disadvantages of arbitrary movements are pronounced. Theoretical analysis of scientific research on the role of the central nervous system in the construction of movements. Spinal cord, medulla, diencephalon, cerebellum, large hemispheres perform their functions. Simple movements (reflective) provide normal performance of more complex movements performed due to the lower parts of the central nervous system (spinal, medulla, midbrain). More complex postures are regulated by the activity of the midbrain, the vestibular system, which obey the cerebellum. The cerebellum coordinates the proportionality of movement. To perform movement in space, it is necessary to combine all types of sensitive sphere (afferentation). This process occurs at the level of the diencephalon and subcortical nuclei. It is proved that part of the vestibular signals must be registered and modulated by the brain. The lack of modulation of vestibular stimuli will be noticeable in bilateral reactions, coordination of the two sides of the body. The postural response may go unnoticed because it is difficult for the child to adopt a particular posture. Sensorimotor development affects the functioning of the body of a child with violation of intellectual development.

Spatial microscopic modeling of collective movements in multi-robot systems: Design choices and calibration.

Despite the strong increase in available computational power enabling an unprecedented level of realism in simulation, modeling robotic systems at higher abstraction level remains crucial to efficiently design robot controllers and analyze their properties. This is especially true for multi-robot systems, with their high computational complexity due to the numerous interactions among individual robots. While multiple contributions in the literature have proposed approaches leading to highly abstracted and therefore computationally efficient models, often such abstractions have been obtained with strong assumptions on the underlying spatiality of the system behavior (e.g., well-mixed system, diffusive system). In this work, we address the modeling of an arbitrary collective movement involving the displacement of a robot ensemble along a certain trajectory overlapped with continuous interactions among the robotic members. Without loss of generality, we have focused our modeling effort on a flocking case study, as a prominent and well-known example of collective movement. We investigate our case study at the microscopic level while leveraging a more faithful submicroscopic model (implemented through a high-fidelity robotic simulator) as ground-truth. More specifically, we illustrate multiple choices for designing and calibrating such microscopic models, so that their faithfulness with the underlying submicroscopic model of the same physical system is preserved. Such effort has produced concrete implementations of three different microscopic models for the same case study, all taking into account the spatiality of the collective movement. We find that all three microscopic models produce quantitatively accurate estimations for our flocking case study. As they rely on different underlying assumptions and modeling techniques, the choice between them is a trade-off between the computational cost, the modeling effort, the metrics considered to evaluate their faithfulness, and the subsequent usage (e.g., control design, system property analysis, control code prototyping).

A Distributed Current Source Model for Analyzing Motion-Induced Eddy-Current in a Conductor With Arbitrary Movements

This article presents a distributed current source (DCS) model for predicting the eddy current (EC) induced in a conductor in a magnetic field due to mechanical motion and the EC-generated magnetic flux density (MFD) for measurements. Formulated in state-space and iteratively solved in time domain, the general motion-induced EC model accounts for the effects of the weak magnetization of the material, the Lorentz force per unit charge, and the relative location between the conductor and external source that generates the magnetic field, and that between the EC field and MFD sensor. Verified numerically by comparing the predicted motion-induced EC with that of a finite element method, parametric effects on motion-induced EC are analyzed. Experiments were conducted on a commercial CNC lathe simulating three practical applications. In all cases the relative differences between the predicted and measured MFD are in the range from 5 to 15%, validating the accuracy of the DCS modeled solutions

Co-generation of Collision-Free Shapes for Arbitrary One-Parametric Motion

Mechanical assemblies can exhibit complex relative motions, during which collisions between moving parts and their surroundings must be avoided. To define feasible design spaces for each part's shape, "maximal" collision-free pointsets can be computed using configuration space modeling techniques such as Minkowski operations and sweep/unsweep. For example, for a pair of parts undergoing a given relative motion, to make the problem well-posed, the geometry of one part (chosen arbitrarily) must be fixed to compute the maximal shape of the other part by an unsweep operation. Making such arbitrary choices in a multi-component assembly can place unnecessary restrictions on the design space. A broader family of collision-free pairs of parts can be explored, if fixing the geometry of a component is not required. In this paper, we formalize this family of collision-free shapes and introduce a generic method for generating a broad subset of them. Our procedure, which is an extension of the unsweep, allows for co-generation of a pair of geometries which are modified incrementally and simultaneously to avoid collision. We demonstrate the effectiveness and scalability of our procedure in both 2D and 3D by generating a variety of collision-free shapes. Notably, we show that our approach can automatically generate freeform cam and follower profiles, gear teeth, and screw threads, starting from colliding blocks of materials, solely from a specification of relative motion and without the use of any feature-informed heuristics. Moreover, our approach provides continuous measures of collision that can be incorporated into standard gradient-descent design optimization, allowing for simultaneous collision-free and physics-informed co-design of mechanical parts for assembly.

Magnetic Force-Assisted Nonlinear Three-Dimensional Wideband Energy Harvester Using Magnetostrictive/Piezoelectric Composite Transducers.

This paper presents a nonlinear magnetoelectric energy harvester which has the potential to harvest vibrational energy over a wide bandwidth in arbitrary motion directions. Three springs with equal intersection angles are adopted to absorb the multi-directional vibration energy. Magnetic interaction between the magnets and ME transducers allows the nonlinear motion with enhanced harvesting frequency range. Very good agreement is observed between the numerical and experimental open-circuit voltage output frequency response curves. The experimental results show that the harvester can harvest vibrational energy in an arbitrary direction, exhibiting a further bandwidth of 5.2 Hz. This study provides a new solution to effectively use the magnetoelectric energy harvester for multi-directional and bandwidth vibrational energy scavenging in the surrounding environment.

A generalized framework for autonomous calibration of wheeled mobile robots

Robotic calibration allows for the fusion of data from multiple sensors such as odometers, cameras etc., by providing appropriate transformational relationships between the corresponding reference frames. For wheeled robots equipped with exteroceptive sensors, calibration entails learning the motion model of the sensor or the robot in terms of the odometric data, and must generally be performed prior to performing tasks such as simultaneous localization and mapping (SLAM). Within this context, the current trend is to carry out simultaneous calibration of odometry and exteroceptive sensors without using additional hardware. Building upon the existing simultaneous calibration algorithms, we put forth a generalized calibration framework that can not only handle robots operating in 2D with arbitrary or unknown motion models but also handle outliers in an automated manner. We first propose an algorithm based on the alternating minimization framework applicable to two-wheel differential drive. Subsequently, for arbitrary but known drive configurations we put forth an iteratively re-weighted least squares methodology leveraging an intelligent weighing scheme. Different from the existing works, these proposed algorithms require no manual intervention and seamlessly handle outliers that arise due to both systematic and non-systematic errors. Finally, we put forward a novel Gaussian Process-based non-parametric approach for calibrating wheeled robots with unknown or un-modeled drive configurations. Detailed experiments are performed to demonstrate the accuracy, usefulness, and flexibility of the proposed algorithms. 11This paper has supplementary downloadable material (available at http://tinyurl.com/simultaneous-calibration) that includes raw-data of all the experiments and implementation codes for the proposed methodologies.

A wireless signal-based sensing framework for robotics

In this paper, we develop the analytical framework for a novel Wireless signal-based Sensing capability for Robotics (WSR) by leveraging a robots’ mobility in 3D space. It allows robots to primarily measure relative direction, or Angle-of-Arrival (AOA), to other robots, while operating in non-line-of-sight unmapped environments and without requiring external infrastructure. We do so by capturing all of the paths that a wireless signal traverses as it travels from a transmitting to a receiving robot in the team, which we term as an AOA profile. The key intuition behind our approach is to enable a robot to emulate antenna arrays as it moves freely in 2D and 3D space. The small differences in the phase of the wireless signals are thus processed with knowledge of robots’ local displacement to obtain the profile, via a method akin to Synthetic Aperture Radar (SAR). The main contribution of this work is the development of (i) a framework to accommodate arbitrary 2D and 3D motion, as well as continuous mobility of both signal transmitting and receiving robots, while computing AOA profiles between them and (ii) a Cramer–Rao Bound analysis, based on antenna array theory, that provides a lower bound on the variance in AOA estimation as a function of the geometry of robot motion. This is a critical distinction with previous work on SAR-based methods that restrict robot mobility to prescribed motion patterns, do not generalize to the full 3D space, and require transmitting robots to be stationary during data acquisition periods. We show that allowing robots to use their full mobility in 3D space while performing SAR results in more accurate AOA profiles and thus better AOA estimation. We formally characterize this observation as the informativeness of the robots’ motion, a computable quantity for which we derive a closed form. All analytical developments are substantiated by extensive simulation and hardware experiments on air/ground robot platforms using 5 GHz WiFi. Our experimental results bolster our analytical findings, demonstrating that 3D motion provides enhanced and consistent accuracy, with a total AOA error of less than 10◦ for 95% of trials. We also analytically characterize the impact of displacement estimation errors on the measured AOA and validate this theory empirically using robot displacements obtained using an off-the-shelf Intel Tracking Camera T265. Finally, we demonstrate the performance of our system on a multi-robot task where a heterogeneous air/ground pair of robots continuously measure AOA profiles over a WiFi link to achieve dynamic rendezvous in an unmapped, 300 m2 environment with occlusions.

A Novel Decomposition Approach Preventing Spurious Entropy Generation in Hybrid Thermoacoustic Stability Computations

Abstract Prominent approaches for the computation of thermoacoustic stability are hybrid methods like the linearized Navier–Stokes equations (LNSE) or the linearized Euler equations (LEE). The transient fluctuations around a precomputed steady-state mean flow field solved with these sets of equations naturally include the energy transition between acoustic, vertical, and entropic modes. It is common practice to account for flame-acoustic interactions by applying measured or computed flame transfer functions (FTF) as a volumetric source term proportional to the mean heat release rate in the energy equation. However, the underlying assumption of a static flame is the root cause of spurious entropy production, which may ultimately falsify the thermoacoustic stability predictions. In the present paper, a methodology to include arbitrary flame movement in the governing set of equations is presented. The procedure makes use of an arbitrary Lagrangian-Eulerian (ALE) description of conservation equations and is demonstrated for the Euler equations. The resulting set of linear perturbation equations is then applied to two test cases. First, the frequency response of a one-dimensional premixed air-methane flame is evaluated. Secondly, the frequency response of the first longitudinal eigenmode of an experimental premixed, swirl-stabilized combustor is computed. To demonstrate the reduction of spurious entropy waves, the results are compared to those of the classic LEE.