Geometric Path Research Articles

Energy-Optimal Coverage Motion Trajectory Generation for Industrial Machines*

Coverage motion of industrial machines are widely used for manufacturing tasks such as milling, polishing, laser cutting, and inspection. Motion smoothness of industrial machines under their kinematic limits are crucial in coverage motion to increase the production efficiency and accuracy. Motion trajectory optimization for typical computer numerical control (CNC) machines plays an important role in achieving smooth motion. In addition, with the current increase in energy costs and environmental concerns, there is a great need to reduce energy consumption by industrial machines which are extensively used in manufacturing industries. This study presents an energy optimization approach for coverage motion of industrial machines, which simultaneously integrates trajectory generation and geometric path optimization. The trajectory along a linear segment is described by the modified S-curve profile with harmonic motion employed for smooth jerk continuity to enhance the motion accuracy. An energy consumption model of the feed drive system is used to achieve energy-optimal. A genetic algorithm is applied for the optimization. Experimental validation of the simulation results is carried out using a two-axis feed drive system. Simulation and experimental results shows that the energy saving of the feed drive system is achieved under machine kinematic limits ensuring smooth motion.

Predictive Trajectory Planning for On-Road Autonomous Vehicles Based on a Spatiotemporal Risk Field

Trajectory planning plays a crucial role in autonomous driving. It generates feasible geometric paths within a certain time horizon to guide autonomous vehicles. However, typical planning methods give little consideration to the motion uncertainty of traffic objects. Therefore, this article proposes a predictive trajectory planning method based on a spatiotemporal risk potential field. And the key notion of this method is to separate the coupled executions, i.e., trajectory generation and risk assessment, into two parallel and independent modules in the curvilinear coordinate. First, the current spatial risks are quantified by artificial potential-like functions. Then, we measure the probabilities of surrounding vehicles driving toward each lane using an interacting multiple model structure. The temporal evolution of the spatial field is computed by incorporating both the probabilities and predicted trajectories. Meanwhile, the generation module focuses on providing sufficient trajectory candidates for the ego vehicle. To allocate computing resources reasonably, feasibility probabilities are calculated with a relational grid, and then candidates are biased sampled in lateral and longitudinal directions. Finally, taking into account driving safety, comfort, and efficiency, the planner selects an optimal trajectory by minimizing a well-designed cost function. In this way, the feasibility of planned trajectories can be greatly improved with limited time consumption. The performance of this proposed method is evaluated in various scenarios using a high-fidelity Unity3D environment.

Doprinos određivanju jonosferskog kašnjenja GNSS satelitskih signala na teritoriji Republike Srbije

Multi-frequency GNSS satellite signals and their availability enable research in undifferentiated and uncombined models in which a single signal at each frequency is a corresponding independent observation. Such possibilities are reflected by the significant interest in geodetic research as well as in many areas of application of GNSS observation. On the geometric path of the signal between the satellite and the receiver, a significant source of GNSS measurement errors comes from the medium of propagation of electromagnetic waves. Errors attributed to signal propagation are ionospheric and tropospheric signal delay. The mentioned error sources significantly affect the quality of certain pseudorange and, thus, the quality of the receiver's position in the form of three-dimensional coordinates. This paper presents the analysis and determination of the ionospheric delay of GNSS satellite signals based on the determination of Total Electron Content - TEC at five stations (Beograd, Leskovac, Sombor, Zaječar, and Kraljevo) in the territory of the Republic of Serbia. In order to determine TEC values, the software called "GPS-TEC analysis" developed within the Institute for Scientific Research, Boston College, USA was used, which enables the determination of the TEC value on the path between the satellite and the receiver. The data collection was carried out within the year 2022 so that the measurement sessions include characteristic dates when the most significant fluctuations are expected in the context of seasonal variations.

Non-contact measurement of insulating bearing coating thickness based on multi-sensor combination

A high-resolution and non-contact method for measuring the thickness of the insulating ceramic coating is proposed. The measurement system consists of a chromatic confocal sensor, eddy-current sensor, prism, mirror, and high-precision rotatable and liftable platform. The chromatic confocal sensor can obtain the distance from the outer surface of the insulating coating, and the eddy-current sensor can get the distance from the inner surface of the insulating coating. The coating thickness can be obtained from the two sensors’ data combination and calculation. The geometrical optical path is analyzed to study the effect of the prism and mirror on the confocal sensor. The eddy-current sensor is simulated by COMSOL software with electromagnetic theories to explore the relationship between its output response and the measured surface's curvature. The sensing parameters of the two sensors are calibrated and optimized through simulation and experimental validation. Measurement software is developed by Labview to display the coating thickness in real time and reveal its distribution by 3D surface reconstruction. The measuring system’s performance is tested by an insulating bearing with a 60 mm outer radius. The results show that the axial resolution of the measuring system is 0.1 μm, the repeatable linearity is less than 3 μm, the dynamic measuring linearity relative to the mean value of the coating’s thickness is less than 8 μm, the detection speed is about 50 points/min. It has the advantages of high precision, non-contact, quick speed, stability, and visual display.

Model Predictive Path Following Control without terminal constraints for holonomic mobile robots

In this paper, a model predictive path following control (MPFC) for holonomic mobile robots is considered. The MPFC is aimed to control a mobile robot to follow a geometric path, where the time evolution of the path parameterization is not fixed a priori. Instead, the time evolution is considered as an extra degree of freedom of the controller. Contrary to previous works, in this study, the closed-loop asymptotic stability of holonomic mobile robots under MPFC without terminal constraints or costs is rigorously proven and a stabilizing-horizon length is calculated. The analysis is based on verifying the cost-controllability assumption by deriving an upper bound of the MPFC value function with a finite prediction horizon. Then, using this bound, the length of a stabilizing prediction horizon is calculated. The analysis is performed in the discrete time settings and theoretical results are verified with numerical simulations as well as implementations on an actual mobile robot.

A finite and fast time-optimal trajectory planning based on velocity sinking method for robots along specified path

Time-optimal trajectory planning is used in many areas of industrial robots and has a wide range of applications. This paper presents a finite and fast computation method for calculating time-optimal robot trajectories along specified geometric paths, namely the velocity sinking method. The velocity sinking method differs from those proposed in the existing literature which solve uncertain optimization problem. Firstly, the maximum velocity in multiple state constraints is calculated using a path parameterization method. Then, the pseudo maximum velocity trajectory is calculated using a numerical integration method. Finally, the time-optimal trajectory planning under path constraints is determined using an iterative velocity sinking algorithm. The experiment demonstrates the effectiveness and efficiency of this method in industrial robotic settings.

Large deflection response of sandwich beams with layered-gradient foam cores subjected to low-velocity impact

The sandwich structures with gradient cores perform a wide application prospect due to their good design potential. Herein, an analytical model of fully clamped sandwich beams (SBs) with layered-gradient foam core (LGFC) under low-velocity heavy-mass impact was formulated, where the interactions between the bending and stretching were incorporated. The dynamic solutions for deflection response of three-layer graded core SBs were attained by introducing the newly developed yield criteria and were quantitatively confirmed by the corresponding numerical simulations and experiments, which allows for parametric study of the influence of core strength on load-bearing capacity of SBs. It demonstrates that the impact resistance of the uniform core SBs is superior to that of layered-gradient core SBs. Except for the top core layer of the positive gradient SBs, the increase in core layer strength will greatly enhance the load-bearing capacity of SBs in large deflection response situations, where membrane force plays a dominant role. Finally, the minimum mass design chart was constructed using the derived analytical formula to give the geometric optimization paths.

Geometric Path Plans for Perpendicular/Parallel Reverse Parking in a Narrow Parking Spot with Surrounding Space

This study proposes geometric path plans composed of two stages to automatically perform perpendicular and parallel parking with a reverse path in a narrow space. In perpendicular parking, the minimum width of the available parking spot is computed before the start of the parking operation, and the availability of parking and the optimal stage of the path plan are determined by considering the surrounding space together. In a similar concept, even in parallel parking, it is possible to determine whether to park by calculating the minimum length of the available parking spot and the number of repetitions of motion before starting the parking operation. The theoretical results for the parking spot and surrounding space related to the geometric path plans of perpendicular and parallel parking were confirmed through model car tests. Efficient automatic parking will be enabled by selecting and establishing an appropriate path plan along with the availability of parking in consideration of the parking spot and the surrounding space before starting the parking operation.

Path Planning of Electric VTOL UAV Considering Minimum Energy Consumption in Urban Areas

As a new mode of transportation in the future, electric vertical take-off and landing unmanned aerial vehicles (eVTOL UAV) can undertake the task of logistics distribution and carry people in urban areas. It is challenging to carry out research designed to plan the path of eVTOL UAVs which can have a safe and sustainable operation mode in urban areas. Therefore, this work proposes a method for planning an obstacle-free path for eVTOL UAVs in urban areas with the goal of minimizing energy consumption. It aims to improve the safety and sustainability of eVTOL UAV operations. Based on variations of air density with height, a more accurate formula for calculating battery energy consumption of eVTOL UAV is derived. It is used in the vertical takeoff and landing phase and horizontal flight phase, respectively. Considering the influence of buildings on eVTOL UAV operation, a path planning method applicable to complex urban environments is proposed. The safe nodes of eVTOL UAV flight are obtained by using Voronoi diagrams based on building locations. Then, the complete shortest and obstacle-free path is obtained by using a Dubins geometric path and Floyd algorithm. After obtaining the obstacle-free paths for all flight height zones, the battery energy consumption of the eVTOL UAV in each flight height zone is calculated. Then, the flight height with the minimum energy consumption is obtained. The simulation results show that the path length obtained by the proposed path planning method is shorter than that obtained by particle swarm optimization; the total battery energy consumption changes in the same pattern in the low-altitude areas and high-altitude areas; the difference between the maximum and minimum energy consumption in the small area enables the eVTOL UAV to cover about 350 m more, and about 420 m more in the large area. Therefore, in future high-frequency UAV mission flights, choosing the altitude with the lowest energy consumption can reduce UAV operator costs. It can also significantly increase UAV transport range and make UAVs operate more sustainably.

Collaborative Mobile Robotics for Semantic Mapping: A Survey

Ensuring safety in human–robot collaboration is one of the main challenges in mobile robotics today. Semantic maps are a potential solution because they provide semantic knowledge in addition to the geometric representation of the environment. They allow robots to perform their basic tasks using geometric representation, mainly localization, path planning and navigation, and additionally allow them to maintain a cognitive interpretation of the environment in order to reason and make decisions based on the context. The goal of this paper is to briefly review semantic mapping for a single mobile robot in indoor environments, and then focus on collaborative mobile semantic mapping. In both contexts, the semantic mapping process is divided into modules/tasks, and recent solutions for each module are discussed. Possible system architectures are also discussed for collaborative semantic mapping. Finally, future directions are highlighted.

Hexagon path planning algorithm

The paper presents a novel 2D geometrical path plan algorithm that reduces calculation load and time by filtering obstacles before path planning starts by the newly introduced hexagon filter and also while path search is in progress. Unlike other methods that use only obstacle filtering before path planning starts. The suggested algorithm was able to solve a randomly created maze that contains 400 obstacles with 800 nodes, which was considered before, as next to impossible to solve. This is because computational time is proportional to n2log(n) where n is the number of obstacles, node suggested algorithm reduced the computational time to about 1 in 2500 times compared to the best of (ESOVG, DVG or ECoVG). In addition, the suggested algorithm can be used in the case of a fixed start point and different target points (e.g. a swarm of robots leaving from the same start point with different targets).

Atmospheric model inversion using infrasound signals from the North Korean underground nuclear explosion and the subsequent collapse event in 2017

SUMMARY This study focuses on the infrasound signals from the September 2017 North Korean underground nuclear explosion (UNE17) and subsequent collapse event (SCE17) that occurred close to the autumnal equinox when the atmospheric temperature structure undergoes rapid change. Multiple arrivals, including contributions from local, diffracted and epicentral infrasound, generated by UNE17, were observed at eight infrasound arrays in the Korean Peninsula and one IMS infrasound station (IS45) in Russia while at the closest five arrays for SCE17 only epicentral infrasound was observed. The UNE17 signals provide the opportunity to explore the utility of each distinct arrival in constraining atmospheric conditions during the change associated with the equinox. The observed characteristics of the multiple epicentral infrasonic phases (celerity, backazimuth, phase velocity and spectra) suggest propagation paths through the tropospheric, stratospheric and thermospheric waveguides, although geometric ray paths based on a global atmospheric model at the time of the explosion predict only thermospheric returns. The absence of predicted stratospheric returns may reflect errors in the atmospheric models due to the lack of predicted stratospheric winds which are weak and changing close to the autumnal equinox or the limited resolution of the fine-scale structure not captured by current atmospheric models. The differences between the model predictions and the observations suggest that the numerical weather forecast models need to be modified to fully explain the observations. In order to explore the model space that can explain the UNE17 data set, an inversion scheme is applied to atmospheric wind model parameters constrained by the multi-array observations. Zonal and meridional wind profiles are parametrized using empirical orthogonal functions (EOFs) estimated from 1-yr of Ground-to-Space atmospheric specifications. A best-fitting atmospheric model is estimated using a Bayesian approach that assesses the uncertainty in the inverse solution using a joint likelihood function combining components of azimuth deviation, traveltime and phase velocity. The updated atmospheric models from six different EOFs inversions have up to 20 m s–1 stronger zonal and meridional wind speeds in the stratosphere compared to the original model, and explain the stratospheric observations in the data set. This investigation illustrates that modest changes to atmospheric wind models at the time of autumnal equinox can improve the prediction of stratospheric returns.

Performance enhancement of multi channel multi beam FSO communication link with the application of Reed Solomon codes

The rising user needs for high speed applications and services have necessitated the requirement of a communication link that can provide the data rate comparable to optical fiber. Free Space Optical (FSO) Communication is an admired means of communication from past few years. To achieve seamless and error free transmission at high speed for heterogeneous multimedia applications at desired bit rates, novel advancements in optical communication technology are being explored along with FSO. However, several constraints such as atmospheric turbulence, uneven terrain, dynamic climatic conditions cause several nonlinearities which limit the connectivity. In this work, a multi channel multi beam FSO communication system by incorporating Reed Solomon (RS) Codes has been proposed at 30 Gbps. The Modified Gamma-Gamma model is being applied for channel turbulences. The application of Forward Error Correction (FEC) coding in the designed system offers ease of error detection and correction with improved performance at higher data rate for implementation over longer link lengths.The system performance has been evaluated for (i) Number of errors corrected, (ii) Bit Error Rate (BER), (iii) Received power, (iv) Geometric path losses and (v) Signal to Noise Ratio (SNR). At an acceptable BER of 10–9, the RS (255, 127, 129) encoded Four channel Four beam FSO communication link is effectively implemented for a distance of 3500 m with − 32.5 dBm received low optical power and 25 dB SNR.

On the use of recurrent neural networks for fast and accurate non-uniform gas radiation modeling

This paper focuses on the construction of a fast though accurate gas radiation model based on a Recurrent neural network (RNN) formulation. The model is founded on recent works in which a solution to a non-uniform technique proposed by Godson in the 50s was derived explicitly. The method uses a non-linear transformation of a set of physical / geometrical paths, directly related to a non-uniform path which is first discretized into uniform sub-layers, into a sequence of equivalent absorption lengths. This process, studied thoroughly within the frame of the development of the ℓ-distribution approach, can be naturally handled using an algorithm that takes the form of an RNN model. The method is assessed against LBL calculations in non-uniform high temperature gaseous media and found to provide more accurate results than a CKD (Correlated K-Distribution) model with 16 gray gases. This paper is the first to suggest an RNN to treat radiative transfer in non-uniform gaseous media. Moreover, all the weights involved in the RNN have a clear physical meaning so that the structure of the RNN can be readily interpreted, avoiding the black box disadvantage of most brute force machine learning strategies.

Geometric rough paths on infinite dimensional spaces

Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For α∈(1/3,1/2), we give criteria for when we can approximate Banach space-valued weakly geometric α-rough paths by signatures of curves of bounded variation, given some tuning of the Hölder parameter. We show that these criteria are satisfied for weakly geometric rough paths on Hilbert spaces. As an application, we obtain Wong-Zakai type result for function space valued martingales using the notion of (unbounded) rough drivers.

Retraction Note: Group intelligent deep learning model based on grouping combinatorial geometric path

Retraction Note: Group intelligent deep learning model based on grouping combinatorial geometric path

Investigating diffusion mechanism for HTO and Se(IV)/Se(VI) in compacted Tamusu clay rock with different column lengths

Abstract Due to continuous self-sealing and good mechanical properties, the Tamusu clay rock of Inner Mongolia has been identified as the pre-selected site for high-level radioactive waste geological disposal site in China. The study of chemical behaviors related to Tamusu clay rock, such as nuclide migration, will be an important content of the performance assessment and safety assessment of the disposal repository in the future. The diffusion behavior of HTO and Se(IV)/Se(VI) with different compacted column lengths in Tamusu clay rock is discussed by the through-diffusion method. The diffusion coefficient, rock capacity factor, effective porosity, and other diffusion parameters closely related to nuclide migration are calculated, and the mechanism of nuclide diffusion is preliminarily discussed. The results show that D a (6.23 × 10−11∼17.96 × 10−11 m2 s−1), D e (1.62 × 10−11∼4.67 × 10−11 m2 s−1) for HTO increase with the increase of the compacted column length, and it is proposed that the diffusion process of HTO is affected by the change of geometrical factor and path tortuosity. D a (7.29 × 10−13∼1.74 × 10−13 m2 s−1), D e (5.15 × 10−12∼2.15 × 10−12 m2 s−1) for Se(IV), D a (3.11 × 10−12∼1.09 × 10−12 m2 s−1), D e (2.53 × 10−12∼1.09 × 10−12 m2 s−1) for Se(VI), which decrease with the increase of the compacted column length, it is mainly due to the existence of anion repulsion effect.

Optical coherence tomography refraction and optical path length correction for image-guided corneal surgery.

Optical coherence tomography (OCT) may be useful for guidance of ocular microsurgeries such as deep anterior lamellar keratoplasty (DALK), a form of corneal transplantation that requires delicate insertion of a needle into the stroma to approximately 90% of the corneal thickness. However, visualization of the true shape of the cornea and the surgical tool during surgery is impaired in raw OCT volumes due to both light refraction at the corneal boundaries, as well as geometrical optical path length distortion due to the group velocity of broadband OCT light in tissue. Therefore, uncorrected B-scans or volumes may not provide an accurate visualization suitable for reliable surgical guidance. In this article, we introduce a method to correct for both refraction and optical path length distortion in 3D in order to reconstruct corrected OCT B-scans in both natural corneas and corneas deformed by needle insertion. We delineate the separate roles of phase and group index in OCT image distortion correction, and introduce a method to estimate the phase index from the group index which is readily measured in samples. Using the measured group index and estimated phase index of human corneas at 1060 nm, we demonstrate quantitatively accurate geometric reconstructions of the true cornea and inserted needle shape during simulated DALK surgeries.

Fuel-Optimal Geometric Path Planning Algorithm for Spacecraft Formation Flying

A novel geometric guidance algorithm is proposed for spacecraft formation flying. The controllability of the full relative motion is analyzed using Lie bracket theory. The fuel-optimal two-point boundary value problem is reframed into a curve minimization on a Riemannian manifold. The optimal path is shown to be a geodesic of the solution manifold, and it is obtained by solving a partial differential equation. The large convergence radius of the proposed method is robust to bad initial guesses. The geometric guidance is used in a multiple-spacecraft architecture, and a collision avoidance scenario illustrates how the geometric path planner solves constrained path planning problems. Finally, the proposed guidance is compared to a regulator path planner to showcase the low fuel requirement associated with traveling along the geodesic.

Shortest path with acceleration constraints: complexity and approximation algorithms

We introduce a variant of the Shortest Path Problem (SPP), in which we impose additional constraints on the acceleration over the arcs, and call it Bounded Acceleration SPP (BASP). This variant is inspired by an industrial application: a vehicle needs to travel from its current position to a target one in minimum-time, following pre-defined geometric paths connecting positions within a facility, while satisfying some speed and acceleration constraints depending on the vehicle position along the currently traveled path. We characterize the complexity of BASP, proving its NP-hardness. We also show that, under additional hypotheses on problem data, the problem admits a pseudo-polynomial time-complexity algorithm. Moreover, we present an approximation algorithm with polynomial time-complexity with respect to the data of the original problem and the inverse of the approximation factor epsilon. Finally, we present some computational experiments to evaluate the performance of the proposed approximation algorithm.