Relative Motion Research Articles

Fast and Accurate Relative Motion Tracking for Dual Industrial Robots

Fast and Accurate Relative Motion Tracking for Dual Industrial Robots

Stable-to-unstable transition in quantum friction

We investigate the frictional force arising from quantum fluctuations when two dissipative metallic plates are set in a shear motion. While early studies showed that the electromagnetic fields in the quantum friction setup reach nonequilibrium steady states, yielding a time-independent force, other works have demonstrated the failure to attain steady states, leading to instability and time-varying friction under sufficiently low-loss conditions. Here, we develop a fully quantum-mechanical theory without perturbative approximations, and we unveil the transition from stable to unstable regimes of the quantum friction setup. Due to the relative motion of the plates, their electromagnetic response may be active in some conditions, resulting in optical gain. We prove that the standard fluctuation-dissipation leads to inconsistent results when applied to our system, and, in particular, it predicts a vanishing frictional force. Using a modified fluctuation-dissipation relation tailored for gain media, we calculate the frictional force in terms of the system Green's function, thereby recovering early works on quantum friction. Remarkably, we also find that the frictional force diverges to infinity as the relative velocity of the plates approaches a threshold. This threshold is determined by the damping strength and the distance between the metal surfaces. Beyond this critical velocity, the system exhibits instability, akin to the behavior of a laser cavity, where no steady state exists. In such a scenario, the frictional force escalates exponentially. Our findings pave the way for experimental exploration of the frictional force in proximity to this critical regime. Published by the American Physical Society 2024

Evasion Maneuver and Timing Strategy for UAVs Under Direct Force Control

Given the capabilities of modern high-performance missiles, efficient evasion maneuver strategies are crucial for enhancing UAV survivability. This paper addresses the integration of evasion strategies and maneuver timing for targeted UAVs. First, a three-dimensional engagement scenario is modeled using the relative motion mechanism. Subsequently, a fundamental evasion strategy focusing on large roll maneuvers and two-phase acceleration is developed. With the initiation timing of direct force control designated as the control variable, the formulation of a constrained optimization problem to maximize miss distance is fully articulated. While preserving the high fidelity of the established switching model, the feasible timing intervals and the optimal timing are determined through numerical optimization. Finally, simulation experiments are conducted focusing on omnidirectional attacks from the upper hemisphere. The results demonstrate that by implementing specific evasion maneuvers at optimal timing, the target successfully escapes the effective range of the proximity fuse, thus confirming the feasibility of the proposed evasion maneuver and timing strategy.

Analytical Second-Order Extended Kalman Filter for Satellite Relative Orbit Estimation

This study considers a relative orbit estimation problem wherein an observing spacecraft navigates with respect to a target space object at a large separation distance (several kilometers) using only the bearing angles obtained by a single onboard camera. Generally, the extended Kalman filter (EKF), which is based on linear relative motion equations such as the Clohessy–Wiltshire equation, is used for the relative navigation of satellites. The EKF linearizes the estimation error around the current estimate and applies the Kalman filter equations to this linearized system. However, it has been shown that nonlinearities of the orbit determination problem can make the linearization assumption insufficient to represent the actual uncertainty. Therefore, an analytical second-order extended Kalman filter (ASEKF) for relative orbit estimation is proposed in this study. The ASEKF, to sequentially estimate the relative states of satellites and their associated uncertainties, is formulated based on a second-order analytic relative-motion equation under J2-perturbtation, which can overcome the deficiencies of existing approaches that mainly focus on applications in two-body, near-circular, and linearized orbit dynamics. Numerical results show that the proposed method provides superior robustness and mean-square error performance compared to linear estimators under the conditions considered.

Identification of ischemia with no obstructive coronary arteries using 13N-ammonia positron emission tomography-derived myocardial strain ratio

Abstract Background Ischemia with no obstructive coronary arteries (INOCA) is a chronic health problem with poor prognosis and remains challenging to diagnose. 13N-ammonia positron emission tomography (NH3-PET) is the most reliable method for detecting INOCA. We recently developed a unique myocardial strain analysis for NH3-PET to detect ischemia-related motion abnormalities. Purpose We examined the usefulness of NH3-PET strain analysis to identify patients with INOCA. Methods Overall, 98 patients with non-obstructive coronary arteries who underwent adenosine-stress NH3-PET were enrolled. INOCA was defined based on the ESC guidelines. Using an original feature-tracking algorithm dedicated to NH3-PET, the circumferential strain was calculated. Myocardial strain ratio (MSR) was defined as the ratio of strains at stress and rest. In addition, global myocardial flow reserve (MFR) was obtained. Results Finally, forty-seven patients were diagnosed with INOCA, and 51 without INOCA. Global MFR were significantly lower in patients with INOCA than in those without INOCA (1.82 ± 0.52 vs. 2.65 ± 0.65, p<0.0001). MSR were significantly lower in patients with INOCA than in those without INOCA (0.94 ± 0.11 vs. 1.04 ± 0.12, p<0.001). Receiver-operating characteristic analysis showed that using the optimal cutoff of the MSR, INOCA could be diagnosed with area under the curve of 0.71. At a median follow-up of 957 days, Kaplan–Meier analysis revealed that the survival rate worsened in patients with INOCA and low MSR (log-rank test, p<0.001). Conclusions MSR derived from feature-tracking of NH3-PET is reduced in patients with INOCA. It might suggest a predictive value to identify microvascular dysfunction or related motion abnormalities in patients with INOCA.

Rapid shear zone weakening during subduction initiation

Subduction zones play a pivotal role in the mechanics of plate tectonics by providing the driving force through slab pull and weak megathrusts that facilitate the relative motion between tectonic plates. The initiation of subduction zones is intricately linked to the accumulation of slab pull and development of weakness at plate boundaries and, by consequence, the largest changes in the energetics of mantle convection. However, the transient nature of subduction initiation accompanied by intense subsequent tectonic activity, leaves critical evidence poorly preserved and making subduction initiation difficult to constrain. We overcome these limitations through a comprehensive analysis focused on Puysegur, a well-constrained extant example of subduction initiation offshore South Island, New Zealand. Through time-dependent, three-dimensional thermo-mechanical computations and quantitative comparison to new geophysical and geological observations, including topography, stratigraphy, and seismicity, we demonstrate that subduction initiation develops with a fast strain weakening described with a small characteristic displacement ([Formula: see text] 4 to 8 km). Potential physical mechanisms contributing to the strain weakening are explored and we find that the observed fast weakening may arise through a combination of grain-size reduction within the lower lithosphere and fluid pressurization at shallower depths. With the shared commonality in the underlying physics of tectonic processes, the rapid strain weakening constrained at Puysegur offers insights into the formation of the first subduction during early Earth and the onset of plate tectonics.

A reproducible representation of healthy tibiofemoral kinematics during stair descent using REFRAME – Part II: Exploring optimisation criteria and inter-subject differences

Kinematic analysis is a central component of movement biomechanics, describing the relative motion of joint segments during different activities, in different subject cohorts, and at different timepoints. Establishing whether two sets of kinematic signals represent fundamentally similar or different underlying motion patterns is especially challenging, given 1) the lack of consensus around reference frame and joint axis definition, and 2) the substantial effect that minimal variations in frame position and orientation are known to have on signal magnitude and characteristics. As such, enormous variability in the reporting of tibiofemoral kinematics has resulted in joint movement patterns that remain controversially discussed. Previously, we demonstrated the ability of the REference FRame Alignment MEthod (REFRAME) to reorientate and reposition differently aligned local segment frames to achieve convergence in signals representing the same underlying motion, thereby offering a novel approach to consistently report joint motion. In this study, for the first time, we apply REFRAME to assess the rotational and translational in vivo tibiofemoral motion of ten healthy subjects during stair descent based on kinematic signals collected using a moving videofluoroscope. Kinematics were analysed before and after different REFRAME implementations, revealing generally neutral ab/adduction behaviour, accompanied by varying degrees of a sinusoidal int/external tibial rotation pattern over the activity cycle. Our data demonstrate that different selected implementations of REFRAME are able to highlight different characteristics of the motion patterns: Minimisation of the translational root-mean-square revealed proximodistal translation patterns with overall neutral progression, while anteroposterior translation showed seemingly different levels of correlation with flexion/extension in different subjects. On the other hand, REFRAME minimisation of translational variances exposed differences in the relative mean displacement between the femoral and tibial origins between subjects, highlighting differences in mean centre of rotation positions. This early application of REFRAME for providing an understanding of tibiofemoral kinematics demonstrates the potential of this novel approach to bring clarity to an otherwise complex representation of highly variable time-series signals, while highlighting the philosophical challenges of clinically interpretating kinematic signals in the first place.

LIVS: a tightly coupled LiDAR, IMU, and camera-based SLAM system under scene degradation

In increasingly complex environments, single-sensor-based SLAM systems face scene degradation problems such as strong light, dynamic obstacle interference, and lack of structural features in the environment, which severely constrain the localization accuracy and mapping effectiveness of SLAM systems. To address this problem, this paper proposes a tightly coupled laser-IMU-visual SLAM system (LIVS) based on factor graph optimization. LIVS consists of two subsystems: the laser inertial system (LIS) and the visual inertial system (VIS). The pose estimation of the LIS can provide an initialization for the VIS; LiDAR suffers scene degradation in environments lacking structural features, while the VIS provides better constraints for Lidar in this environment. Firstly, a method of selecting keyframes based on ORB features and the relative motion of the mobile robot is proposed as a means of improving the positioning accuracy and tracking ability of the system in the case of strenuous motion, and a strategy of local sliding window optimization is adopted to effectively improve the real-time performance and robustness of the system. Meanwhile, in order to further improve the global map consistency and positioning accuracy, a hybrid closed-loop detection method based on laser and vision is proposed, which utilizes the geometrical features of laser and the image features of vision to accomplish the hybrid closed-loop detection. Secondly, the laser inertia factor, IMU pre-integration factor, vision inertia factor, and closed-loop factor are globally optimized in a factor map framework to achieve accurate estimation of the robot pose. Finally, this paper presents experimental evaluations on both public and homemade datasets and compares the performance of the proposed algorithm with that of other algorithms. Experimental results show that the algorithm in this paper exhibits better performance in both localization accuracy and mapping effectiveness.

An optimization DEM modelling method for soil-fibre undrained cyclic loading tests model based on the influence range of fibre

The computational cost of discrete element modelling is high owing to the limitations of particle size and contact in fibre modelling. This paper proposes an optimised discrete element method (DEM) for a hybrid model of soil and fibres based on the fibre influence range. First, a relative velocity state function is established based on the relative motion state between the fibres and soil particles under undrained cyclic loading. Subsequently, the influence range of the fibres is determined using the relative velocity function based on the first few cycles of the undrained cyclic loading numerical tests. Cluster and clump models of the fibre are then generated based on the influence range of the fibre. Finally, a symmetrical shape of the optimised model is developed by extracting the distribution length of the edge curve of the influence range along the vertical direction of the axis. In this study, the proposed optimised DEM was validated through a series of undrained cyclic loading numerical tests on fibre-reinforced soil. The results of the optimised model were highly consistent with those of the traditional model, and the computational time was significantly reduced. The cyclic loading timing for determining the range of influence of the fibre was analysed. The optimised model based on the influence range of the 15th cycles not only restored almost the same results but also saved the calculation cost by nearly eight times. The optimised model established based on the influence range after the 15th cycles had a slight influence on the results. In addition, the applicability of the optimised model is discussed. This paper provides new insights into the establishment of a hybrid model of soil and fibres.

Six-degrees-of-freedom pelvic bone monitoring on 2D kV intrafraction images to enable multi-target tracking for locally advanced prostate cancer.

Patients with locally advanced prostate cancer require the prostate and pelvic lymph nodes to be irradiated simultaneously during radiation therapy treatment. However, relative motion between treatment targets decreases dosimetric conformity. Current treatment methods mitigate this error by having large treatment margins and often prioritize the prostate at patient setup at the cost of lymph node coverage. Treatment accuracy can be improved through real-time multi-target adaptation which requires simultaneous motion monitoring of both the prostate and lymph node targets. This study developed and evaluated an intrafraction pelvic bone motion monitoring method as a surrogate for pelvic lymph node displacement to be combined with prostate motion monitoring to enable multi-target six-degrees-of-freedom (6DoF) tracking using 2D kV projections acquired during treatment. A method to monitor pelvic bone translation and rotation was developed and retrospectively applied to images from 20 patients treated in the TROG 15.01 Stereotactic Prostate Ablative Radiotherapy with Kilovoltage Intrafraction Monitoring (KIM) trial. The pelvic motion monitoring method performed template matching to calculate the 6DoF position of the pelvis from 2D kV images. The method first generated a library of digitally reconstructed radiographs (DRRs) for a range of imaging angles and pelvic rotations. The normalized 2D cross-correlations were then calculated for each incoming kV image and a subset of DRRs and the DRR with the maximum correlation coefficient was used to estimate the pelvis translation and rotation. Translation of the pelvis in the unresolved direction was calculated using a 3D Gaussian probability estimation method. Prostate motion was measured using the KIM marker tracking method. The pelvic motion monitoring method was compared to the ground truth obtained from a 6DoF rigid registration of the CBCT and CT. The geometric errors of the pelvic motion monitoring method demonstrated sub-mm and sub-degree accuracy and precision in the translational directions ( , , ) and rotational directions ( , , ). The 3D relative displacement between the prostate and pelvic bones exceeded 2, 3, 5, and 7mm for approximately 66%, 44%, 12%, and 7% of the images. Accurate intrafraction pelvic bone motion monitoring in 6DoF was demonstrated on 2D kV images, providing a necessary tool for real-time multi-target motion-adapted treatment.

Multi-digit touch II: perceptual weighting during integration follows a leading-finger priority.

When we run our hand across a surface, each finger typically repeats the sensory stimulation that the leading finger has already experienced. Because of this redundancy, the leading finger may attract more attention and contribute more strongly when tactile signals are integrated across fingers to form an overall percept. To test this hypothesis, we re-analysed data collected in a previous study (Arsanova et al., 1), where two probes were moved in different directions on two different fingerpads and participants reported the probes' average direction. Here, we evaluate the relative contribution of each finger to the percept and examine whether multi-digit integration gives priority to the leading finger. Although the hand actually remained static in these experiments, a 'functional leading finger' could be defined with reference to the average direction of the stimuli, and the direction of hand-object relative motion that this implied. When participants averaged the motion direction across fingers of the same hand, the leading finger received a higher weighting than the non-leading finger, even though this biased estimates of average direction. Importantly, this bias disappeared when averaging motion direction across the two hands. Both the reported average direction and its systematic relation to the difference between the individual stimulus directions were explained by a model of motion integration in which the sensory weighting of stimuli depends on the directions of the applied stimuli. Our finding supports the hypothesis that the leading finger, which often receives novel information in natural hand-object interactions, is prioritized in forming our tactile perception.

Synchronous flying-around control for uncontrolled tumbling spacecraft

The problem of synchronous flying-around control for uncontrolled tumbling target spacecraft is investigated in the paper. Firstly, the relative motion equations of the chaser and the target is established based on the line of sight (LOS) coordinate system, and the scenario of the chaser flying-around uncontrolled tumbling target is analyzed. Secondly, the attitude motion model of the uncontrolled tumbling target is established, and the attitude of the target is described by the Modified Rodriguez Parameters (MRPs). The synchronous flying-around problem is transformed into a two-dimensional control problem in the instantaneous rotation plane of LOS (IRPL). The sliding mode controller is designed to control the LOS direction and vertical LOS direction of the chaser in the IRPL, and the stability of the controller is analyzed. In order to verify the effectiveness of the synchronous flying-around control method, three simulation scenarios are designed. The simulation results verify the effectiveness of the proposed method.

An Efficient Attentive-GRU Structure for Uncertainty Modelling of Crowdsourced Human Trajectories Under Building-obscured Urban Scenes

Abstract. Uncertainty modelling is regarded as one of the core components in the field of human mobility analysis and urban navigation, that can affect the performance of human behaviour modelling and location information acquisition. Existing uncertainty modelling algorithms towards the human movement trajectory are subjected to random and highly dynamic human motion characteristics and sampling and observation errors of Global Navigation Satellite System (GNSS) signals caused by the occlusion of buildings in urban scenes, which lead to the insufficient spatiotemporal correlation and poor accuracy of uncertainty modelling. To fill in this gap, this paper proposes an efficient attentive-GRU structure for uncertainty modelling of crowdsourced human trajectories under building-obscured urban scenes, that takes into account both temporal correlation and spatial correlation of human-originated GNSS trajectories and related motion features. A period of human motion data is modelled instead of only one or adjacent location points to avoid interference factors caused by the obstruction of urban buildings, and time-varying measurement and sampling errors are further estimated and combined with comprehensive human motion features to improve the accuracy of final uncertainty modelling. Comprehensive experiments indicate that compared with existing uncertainty modelling methods including physical models and deep-learning models, the proposed attentive-GRU structure realizes much better performance under different accuracy indexes.

Fracture mechanism and constitutive model considering post-peak plastic deformation of marble under thermal–mechanical action

Temperature plays an important impact on rock mechanical properties. In this paper, the mechanical properties, fracture mechanism and constitutive model of marble under 20–120 °C and 15 MPa are studied. The results show marble deformation can be divided into four stages: compaction, linear elasticity, crack propagation and post-peak failure. Stress–strain curve is not obviously affected by temperature. Macroscopic fracture characteristics change from shear failure to tensile mixed failure with temperature increasing. With the increase of temperature, the strength of marble tends to decrease, indicating that temperature increase has a weakening effect on marble, and there are temperature-sensitive areas of 20–60 °C and temperature sub-sensitive areas of 60–120 °C. The elastic modulus of marble decreases and Poisson’s ratio increases with increasing temperature. The energy evolution law of marble under different temperature is basically the same, which shows that before crack initiation, the energy dissipation is less, and after the damage and yielding occurs, the energy dissipation increases quickly. The energy dissipation in the failure process is mainly used for crack initiation-connection-penetration, as well as plastic deformation caused by friction and slip of cracks, and the plastic deformation and energy dissipation have good linear characteristics. The statistical damage constitutive model based on three-parameter Weibull distribution function can effectively reflect the characteristics of post-peak plastic deformation and strain softening. The weakening effect of marble at 20–120 °C is related to its internal moisture excitation. With the increase of temperature, water is stimulated to absorb and attach to the original relatively dry interface, which plays a role in lubrication. The relative motion friction resistance between solid particles or crack surfaces decreases, which leads to crack initiation and friction energy consumption reduction, changes the specific surface energy of rocks and weakens the strength of marble. The results provide a theoretical basis for predicting and evaluating the long-term stability and safety of surrounding rock of underground deep engineering in complex environment with high ground temperature and high geo-stress.

Aerodynamic Feasibility Investigation of the Novel Experimental Rig on Turbine Blade Tip With High Relative Motion

Abstract The relative casing motion can significantly alter the over-tip-leakage (OTL) flow aerodynamic performances. Traditional tip experimental facilities for relative motion researches, including stationary linear cascade with low-speed moving belt, annular cascade with rotating outer wall, and full-scale experimental rig with rotating blade, were either extremely costly or not capable to reproduce engine-representative casing Mach number. Very recently, a novel design concept for high-speed disk rotor rig has been proposed for tip research. Subsequent to this research, the present study evaluates the aerodynamic performances and the periodicity of the disk rotor rig design using Reynolds-averaged Navier–Stokes computational fluid dynamics simulation. Furthermore, first-of-its-kind experimental results of total pressure loss distributions measured by five-hole probe under high relative casing Mach number are reported. The results demonstrate the applicability of the disk rotor experimental rig for tip aerodynamic investigations.

The deceleration parameter in perturbed Bianchi universes with a peculiar-velocity “tilt”

Bianchi cosmologies are “natural” anisotropic extensions of the Friedmann universes and they have long been used to investigate the cosmological implications of anisotropy. The latter introduces new ingredients to the standard scenarios, although there are physical processes and effects that maintain their basic Friedmann features when extended to Bianchi universes. Here, we assume a perturbed Bianchi model and look into the implications of the observers’ peculiar flow for their measurement and their interpretation of the deceleration parameter. Our motivation is twofold. To begin with, relative motions have long been known to deceive the observers by “contaminating” the observations, which also still suffer from sample limitations that cloud the statistical significance of the findings. Further motivation comes from claims that observers in bulk flows that expand slightly slower than their surroundings can have the illusion of cosmic acceleration in a universe that is actually decelerating. The claim was originally based on studies of a perturbed tilted Einstein–de Sitter model, but persisted when the background cosmology was replaced by any of the three Friedmann universes. This raised the possibility that the peculiar-motion effect on the deceleration parameter may be generic and largely independent of the host spacetime. Here, we investigate this possibility by extending the earlier studies to perturbed Bianchi models. We find that the Friedmann picture remains unchanged, unless the Bianchi background has unrealistically high anisotropy. The bulk-flow observers can still be misled to the illusion of accelerated expansion by their own peculiar motion.

A novel collaborative collision avoidance decision method for multi-ship encounters in complex waterways

With the continuous growth of maritime traffic volume, multi-ship collision avoidance has gradually become one of the most crucial issues in ensuring the safety of ship navigation. This study proposes a multi-ship collaborative collision avoidance decision model (MCCA) to address the issue of multi-ship encounters in complex waterways. The model takes into account the ship spatio-temporal collision risk, relative motion trends, as well as the safety and economic considerations of ship navigation. A comprehensive collision avoidance method is designed based on the velocity obstacle method, enabling simultaneous adjustments both course and speed, with the aim of minimizing economic losses incurred by ships due to avoidance operations while ensuring ship navigation safety. Meanwhile, the NSGA-II algorithm, which has faster convergence and better effect, is used to calculate the optimal collaborative collision avoidance decision of multiple ships. Besides, both simulation and example validation are used to test the validity of the model. The results indicate that the proposed model can effectively achieve multi-ship collaborative collision avoidance in the region. Simultaneously, it holds significant reference value for guaranteeing the safety of ship navigation, enhancing supervision efficiency, and promoting the development of intelligent ship navigation systems.

Synergistic Tribological Effects of Ti3C2Tx MXene and ZDDP under Simple Grafting Strategies for Efficient Lubrication.

MXenes, a novel class of two-dimensional materials, possess exceptional physical and chemical properties, positioning them as promising candidates for lubricant additives. However, their potential is constrained by challenges in dispersion and stability, coupled with a paucity of research on interactions with additives in full-formula oils. In this study, hexadecylphosphonic acid (HDPA) is grafted onto Ti3C2Tx to formulate a polyalkylene glycol dispersion system. The findings reveal that the HDPA-modified Ti3C2Tx (HDPA-Ti3C2) is successfully synthesized, demonstrating superior dispersion stability and notable friction-reduction and antiwear properties. Notably, when combined with zinc dialkyl dithiophosphate (ZDDP), the HDPA-Ti3C2/ZDDP composite additive outperforms single additives in tribological performance, suggesting synergistic effects between them. This enhanced performance may be attributed to the formation of an amorphous polyphosphate tribofilm offering wear resistance, followed by the generation of a TiO2 tribofilm that further safeguards and repairs the worn surface, thereby enhancing the load-bearing capacity. Concurrently, the interlayer sliding mechanism of nanosheets, which substitutes the relative motion of the friction pair, reduces friction under boundary lubrication, ensuring prolonged effective lubrication. This work broadens the application prospects of Ti3C2Tx MXene for the design and development of commercial lubricating additives.

A review of research on the development of low-orbit Internet constellations

In recent years, with the surge in Internet users, innovative companies such as SpaceX and OneWeb have planned to build low-orbit Internet constellations, triggering a global boom in the development of low-orbit satellite Internet constellations. Therefore, it is of great significance to study the development of low-orbit Internet constellations at home and abroad and the technical difficulties currently faced by low-orbit Internet constellations in their development. This paper first introduces three representative low-orbit Internet constellation plans abroad (Starlink, OneWeb, Lightspeed) and the latest development of domestic constellations. Then, based on the characteristics of low-orbit Internet constellations, the five major technical challenges faced by low-orbit Internet constellations are analyzed in detail: constellation relative motion evolution prediction, constellation autonomous navigation and orbit determination, constellation variable path planning, constellation self-organization collaborative control, constellation communication and network services. Finally, based on the current development trend of low-orbit Internet constellations, suggestions are given for the development of low-orbit Internet constellations in my country based on my country's national conditions.

Effects of gravity rainbow on scalar bosonic and oscillator fields in Bonnor–Melvin space-time with a cosmological constant

In this paper, we explore the relativistic quantum motion of spin-zero scalar charge-free particles influenced by rainbow gravity’s (RG’s) in Bonnor–Melvin magnetic space-time, a four-dimensional solution featuring a positive cosmological constant. We solve the Klein–Gordon equation in this scenario by using two sets of rainbow function: (i) f(χ)=1(1-βχ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\chi )=\\frac{1}{(1-\\beta \\,\\chi )}$$\\end{document}, h(χ)=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h(\\chi )=1$$\\end{document} and (ii) f(χ)=1(1-βχ)=h(χ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\chi )=\\frac{1}{(1-\\beta \\,\\chi )}=h(\\chi )$$\\end{document}, where 0<χ=|E|Ep≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0 < \\chi \\left( =\\frac{|E|}{E_p}\\right) \\le 1$$\\end{document} with Ep\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_p$$\\end{document} being the Planck’s energy, E is the particle’s energy, and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} is the rainbow parameter. Furthermore, we study the relativistic quantum oscillator through the Klein–Gordon oscillator equation in the same Bonnor–Melvin magnetic space-time under RG effects. Employing the first pair of rainbow function, we obtain an approximate eigenvalue solution of the quantum oscillator fields. Notably, we demonstrate that the relativistic energy profile of scalar and oscillator particles are influenced by the topology of the geometry and the cosmological constant which is related with the magnetic field strength lies along the symmetry axis. Additionally, we see the impact of rainbow parameter on these approximate relativistic energy profiles in both quantum systems.