Ideal Trajectory Research Articles

Assessment of Transitional Orbits from a High Eccentricity LEO to a Circumlunar Orbit

This study presents an evaluation of the achievability and execution of transitional orbits for spacecraft transitioning from a high eccentricity Low Earth Orbit (LEO) to a circumlunar orbit, with the point of distinguishing the foremost proficient and ideal trajectory while considering variables such as velocity and required fuel. Transitional orbits have a role in space exploration, and optimizing their characteristics can enormously advantage mission planning and spacecraft design. A numerical simulation model was developed to attain this objective, A gravity perturbations effect is included in the calculation of the transition. The model utilized progressed numerical integration strategies for exact trajectory analysis. Three cases were examined to investigate the impacts of varying eccentricity and the argument of perigee on the ideal transition, In the first case, eccentricity values of [0.001, 0.01, 0.1] were inspected, whereas the argument of perigee was fixed at 80 degrees. Within the second case, the argument of perigee values of [80, 170, 260] was considered, with the eccentricity fixed at 0.1. The third case included at the same time varying the eccentricity and argument of perigee values. The results showed that the three cases agreed the most favorable transition occurred when eccentricity was set to 0.001 and the argument of perigee was set to 260 degrees. This produced a velocity increase of 2.195694 km/s, which is the lowest increase in ΔV, a metric used to measure fuel efficiency and power required. This finding also demonstrated the lowest change in eccentricity, the lowest change in inclination, and the lowest change in the ascending node, all of which are indicative of increased orbit stability.

Anatomical Parameters of Percutaneous, Minimally Invasive, Direct Intralaminar Pars Screw Fixation of Spondylolysis

ObjectiveTo investigate the anatomical parameters of the ideal screw trajectory for percutaneous intralaminar screw fixation of a pars defect in lumbar spondylolysis using computed tomography scans. MethodsUsing advanced radiological software, the ideal intralaminar screw trajectory was determined. The anatomical parameters of this trajectory were analyzed using a total of 80 single-level lumbar tomography scans in patients with spondylolysis at the L4 and L5 levels. The ideal intralaminar screw trajectory started from the inferolateral edge of the lamina and was between the intralaminar region, pars defect, and defective pars neck and pedicle. Along this trajectory, the skin–lamina distance, intralaminar screw length, isthmic lamina length and width, defective pars neck width, lateral entry distance of the screw to the center of the spinous process, and sagittal and coronal screw application angles were analyzed. ResultsWhen comparing the L4 and L5 parameters, the mean skin-to-lamina distances were 11-9 cm (p=0.000), intralaminar screw lengths 3.5-3.6 cm (p=0.067), isthmic lamina lengths 2-2 cm (p=0.698), mid-lamina widths 1-1 cm (p=0.941), defective pars neck widths 1-1 cm (p=0.674), screw lateral entry distances according to the spinous process 1-1.5 cm (p=0.000), sagittal screw angles 45°-45° (p=0.870), and coronal screw angles 10°-20° (p=0.000) respectively. There were no differences based on age and gender (p<0.05). ConclusionPercutaneous intralaminar rigid screw fixation of a pars defect in spondylolysis provides minimally invasive, low-profile instrumentation. In spondylolysis, a screw length of 3–4 cm and a screw diameter of 4–5 mm may be sufficient for pars fixation with intralaminar screws.

Finite-time consensus of heterogeneous unmanned aerial agents in network with fixed and switching topology

A finite-time consensus protocol is presented in this paper for a network of connected heterogeneous agents with fixed and switching topology. In this study, two cases directed networks with fixed topology and directed networks with switching topology are examined. Convergence analysis for both the cases are presented. An independent tracking controller, which assures that an agent follows an ideal trajectory designed by sliding mode based consensus control, is devised. Agents stability are independent of the distributed consensus algorithm. Under the proposed control methodology, the measurement vectors of heterogeneous agents converge to the agreement value in a finite amount of time. The comparison results with the existing works show the proposed algorithm’s improved performance in terms of convergence time in presence of disturbances.

Individual and typological features of motor memory in problems of control of ergacy systems in the absence of visual feedback

The purpose of the study was to determine the impact of the presence of visual feedback on the quality of user experience with a number of human-computer interfaces, as well as the process of mastering the interfaces. As a result of the work, the features of the generation of control commands by operators of ergatic systems using an oculographic interface, interfaces for controlling hand movements and head movements were assessed. In the absence of visual feedback, users relied on motor memory formed during the learning process, and in the case of head control, on data from the vestibular analyzer. The presence of visual feedback was found to be important for accurate command generation in all cases. However, when controlling the head and eyes, the presence of visual feedback led to a greater deviation from the ideal trajectory and an increase in the distance that the cursor traveled before reaching the goal. Localization of the target position did not have a significant effect on the performance of the operator interface, regardless of the presence of visual feedback. Analysis of typical reactions in all experiments made it possible to identify three types of control, differing for eye and head movements, but not for hand movements in the ergatic system mode. Types 1 and 2 exhibited more errors compared to type 3, and the number of errors varied between them, especially for hand control. The results obtained can be used in the development of promising interfaces for ergatic systems, including the determination of the necessary visual feedback components for this class of technical devices.

A trajectory planning method for robotic arms based on improved dynamic motion primitives

PurposeTraditional robot arm trajectory planning methods have problems such as insufficient generalization performance and low adaptability. This paper aims to propose a method to plan the robot arm’s trajectory using the trajectory learning and generalization characteristics of dynamic motion primitives (DMPs).Design/methodology/approachThis study aligns multiple demonstration motion primitives using dynamic time warping; use the Gaussian mixture model and Gaussian mixture regression methods to obtain the ideal primitive trajectory actions. By establishing a system model that improves DMPs, the parameters of the nonlinear function are learned based on the ideal primitive trajectory actions of the robotic arm, and the robotic arm motion trajectory is reproduced and generalized.FindingsExperiments have proven that the robot arm motion trajectory learned by the method proposed in this article can not only learn to generalize and demonstrate the movement trend of the primitive trajectory, but also can better generate ideal motion trajectories and avoid obstacles when there are obstacles. The maximum Euclidean distance between the generated trajectory and the demonstration primitive trajectory is reduced by 29.9%, and the average Euclidean distance is reduced by 54.2%. This illustrates the feasibility of this method for robot arm trajectory planning.Originality/valueIt provides a new method for the trajectory planning of robotic arms in unstructured environments while improving the adaptability and generalization performance of robotic arms in trajectory planning.

An integrated method for compensating and correcting nonlinear error in five-axis machining utilizing cutter contacting point data

In current five-axis computer numerical control (CNC) machining, the use of minute linear path segments as an approximation for the ideal cutter contacting (CC) point trajectory is still prevalent. However, introducing rotation axes leads to a deviation of the actual CC point trajectory from the ideal, resulting in nonlinear errors. An integrated method is proposed in this paper for compensating and correcting both the contour error, associated with the approximation of the part surface by the ideal CC point trajectory and the nonlinear error of the CC point trajectory based on the information in the CC point data. By analyzing the spatial relationship between the tool posture and the CC point path during the five-axis linear interpolation process, two adjacent machining tool positions containing CC point data information are selected as the starting and ending points of the five-axis linear interpolation machining. The ideal tool center point and the actual CC point are calculated during the interpolation process, as well as the distance and the unit vector in the perpendicular direction between the actual CC point and the ideal CC point trajectory segment. In the comprehensive error compensation and correction phase, the obtained unit vectors are used as direction vectors for error compensation, and the tool center point during interpolation is first compensated and corrected. This ensures the actual CC point and the contour curve are on the same plane. The compensation direction for contour error is calculated using the start/end tool axis vectors and the ideal CC point trajectory vectors. The size of the contour error approximating the contour curve is calculated through the chord error. A second compensation and correction are applied to the tool center point for interpolation, ultimately achieving comprehensive compensation and correction of nonlinear errors. The data calculations were conducted in the MATLAB environment using actual machining data. After compensation and correction, the contour error was reduced by 76%, the nonlinear error of the CC point trajectory decreased to below 0.88 μm, and the comprehensive nonlinear error of the CC point trajectory was reduced from 19 to 1.5 μm, a reduction of 93%. This demonstrates significant practical value in enhancing the accuracy of five-axis CNC machining. Through actual machining verification, after using the method described in this paper, the average surface roughness decreased from 1.133 to 0.220 μm, and the maximum surface roughness decreased from 6.667 to 1.240 μm. This significantly demonstrates that the compensation and correction method proposed in this paper can significantly improve the surface quality of machined parts.

An Improved Trilateral Localization Technique Fusing Extended Kalman Filter for Mobile Construction Robot

Semi-open and chaotic environments of building sites are considered primary challenges for the localization of mobile construction robots. To mitigate environmental limitations, an improved trilateral localization technique based on artificial landmarks fusing the extended Kalman filters (EKFs) is proposed in this paper. The reflective intensity of the onboard laser is employed to identify artificial landmarks arranged in the ongoing construction environment. A trilateral positioning algorithm is then adopted and evaluated based on artificial landmarks. Multi-sensor fusion, combined with the EKF, is included to improve the positioning accuracy and reliability of the robot in complex conditions. We constructed validation scenarios in the Gazebo simulation environment to verify the required localization functionality. Concurrently, we established simulated testing environments in real-world settings, where the practicality of the proposed technique was validated through the fitting of ideal and actual localization trajectories. The effectiveness of the proposed technique was corroborated through comparative experimental results.

Improved Immune Moth-Flame Optimization Based on Gene Correction for Automatic Reverse Parking.

During the process of reverse parking, it is difficult to achieve the ideal reference trajectory while avoiding collision. In this study, with the aim of establishing reference trajectory optimization for automatic reverse parking that smooths and shortens the trajectory length and ensures the berthing inclination angle is small enough, an improved immune moth-flame optimization method based on gene correction is proposed. Specifically, based on the standard automatic parking plane system, a reasonable high-quality reference trajectory optimization model for automatic parking is constructed by combining the cubic spline-fitting method and a boundary-crossing solution based on gene correction integrated into moth-flame optimization. To enhance the model's global optimization performance, nonlinear decline strategies, including crossover and variation probability and weight coefficient, and a high-quality solution-set maintenance mechanism based on fusion distance are also designed. Taking garage No.160 of the Dalian Shell Museum located in Dalian, Xinghai Square, as the experimental site, experiments on automatic parking reference trajectory optimization and tracking control were carried out. The results show that the proposed optimization algorithm provides higher accuracy for reference trajectory optimization and can achieve better tracking control of the reference trajectory.

129 Neuroimaging Analysis of Bilateral Thalamic Delivery for Gene Therapy

INTRODUCTION: Axonal transport from the thalamus (an integrative hub for the entire cortex) has been shown to facilitate widespread gene/protein delivery. Here, we report our neuroimaging experience with bilateral thalamic convection-enhanced delivery of adeno-associated virus (AAV) vectors for GM2 gangliosidoses. METHODS: Magnetic resonance imaging (MRI) of eight pediatric patients who underwent bilateral thalamic HEXA/HEXB delivery were retrospectively reviewed. Quantitative three-dimensional volumetric analyses of MRI thalamic signals were used to establish volume of distribution (Vd) versus volume of infusion (Vi). The distance of cannula placement within the thalamus was calculated and validated using the numbers used in the intraoperative ROSA robotic software. Backflow and leakage into surrounding structures were also analyzed. RESULTS: Fourteen thalamic injection volumes were considered in the final analysis. Calculated volume of thalamic infusate signal was up to 43.8% (mean = 21.3±13.3) of the thalamic volume. The Vd/Vi ratio ranged from 0.4-2.7 (mean = 1.9±0.7), depending on infusate volume. Diffusate shape was round to slightly ellipsoid in all patients. Backflow and leakage were encountered in 14.3% and 12.5%, respectively, of thalamic injections. CONCLUSIONS: This study provides the first in-human quantitative MRI data for intrathalamic infusion. The ideal location for the cannula tip was determined to be between the mediodorsal and lateral dorsal nuclei and the ideal trajectory keeps all of the cannula steps within the thalamic boundaries. We also compare these data to published NHP and our own NHP and sheep data. Overall, the Vd/Vi ratios are lower in human subjects (∼2) than in animal subjects (∼3). We hypothesize that this may be due in part to species specific differences in displacement of extracellular fluid versus infusion volume.

Association between circadian physical activity trajectories and incident type 2 diabetes in the UK Biobank

Physical activity (PA) is linked to a decreased risk of type 2 diabetes mellitus (T2DM). However, the influence of circadian PA trajectories remains uncertain. This study aims to explore the optimal circadian PA trajectory pattern for reducing the risk of T2DM. Methods: A total of 502,400 participants were recruited from the UK Biobank between 2006 and 2010, and 102,323 participants provided valid accelerometer-captured acceleration data. After excluding individuals with prior T2DM, 99,532 participants were included in the final analysis. We initially investigated the association between PA intensity at 24 hourly time points and T2DM. Subsequently, PA trajectories were identified using K-means cluster analysis. Cox proportional hazard models were employed to estimate hazard ratios (HR). Four distinct PA trajectories were identified: consistently low, single peak, double peak, and intense trajectories. Compared to consistently low, single peak, double peak and intense PA trajectory reduced the risk of T2DM progressively. Sensitivity analyses, further excluding individuals with glycated hemoglobin (HbA1c) ≥ 6.5% or random glucose ≥ 11.1 mmol/L and adjusted for daily average acceleration, yielded consistent results. This confirms that the ideal circadian PA trajectory serves as a protective factor, independently of PA intensity. Subgroup analyses indicated that these effects were more pronounced in men and individuals with eGFR < 60 mL/(min*1.73 m2). In conclusion, ideal circadian PA trajectory patterns (especially intense and then double peak) reduced risk of T2DM.

Real-time motion force-feedback system with predictive-vision for improving motor accuracy

Many haptic guidance systems have been studied over the years; however, most of them have been limited to predefined guidance methods. Calculating guidance according to the operator’s motion is important for efficient human motor adaptation and learning. In this study, we developed a system that haptically provides guidance trajectory by sequential weighting between the operator’s trajectory and the ideal trajectory calculated from a predictive-vision system. We investigated whether motion completion with a predictive-vision system affects human motor accuracy and adaptation in time-constrained goal-directed reaching and ball-hitting tasks through subject experiments. The experiment was conducted with 12 healthy participants, and all participants performed ball-hitting tasks. Half of the participants get forceful guidance from the proposed system in the middle of the experiment. We found that the use of the proposed system improved the operator’s motor performance. Furthermore, we observed a trend in which the improvement in motor performance using this system correlated with that after the washout of this system. These results suggest that the predictive-vision system effectively enhances motor accuracy to the target error in dynamic and time-constrained reaching and hitting tasks and may contribute to facilitating motor learning.

Implantation Corridors in Canine Thoracic Vertebrae: A Morphometric Study in Dogs of Varying Sizes.

Surgical stabilization to treat fractures, luxations, and congenital malformations in the thoracic spine can be difficult due to its unique anatomy and surrounding structures. Our objective was to document the morphometrics of the thoracic vertebrae relating to an ideal trajectory for dorsolateral implant placement in a variety of dog sizes and to assess proximity to important adjacent critical anatomical structures using computed tomography (CT) studies. Medical records for 30 dogs with thoracic CT were evaluated. Implantation corridor parameters for thoracic vertebrae (T1-T13) were measured, including the length, width, angle from midline, and allowable deviation angle for corridors simulated using an ideal implant trajectory. The distances from each vertebra to the trachea, lungs, aorta, subclavian artery, and azygos vein were also measured. Implantation corridor widths were often very narrow, particularly in the mid-thoracic region, and allowable deviation angles were frequently small. Distances to critical anatomical structures were often less than 1 mm, even in larger dogs. Thoracic implantation requires substantial precision to avoid breaching the canal, ineffective implant placement, and potential life-threatening complications resulting from invasion of surrounding anatomical structures.

Space Robot Sensor Noise Amelioration Using Trajectory Shaping.

Robots in space are necessarily extremely light and lack structural stiffness resulting in natural frequencies of resonance so low as to reside inside the attitude controller's bandwidth. A variety of input trajectories can be used to drive a controller's attempt to ameliorate the control-structural interactions where feedback is provided by low-quality, noisy sensors. Traditionally, step functions are used as the ideal input trajectory. However, step functions are not ideal in many applications, as they are discontinuous. Alternative input trajectories are explored in this manuscript and applied to an example system that includes a flexible appendage attached to a rigid main body. The main body is controlled by a reaction wheel. The equations of motion of the flexible appendage, rigid body, and reaction wheel are derived. A benchmark feedback controller is developed to account for the rigid body modes. Additional filters are added to compensate for the system's flexible modes. Sinusoidal trajectories are autonomously generated to feed the controller. Benchmark feedforward whiplash compensation is additionally implemented for comparison. The method without random errors with the smallest error is the sinusoidal trajectory method, which showed a 97.39% improvement when compared to the baseline response when step trajectories were commanded, while the sinusoidal method was inferior to traditional step trajectories when sensor noise and random errors were present.

Audio-Visual Bimodal Combination-Based Speaker Tracking Method for Mobile Robot

Initiative service is a key research direction for the new generation of service robots. It is important to automatically track humans for initiative service in human-robot interaction. To solve the problems of low precision and poor anti-interference capability of only using single-modal (audio or visual) information, a speaker positioning and tracking method based on an audio-visual bimodal combination is proposed. First, the azimuth of the speaker is obtained based on the time difference of arrival using a microphone array, and face detection based on AdaBoost is carried out using the camera. A distance and azimuth calculation model is established to obtain the position of the speaker. Second, a speaker positioning strategy based on an audio-visual bimodal combination is designed to handle different situations. Third, the path is planned by which the azimuth and distance between the robot and the speaker are maintained in a limited range. Different azimuths and distances for speaker tracking are set to perform various simulations. Finally, the mobile robot is driven to follow the path using the STM32 real-time control system. Information from the microphone array and the camera is collected and processed by Raspberry Pi. The tracking accuracy was tested under a single-face situation by setting 20 different target points, and 10 tests were carried out under each point. Under multi-face situations, the audio-visual bimodal information is combined to identify the speaker, and then the Kalman filter is used in face tracking. The experimental results demonstrate that the running trajectory of the mobile robot is close to the ideal trajectory, which ensures effective speaker tracking.

Safe Motion Planning and Control Framework for Automated Vehicles with Zonotopic TRMPC

Model mismatches can cause multi-dimensional uncertainties for the receding horizon control strategies of automated vehicles (AVs). The uncertainties may lead to potentially hazardous behaviors when the AV tracks ideal trajectories that are individually optimized by the AV's planning layer. To address this issue, this study proposes a safe motion planning and control (SMPAC) framework for AVs. For the control layer, a dynamic model including multi-dimensional uncertainties is established. A zonotopic tube-based robust model predictive control scheme is proposed to constrain the uncertain system in a bounded minimum robust positive invariant set. A flexible tube with varying cross-sections is constructed to reduce the controller conservatism. For the planning layer, a concept of safety sets, representing the geometric boundaries of the ego vehicle and obstacles under uncertainties, is proposed. The safety sets provide the basis for the subsequent evaluation and ranking of the generated trajectories. An efficient collision avoidance algorithm decides the desired trajectory through the intersection detection of the safety sets between the ego vehicle and obstacles. A numerical simulation and hardware-in-the-loop experiment validate the effectiveness and real-time performance of the SMPAC. The result of two driving scenarios indicates that the SMPAC can guarantee the safety of automated driving under multi-dimensional uncertainties.

Ideal 24-h physical activity trajectory reduces all-cause, cause-specific mortality and cardiovascular outcomes through aging deceleration and inflammation regulation: A UK biobank study

BackgroundPhysical activity (PA) is associated with mortality and cardiovascular disease (CVD). However, the effect of circadian PA trajectories remains ambiguous. This study aimed to explore ideal circadian PA patterns to reduce mortality and CVD, and potential mediators. Methods502,400 participants from UK Biobank were recruited between 2006 and 2010. Among them, 102,323 participants got valid continuously capturing acceleration data over 7 days by wrist-worn accelerometer. K-means cluster analysis was used to identify PA trajectories. The associations of PA with all-cause, cause-specific mortality and CVD were assessed by cox regression. A sensitivity test was also conducted, starting from the time of acceleration collection and excluding participants with corresponding disease prior to it. Furthermore, the mediation of aging and inflammation were explored. ResultsDuring a median follow-up of 12.9 years, 3482 deaths were recorded (704 were due to CVD). Five distinct PA trajectories were identified: Persistently Low, Moderate and Stable, Single Increase, Double Increase, and Vigorous patterns. Ideal PA trajectory patterns offered progressively protective benefits against all-cause, CVD caused mortality and CVD, especially in Double Increase and Vigorous patterns. Other cause-specific mortality and renal failure incidence showed similar trend. The sensitivity result was consistent. The mediating effects of phenotypic age and inflammation markers were statistically significant. ConclusionIdeal PA trajectories offered protective benefits against all-cause, cause-specific mortality and CVD. The protection was associated with both intensity and circadian distribution. Double Increase and Vigorous activity patterns decreased these risks more significantly. Crucially, this protection was mediated by aging deceleration and inflammation regulation.

Research on the New Power of Car Making Ideal Car

In response to the escalating depletion of fossil fuel reserves and the detrimental environmental impacts of conventional internal combustion engine vehicles, the global automotive industry is undergoing a transformative shift towards clean, sustainable, and energy-efficient new energy vehicles (NEVs). This article scrutinizes the remarkable ascent of Ideal Cars, a prominent player in the burgeoning Chinese NEV market. In light of these developments, this scholarly examination explores the multifaceted determinants underpinning Ideal Cars' remarkable trajectory, encompassing its foundational evolution, distinctive technological orientation, nuanced user-centric approach, financial performance, scene-based marketing strategies, and innovative organizational structure. This comprehensive analysis underscores the imperative nature of consumer-oriented product design, the psychological aspects of consumer satisfaction, and the paramount influence of market dynamics in shaping the success of high-end automotive ventures. Ideal Cars' unprecedented journey serves as an instructive case study for the prospective evolution of the NEV industry in China and globally.

Analysis of Hail Production via Simulated Hailstone Trajectories in the 29 May 2012 Kingfisher, Oklahoma, Supercell

Abstract This study uses a new, unique dataset created by combining multi-Doppler radar wind and reflectivity analysis, diabatic Lagrangian analysis (DLA) retrievals of temperature and water substance, and a complex hail trajectory model to create millions of numerically simulated hail trajectories in the Kingfisher, Oklahoma, supercell on 29 May 2012. The DLA output variables are used to obtain a realistic, 4D depiction of the storm’s thermal and hydrometeor structure as required input to the detailed hail growth trajectory model. Hail embryos are initialized in the hail growth module every 3 min of the radar analysis period (2251–0000 UTC) to produce over 2.7 million hail trajectories. A spatial integration technique considering all trajectories is used to identify locations within the supercell where melted particles and subsevere and severe hailstones reside in their lowest and highest concentrations. It is found that hailstones are more likely to reside for longer periods closer to the downshear updraft within the midlevel mesocyclone in a region of decelerated midlevel mesocyclonic horizontal flow, termed the downshear deceleration zone (DDZ). Additionally, clusters of trajectories are analyzed using a trajectory clustering method. Trajectory clusters show there are many trajectory pathways that result in hailstones ≥ 4.5 cm, including trajectories that begin upshear of the updraft away from ideal growth conditions and trajectories that grow within the DDZ. There are also trajectory clusters with similar shapes that experience widely different environmental and hailstone characteristics along the trajectory. Significance Statement The purpose of this study is to understand how hail grew in a thunderstorm that was observed by numerous instruments. The observations were input into a hail trajectory model to simulate hail growth. We found a part of the storm near the updraft where hailstones could remain aloft longer and therefore grow larger. Most modeled severe hailstones were found in the storm in this region. However, we also found that there are many different pathways hailstones can take to become large, although there are still some common characteristics among the pathways.

Eighth order, Numerov-like schemes with coefficients tailored for superior performance on ODE systems with oscillatory solutions

&lt;p&gt;Second order Ordinary Differential Equations (ODE) were considered. Numerov-like techniques employing effectively seven stages per step and sharing eighth algebraic order were under examination for numerically solving them. The coefficients of these methods were contingent on four independent parameters. To tackle issues with oscillatory solutions, we typically aimed to fulfill specific criteria such as minimizing phase-lag, expanding the periodicity interval, or even neutralizing amplification errors. These latter attributes stemmed from a test problem mimicking an ideal trigonometric trajectory. Here, we suggested training the coefficients of the chosen method family across a broad spectrum of pertinent problems. Following this training using the differential evolution method, we identified a particular method that surpassed others in this category across an even broader array of oscillatory problems.&lt;/p&gt;

Inter-robot management via neighboring robot sensing and measurement using a zeroing neural dynamics approach

This paper proposes a complex number representation method for dynamically recording robot positions and develops an optimization strategy for measuring and minimizing inter-robot distances in real-time. Based on this, the optimization strategy is transformed into finding the theoretical solution of the complex time-varying matrix equation by combining the leader–follower frameworks, and a complex zeroing neural dynamics (CZND) model is proposed for this objective. Meanwhile, the effectiveness of the proposed CZND model and the ideal trajectories of the follower robots are ensured and given through rigorous theoretical analyses. Subsequently, these theoretical findings are validated by two numerical experiments (four cases). In addition, the superiority of the CZND model for inter-robot management tasks is comparatively analyzed from three perspectives: initial positions, number of follower robots, and design parameters. Compared to conventional gradient-based neural network (CGNN) methods, the proposed CZND model, based on a dynamic error function (which is not required to be non-negative as in CGNN), demonstrates improved handling of the dynamic behavior of the system by utilizing the first-order time derivatives of matrices, resulting in lower residual errors in the implementation of inter-robot management. Specifically, for the same inter-robot management task, the steady-state error implemented by CZND is on the order of 10−4, whereas for CGNN, it is on the order of 10−1, indicating a significantly larger lagging error.