Kinematic Constraints Research Articles

A kinematically reasonable mechanism of tongue forward protrusion considering hyoid bone movements

The tongue has a wide variety of motor functions, which are driven by tongue muscle contractions and associated with movements of the hyoid bone (HB) connected to the tongue root. HB movement has been observed in many situations, including swallowing, breathing, and speech. However, the relationships between HB movement and tongue kinematic function have received little attention, and have not been considered in most previous biomechanical tongue modeling research, except studies of swallowing. The current study aimed to clarify the effects of HB movement on tongue kinematics during tongue forward protrusion, which is an essential tongue motor function associated with speech disorder. HB displacement during tongue forward protrusion was quantified using ultrasound imaging in four healthy controls. Furthermore, computational mechanical simulations of tongue forward protrusion were conducted with observed HB movements and active contraction of the genioglossus (GG) muscle, which is conventionally considered to be the driving muscle in tongue forward protrusion. Ultrasound imaging revealed anterosuperior HB displacement in tongue forward protrusion, with a similar magnitude in each direction (anterior: 6.3 ± 2.8 mm, superior: 5.8 ± 1.6 mm). Computational simulation demonstrated that the HB movement described above caused not only anterosuperior displacement, but also forward rotation of the tongue body, which was caused by kinematic constraints of GG. The resulting anterior displacement of the tongue tip was 1.5 times greater compared with that without HB movement. These findings indicate that the HB and associated tongue body movements play non-negligible roles in the tongue kinematics of forward protrusion.

Obstacle avoidance path planning for AUVs in a three-dimensional unknown environment based on the C-APF-TD3 algorithm

To enhance the obstacle avoidance path planning ability of AUV in three-dimensional unknown underwater environments with obstacle constraints, an improved algorithm combining Constrained Artificial Potential Field (C-APF) and the Twin Delayed Deep Deterministic Policy Gradient algorithm (TD3) is proposed (C-APF-TD3). First, the kinematic constraints of AUV are incorporated into the APF algorithm, allowing C-APF to generate an approximate path for the AUV. Then, the AUV obstacle avoidance path planning problem is formulated as a Markov Decision Process (MDP), designing state space, action space, and reward functions. The TD3 training is guided by the approximate path planned using C-APF, ultimately resulting in a policy model for AUV path planning. Finally, various simulation experiments are established and designed for different obstacle scenarios. The experimental results show that the C-APF-TD3 algorithm produces more optimized trajectories compared to the C-APF algorithm. Furthermore, compared to the C-APF-DDPG algorithm, it achieves a policy model with efficient control performance with higher convergence efficiency and average returns, enhancing the adaptability and robustness of AUV obstacle avoidance path planning in three-dimensional unknown environments.

Local weather routing in avoidance of adverse sea conditions based on reachability theory

In this paper, we put forward a local weather routing framework based on reachability theory to plan a time-optimal risk avoidance path in face of sudden changes in sea conditions. Our framework comprises of two phases, where the escape phase directs the vessel to withdraw from risky heading-speed combinations dictated by MSC.1/Circ. 1228. Subsequently, in the return phase, the algorithm guides the vessel back to its original global route while staying outside dangerous zones. Notably, our application of a four-dimensional state space for the description of a vessel’s configuration can accommodate both the safety and kinematic constraints. In the proposed state space, the path-finding algorithm based on reachability theory can figure out the optimal heading and speed of vessel simultaneously, providing a formal assurance of safety and global time-optimality for returning. To achieve this objective, we formulate and solve a new variational-inequality (VI) governing the forward propagation of the reachable set with both angular and acceleration rate treated as control inputs. Last but not least, we provide a rigorous proof for the proposed VI in the framework of viscosity solution and demonstrate the validity of our approach in two test scenarios including one integrated with a realistic control architecture.

Real-time position path smoothing for robotic manipulators by constructing Composite Trajectory Spline

Aiming at smoothing discontinuous corners in robotic tool paths, a novel spline named “Composite Trajectory Spline”(CT-Spline) is proposed in this paper. Based on CT-Spline, the real-time position path smoothing for robotic manipulators is realized. CT-Spline enables analytical trajectory planning and interpolation without curve length computation, significantly enhancing trajectory generation efficiency and avoiding numerical errors. By directly controlling resultant trajectory acceleration, CT-Spline avoids decomposing it into tangential and normal accelerations, ensuring adherence to the maximum acceleration constraint while fully utilizing acceleration potential. The geometric shape of CT-Spline is determined by three control points and a trajectory model. This paper further develops C1 and C3 continuous CT-Splines based on two different trajectory models, combined with a velocity look-ahead algorithm to achieve real-time local smoothing of path corners. Additionally, an adaptive control algorithm of smoothing error is introduced to dynamically maximize trajectory velocity. Simulations and experiments validate the effectiveness of CT-Spline, and demonstrate that the proposed C3 continuous trajectory smoothing method has several advantages over the method based on Pythagorean-hodograph splines in terms of kinematic constraints, velocity, smoothing errors, and real-time performance.

Estimation of the Chances to Find New Phenomena at the LHC in a Model-Agnostic Combinatorial Analysis

In this paper, we estimate the number of event topologies that have the potential to be produced in pp collisions at the Large Hadron Collider (LHC) without violating kinematic and other constraints. We use numerical calculations and combinatorics, guided by large-scale Monte Carlo simulations of Standard Model (SM) processes. Then, we set the upper limit on the probability that new physics may escape detection, assuming a model-agnostic approach. The calculated probability is unexpectedly large, and the fact that LHC has not found new physics until now is not entirely surprising. Theoretical limitations and experimental challenges in observing new physics within the studied exclusive event classes are examined.

Elastic bodies with kinematic constraints on many small regions

We study the equilibrium of hyperelastic solids subjected to kinematic constraints on many small regions, which we call perforations. Such constraints on the displacement u are given in the quite general form u(x)∈Fx, where Fx is a closed set, and thus comprise confinement conditions, unilateral constraints, controlled displacement conditions, etc., both in the bulk and on the boundary of the body. The regions in which such conditions are active are assumed to be so small that they do not produce an overall rigid constraint, but still large enough so as to produce a non-trivial effect on the behaviour of the body. Mathematically, this is translated in an asymptotic analysis by introducing two small parameters: ɛ, describing the distance between the elements of the perforation, and δ, the size of the element of the perforation. We find the critical scale at which the effect of the perforation is non-trivial and express it in terms of a Γ-limit in which the constraints are relaxed so that, in their place, a penalization term appears in the form of an integral of a function φ(x,u). This function is determined by a blow-up procedure close to the perforation and depends on the shape of the perforation, the constraint Fx, and the asymptotic behaviour at infinity of the strain energy density σ. We give a concise proof of the mathematical result and numerical studies for some simple yet meaningful geometries.

An open-source, adaptive solver for particle-resolved simulations with both subcycling and non-subcycling methods

We present the IAMReX (incompressible flow with adaptive mesh refinement for the eXascale), an adaptive and parallel solver for particle-resolved simulations on the multi-level grid. The fluid equations are solved using a finite-volume scheme on the block-structured semi-staggered grids with both subcycling and non-subcycling methods. The particle-fluid interaction is resolved using the multidirect forcing immersed boundary method. The associated Lagrangian markers used to resolve fluid-particle interface only exist on the finest-level grid, which greatly reduces memory usage. The volume integrals are numerically calculated to capture the free motion of particles accurately, and the repulsive potential model is also included to account for the particle–particle collision. We demonstrate the versatility, accuracy, and efficiency of the present multi-level framework by simulating fluid-particle interaction problems with various types of kinematic constraints. The cluster of monodisperse particles case is presented at the end to show the capability of the current solver in handling multiple particles. It is demonstrated that the three-level AMR (Adaptive Mesh Refinement) simulation leads to a 72.46% grid reduction compared with the single-level simulation. The source code and testing cases used in this work can be accessed at https://github.com/ruohai0925/IAMR/tree/development. Input scripts and raw postprocessing data are also available for reproducing all results.

Multi-objective optimal trajectory planning for manipulators based on CMOSPBO

Feasible, smooth, and time-jerk optimal trajectory is essential for manipulators utilized in manufacturing process. A novel technique to generate trajectories in the joint space for robotic manipulators based on quintic B-spline and constrained multi-objective student psychology based optimization (CMOSPBO) is proposed in this paper. In order to obtain the optimal trajectories, two objective functions including the total travelling time and the integral of the squared jerk along the whole trajectories are considered. The whole trajectories are interpolated by quintic B-spline and then optimized by CMOSPBO, while taking into account kinematic constraints of velocity, acceleration, and jerk. CMOSPBO mainly includes improved student psychology based optimization, archive management, and an adaptive ε-constraint handling method. Lévy flights and differential mutation are adopted to enhance the global exploration capacity of the improved SPBO. The ε value is varied with iterations and feasible solutions to prevent the premature convergence of CMOSPBO. Solution density estimation corresponding to the solution distribution in decision space and objective space is proposed to increase the diversity of solutions. The experimental results show that CMOSPBO outperforms than SQP, and NSGA-II in terms of the motion efficiency and jerk. The comparison results demonstrate the effectiveness of the proposed method to generate time-jerk optimal and jerk-continuous trajectories for manipulators.

Kinematic Constrained RRT Algorithm with Post Waypoint Shift for the Shortest Path Planning of Wheeled Mobile Robots.

This paper presents a rapidly exploring random tree (RRT) algorithm with an effective post waypoint shift, which is suitable for the path planning of a wheeled mobile robot under kinematic constraints. In the growth of the exploring tree, the nearest node that satisfies the kinematic constraints is selected as the parent node. Once the distance between the new node and the target is within a certain threshold, the tree growth stops and a target connection based on minimum turning radius arc is proposed to generate an initial complete random path. The most significant difference from traditional RRT-based methods is that the proposed method optimizes the path based on Dubins curves through a post waypoint shift after a random path is generated, rather than through parent node selection and rewiring during the exploring tree growth. Then, it is proved that the method can obtain an optimal path in terms of the shortest length. The optimized path has good convergence and almost does not depend on the state of the initial random path. The comparative test results show that the proposed method has significant advantages over traditional RRT-based methods in terms of the sampling point number, the tree node number, and the path node number. Subsequently, an efficient method is further proposed to avoid unknown obstacles, which utilizes the original path information and thus effectively improves the new path planning efficiency. Simulations and real-world tests are carried out to demonstrate the effectiveness of this method.

Distributed Neural Adaptive Impedance Control for Cooperative Manipulation With Unknown Objects.

Existing cooperative manipulation methods for multiple manipulator systems usually assume that the grasp matrix and the desired trajectory of each manipulator are known in advance. In this work, distributed neural adaptive impedance control (AIC) strategies integrating fully distributed observers are proposed to remove both limitations. Specifically, two fully distributed finite-time observers are designed to estimate the actual and ideal states of the reference point without using global information. The estimates of the grasp matrix and the desired trajectory of each end-effector (EE) are then obtained by kinematic constraints and the estimates of the reference point's states. At the controller development, a distributed adaptive impedance model is established to achieve an adaptive trade-off between tracking performance and compliance. Then, distributed neural network (NN)-based tracking control strategies are developed to asymptotically realize the desired adaptive impedance dynamics in the presence of uncertainties. Additionally, a virtual energy tank (EK) is employed to interact with the impedance system to correct the adaptive impedance laws for system passivity. A simulation for four mobile manipulators tightly cooperative transport an unknown object is carried out to demonstrate the established results.

Stair-Climbing Wheeled Robot Based on Rotating Locomotion of Curved-Spoke Legs.

This study proposes a new wheel-leg mechanism concept and formulations for the kinematics and dynamics of a stair-climbing robot utilizing the rotating leg locomotion of curved spokes and rolling tires. The system consists of four motor-driven tires and four curved-spoke legs. The curved-spoke leg is semicircle-like and is used to climb stairs. Once the spoke leg rolls on the surface, it lifts and pulls the mating wheel toward the surface, owing to the kinematic constraint between the spoke and the wheel. Single-wheel climbing is a necessary condition for the stair climbing of whole robots equipped with front and rear axles. This study proposes the design requirements of a spoke leg for the success of single-wheel climbing in terms of kinematic inequality equations according to the scenario of single-wheel climbing. For a design configuration that enables single-wheel climbing, the required minimum friction coefficient for the static analysis of the stair-climbing wheeled robots is demon-strated. Thereafter, the stair-climbing ability is validated through the dynamic equations that enable the frictional slip of the tires, as well as the curved-spoke legs. Lastly, the results revealed that the rotating locomotion of the well-designed curved-spoke legs effectively enables the stair climbing of the whole robot.

Quantifying Creep on the Laohushan Fault Using Dense Continuous GNSS

The interseismic behavior of faults (whether they are locked or creeping) and their quantitative kinematic constraints are critical for assessing the seismic hazards of faults and their surrounding areas. Currently, the creep of the eastern segment of the Laohushan Fault in the Haiyuan Fault Zone at the northeastern margin of the Tibetan Plateau, as revealed by InSAR observations, lacks confirmation from other observational methods, particularly high-precision GNSS studies. In this study, we utilized nearly seven years of observation data from a dense GNSS continuous monitoring profile (with a minimum station spacing of 2 km) that crosses the eastern segment of the Laohushan Fault. This dataset was integrated with GNSS data from regional continuous stations, such as those from the Crustal Movement Observation Network of China, and multiple campaign measurements to calculate GNSS baseline change time series across the Laohushan Fault and to obtain a high spatial resolution horizontal crustal velocity field for the region. A comprehensive analysis of this primary dataset indicates that the Laohushan Fault is currently experiencing left-lateral creep, characterized by a partially locked shallow segment and a deeper locked segment. The fault creep is predominantly concentrated in the shallow crustal region, within a depth range of 0–5.7 ± 3.4 km, exhibiting a creep rate of 1.5 ± 0.7 mm/yr. Conversely, at depths of 5.7 ± 3.4 km to 16.8 ± 4.2 km, the fault remains locked, with a loading rate of 3.9 ± 1.1 mm/yr. The shallow creep is primarily confined within 3 km on either side of the fault. Over the nearly seven-year observation period, the creep movement within approximately 5 km of the fault’s near field has shown no significant time-dependent variation, instead demonstrating a steady-state behavior. This steady-state creep appears unaffected by postseismic effects from historical large earthquakes in the adjacent region, although the deeper (far-field) tectonic deformation of the Laohushan Fault may have been influenced by the postseismic effects of the 1920 Haiyuan M8.5 earthquake.

Innovation Adaptive UKF Train Location Method Based on Kinematic Constraints

To address the issue of reduced positioning accuracy caused by satellite signal interruptions when trains pass through long tunnels, a novel train positioning method based on an innovative adaptive unscented Kalman filter (UKF) under kinematic constraints is proposed. This method aims to improve the accuracy of the location of trains during operation. By considering the dynamic characteristics of the train, a dynamic kinematic-constrained inertial navigation system (INS)/odometer (ODO) combination positioning system is established. This system utilizes kinematic constraints to correct the accumulated errors of the INS. Additionally, the algorithm incorporates real-time estimation of the measurement noise covariance using innovation sequences. The updated adaptive estimation algorithm is applied within the UKF framework for nonlinear filtering, forming the innovative adaptive UKF algorithm. At each time step, the difference between the ODO sensor data and the INS output is used as the measurement input for the innovative adaptive UKF algorithm, enabling global estimation. This process ultimately yields the actual positioning result for the train. Simulation results demonstrate that the innovative adaptive UKF train positioning method, incorporating kinematic constraints, effectively mitigates the impact of satellite signal interruptions. Compared with the traditional INS/ODO positioning method, the innovative adaptive UKF method reduces position errors by 34.35% and speed errors by 36.33%. Overall, this method enhances navigation accuracy, minimizes train positioning errors, and meets the requirements of modern train positioning systems.

Enhancing Planning for Autonomous Driving via an Iterative Optimization Framework Incorporating Safety-Critical Trajectory Generation

Ensuring the safety of autonomous vehicles (AVs) in complex and high-risk traffic scenarios remains a critical unresolved challenge. Current AV planning methods exhibit limitations in generating robust driving trajectories that effectively avoid collisions, highlighting the urgent need for improved planning strategies to address these issues. This paper introduces a novel iterative optimization framework that incorporates safety-critical trajectory generation to enhance AV planning. The use of the HighD dataset, which is collected using the wide-area remote sensing capabilities of unmanned aerial vehicles (UAVs), is fundamental to the framework. Remote sensing enables large-scale real-time observation of traffic conditions, providing precise data on vehicle dynamics, road structures, and surrounding environments. To generate safety-critical trajectories, the decoder within the conditional variational auto-encoder (CVAE) is innovatively designed through a data-mechanism integration method, ensuring that these trajectories strictly adhere to vehicle kinematic constraints. Furthermore, two parallel CVAEs (Dual-CVAE) are trained collaboratively by a shared objective function to implicitly model the multi-vehicle interactions. Inspired by the concept of “learning to collide”, adversarial optimization is integrated into the Dual-CVAE (Adv. Dual-CVAE), facilitating efficient generation from normal to safety-critical trajectories. Building upon this, these generated trajectories are then incorporated into an iterative optimization framework, significantly enhancing the AV’s planning ability to avoid collisions. This framework decomposes the optimization process into stages, initially addressing normal trajectories and progressively tackling more safety-critical and collision trajectories. Finally, comparative case studies of enhancing AV planning are conducted and the simulation results demonstrate that the proposed method can efficiently enhance AV planning by generating safety-critical trajectories.

Kineto-static analysis of a hybrid manipulator consisting of rigid and flexible limbs with locking function for planar shape morphing

The incorporation of lockable passive backbones into active compliant morphing systems efficiently results in lightweight, high-load, and large deformation systems. However, there exist challenges in kineto-static analysis due to the interaction between rigid reconfigurable kinematic constraints and the nonlinear deformation of actuated flexible limbs. This paper addresses these issues by developing a kineto-static method to analyze the motion in a novel planar 3-DOF shape-morphing manipulator. The manipulator features two actuated flexible limbs with a lockable variable geometry truss (LVGT). In this study, two isostatic topologies are selected for reconfigurable motion control under external tip loads. A multi-step sequential control strategy is proposed to maneuver the manipulator's platform for desired poses. Then, a constrained-trajectory-based kinematic model is proposed for an inverse kinematic solution considering motion planning. Subsequently, a kineto-static model is introduced, considering constraints from rigid and flexible limbs, aiming to distribute distributing redundant actuation forces. Finally, nonlinear finite element analysis (FEA) and experiments are carried out to validate the effectiveness of the proposed method.

PB-Trajectron: Physics bounded neural network for generalized trajectory prediction

Vehicle trajectory prediction is a critical technology in autonomous driving systems, as the quality of prediction directly affects downstream path planning and vehicle control. Although recent studies have shown that models combining kinematic rules with data-driven methods exhibit better interpretability in trajectory prediction, these models often adopt fixed constraint strengths, limiting their generalization ability in diverse traffic scenarios. This fixed constraint strength design restricts the model’s adaptability to different traffic environments.To address this issue, we propose PB-Trajectron, a dynamic integration mechanism that enhances the model’s prediction performance and generalization capability. PB-Trajectron is a dynamic integration mechanism that combines vehicle kinematic rules with deep learning prediction models for generalized vehicle trajectory prediction. The model integrates physics-based motion models and Deep Neural Networks (DNNs) to provide reasonable physical explanations for predicting vehicle trajectories at different speeds. First, we establish two vehicle kinematic constraints applicable to different prediction scenarios, enabling the agent to switch between these constraints based on the causal relationships between vehicle motion states to avoid generating non-physical trajectory results. Second, we propose a kinematic constraint decision framework based on velocity thresholds, which demonstrates adaptive adjustment, allowing the agent to switch tasks according to real-time state conditions and adaptively adjust the contribution of different physical constraints based on actual vehicle speeds. Finally, we investigate the advantages of PB-Trajectron in Out-of-Domain(OOD) generalization.Cross-scenario experiments on the nuScenes dataset show that, compared to previous methods, PB-Trajectron reduces the final displacement error by 7.69% when the prediction step length is 4. Furthermore, out-of-domain generalization tests on the INTERACTION dataset demonstrate that PB-Trajectron achieves a 12.23% reduction in average prediction error on datasets from different countries and scenarios compared to previous methods. The proposed mechanism can better adapt to complex and diverse traffic scenarios, laying the foundation for explainable and robust autonomous driving systems.

A real-time dual NURBS interpolator with optimised control of flexible acceleration and deceleration for five-axis CNC machining

The limited computing capacity makes it difficult to plan a suitable feedrate profile in real-time for high speed and high accuracy machining of five-axis parametric toolpaths. In this paper, a real-time interpolation algorithm with optimised control of flexible acceleration and deceleration (acc-dec) for the dual NURBS toolpath is proposed. The toolpath is marked as subsegments with similar geometric properties by introducing the five-axis curvature. Machine kinematic and toolpath geometry constraints are considered in the kinematic parameter constraint model. Initial feedrate profiles are solved in a dynamic 3D window which preserves the motion performance of machine tools to a great extent. Convolution is used to smooth the initial feedrate profile to achieve a higher order continuity over the global range. Feedrate fluctuations caused by imprecise parameter interpolation are eliminated through modifying each interpolation periods. Resampling adjusts the position of interpolation points and unify the interpolation periods. All operations mentioned are in series and real-time is strictly guaranteed. Effectiveness of the developed algorithm is validated in simulations and also experimentally on a Self-developed-NC controlled 5-axis machine tool.

JADES Ultrared Flattened Objects: Morphologies and Spatial Gradients in Color and Stellar Populations

One of the more surprising findings after the first year of JWST observations is the large number of spatially extended galaxies (ultrared flattened objects, or UFOs) among the optically faint galaxy (OFG) population otherwise thought to be compact. Leveraging the depth and survey area of the JWST Advanced Deep Extragalactic Survey, we extend observations of the OFG population to an additional 112 objects, 56 of which are well-resolved in F444W with effective sizes, R e > 0.″25, more than tripling previous UFO counts. These galaxies have redshifts around 2 < z < 4, high stellar masses ( log(M*/M⊙)∼10–11 ), and star formation rates around ∼100–1000 M ⊙ yr−1. Surprisingly, UFOs are red across their entire extents, which spatially resolved analysis of their stellar populations shows is due to large values of dust attenuation (typically A V > 2 mag even at large radii). Morphologically, the majority of our UFO sample tends to have low Sérsic indices (n ∼ 1) suggesting that these large, massive, OFGs have little contribution from a bulge in F444W. Further, a majority have axis ratios between 0.2 < q < 0.4, which Bayesian modeling suggests that their intrinsic shapes are consistent with being a mixture of inclined disks and prolate objects with little to no contribution from spheroids. While kinematic constraints will be needed to determine the true intrinsic shapes of UFOs, it is clear that an unexpected population of large, disky or prolate objects contributes significantly to the population of OFGs.

Multi-AUV Kinematic Task Assignment Based on Self-Organizing Map Neural Network and Dubins Path Generator.

To deal with the task assignment problem of multi-AUV systems under kinematic constraints, which means steering capability constraints for underactuated AUVs or other vehicles likely, an improved task assignment algorithm is proposed combining the Dubins Path algorithm with improved SOM neural network algorithm. At first, the aimed tasks are assigned to the AUVs by the improved SOM neural network method based on workload balance and neighborhood function. When there exists kinematic constraints or obstacles which may cause failure of trajectory planning, task re-assignment will be implemented by changing the weights of SOM neurals, until the AUVs can have paths to reach all the targets. Then, the Dubins paths are generated in several limited cases. The AUV's yaw angle is limited, which results in new assignments to the targets. Computation flow is designed so that the algorithm in MATLAB and Python can realize the path planning to multiple targets. Finally, simulation results prove that the proposed algorithm can effectively accomplish the task assignment task for a multi-AUV system.

Hierarchical decision-making approach for the task planning of the BWBUG cluster with three-dimensional time-varying ocean currents

This study concerns the task planning problem for a Blended-Wing-Body Underwater Glider (BWBUG) cluster with three-dimensional, time-varying ocean currents. The objective is to achieve task allocation and three-dimensional glide path planning for the BWBUG cluster in a manner that ensures safety and cost-effectiveness. First, the task planning problem for the BWBUG cluster is analyzed, detailing the task requirements and operational space. Next, a hierarchical decision-making approach is proposed, which comprises an upstream planner and a downstream planner. The upstream planner aims to determine a feasible task space for the BWBUG cluster while satisfying task constraints. The downstream planner fully considers the impact of ocean currents on BWBUG movement, as well as the safety and kinematic constraints of BWBUGs. It optimizes the three-dimensional movement trajectories of each BWBUG with the objective of minimizing energy consumption. Inspired by the nest-seeking behavior of bees, a novel heuristic algorithm called the Bee Nesting Optimization Algorithm (BNOA) is proposed to solve both upstream and downstream planning problems. The results of the simulations demonstrate the efficacy of the hierarchical decision-making approach developed in this study. Additionally, the proposed BNOA is highly competitive, offering reasonable task allocations and optimal three-dimensional glide paths for the BWBUG cluster.