Kinematic Relations Research Articles

Non-invasive calibration of a Stewart platform by photogrammetry

AbstractAccurate calibration of a Stewart platform is important for their precise and efficient operation. However, the calibration of these platforms using forward kinematics is a challenge for researchers because forward kinematics normally generates multiple feasible and unfeasible solutions for any pose of the moving platform. The complex kinematic relations among the six actuator paths connecting the fixed base to the moving platform further compound the difficulty in establishing a straightforward and efficient calibration method. The authors developed a new forward kinematics-based calibration method using Denavit-Hartenberg (DH) convention and used the Stewart platform “Tiger 66.1” developed in their lab for experimenting with the photogrammetry-based calibration strategies described in this paper. This system became operational upon completion of construction, marking its inaugural use. The authors used their calibration model for estimating the errors in the system and adopted three compensation options or strategies as per least-square method to improve the accuracy of the system. These strategies leveraged a high-resolution digital camera and off-the-shelf software to capture the poses of the moving platform’s center. This process is non-invasive and does not need any additional equipment to be attached to the hexapod or any alteration of the hexapod hardware. This photogrammetry-based calibration process involves multiple high-resolution images from different angles to measure the position and orientation of the platform center in the three-dimensional space. The target poses and actual poses are then compared, and the error compensations are estimated using the least-square methods to calculate the predicted poses. Results from each of the three compensation approaches demonstrated noticeable enhancements in platform pose accuracies, suggesting room for further improvements. Given that “Tiger 66.1” is based on the general Stewart platform structure, the proposed calibration method holds promise for extension to machines operating on similar principles where non-invasive calibration is desirable. This study contributes to advancing the field of Stewart platform calibration, paving the way for more precise and efficient applications in various domains.

Model-Based Analysis of the Accuracy of Tracking Control and Energy Efficiency of a Six-Wheeled Skid-Steered Robot

This article concerns the modeling and motion control of a mobile robot with six independently driven and non-steered wheels. The main research issue is analyzing the influence of the structure of the control system and wheel track on the control accuracy and energy efficiency during robot motion on horizontal paved ground. For this purpose, the kinematic relationships for the robot are discussed and a simplified dynamics model for control applications is developed. The robot’s dynamics model takes into account the most important phenomena of the wheel interaction with the paved ground, including slip. In addition, it is supplemented with a model of the robot’s drive units. Two versions of the control system were adopted for analysis, i.e., with the wheels’ controller only and additionally equipped with a pose controller. Simulation studies were carried out for the developed robot dynamics model and the analyzed versions of the control system in order to investigate the influence of the track width of the wheels and the structure of the control system on motion accuracy and energy efficiency. In order to quantitatively compare the results for the analyzed solutions, quality indices were introduced. The results of the simulation research indicate the influence of the track width of the wheels on the accuracy of motion when using the wheels’ controller, as well as its impact on energy efficiency. Moreover, they show that it is possible to significantly improve the accuracy of motion by using an additional pose controller, which allows limiting the impact of the non-optimal geometric parameters of the robot and the slip of the wheels on trajectory tracking errors. However, the addition of the pose controller does not significantly affect the energy efficiency during the robot’s motion, which may be even worse in this case.

New Magnetotelluric Data Reveal Deep Fault Boundaries and Contrasting Late Cenozoic Fault Kinematics Between the Qilian Shan Thrust Wedge and Beishan‐Alxa Block, Western China

AbstractThe structural connectivity and kinematic relationship between the Altyn Tagh sinistral strike‐slip fault (ATF) and Qilian Shan fold‐and‐thrust belt along the north Tibetan margin east of 96°E is an important question for tectonicists interested in the evolving active deformation field of Central Asia and associated earthquake hazards of China's Hexi Corridor region. New results from a detailed 130‐km‐long N‐S magnetotelluric (MT) survey from the Qilian Shan to Beishan elucidates the locations and down‐dip orientations of major faults. Importantly, the results indicate that the Heishan‐Jinta’Nanshan fault system roots steeply into the lower crust, is unconnected to the Qilian Shan thrust wedge, and has reactivated the margin of the North China Craton and an older, regional ductile shear belt. The structurally linked ATF‐Heishan‐Jinta’Nanshan system defines a fundamental kinematic boundary in central Asia between the NE directed Qilian Shan thrust belt to the south and the eastwardly extruding Beishan‐Alxa Block to the north.

A Complex Interplay Between Pluton Emplacement, Tectonic Deformation, and Plate Kinematics in the Cretaceous Sierra Nevada Magmatic Arc, California

AbstractThe relation of plate kinematics to the structural record of arc plutons and their host rocks is complex and still not fully understood. We address this issue through a combination of field mapping, structural analysis, anisotropy of magnetic susceptibility analysis, and fabric modeling in the Late Cretaceous Tuolumne Intrusive Complex, Sierra Nevada, California. A pattern of anti‐clockwise rotation from ∼NNW–SSE to WNW–ESE steep foliations and change in fabric ellipsoid shape from oblate to prolate was revealed in successively emplaced Kuna Crest (∼95–92 Ma), Half Dome (∼92–89 Ma), and Cathedral Peak (∼89–84 Ma) granodiorites. The numerical model indicates that the Kuna Crest was emplaced in a transpressional setting with an angle of convergence α = 60–40°, whereas the Half Dome and Cathedral Peak required simultaneous vertical constriction overprinted by transpression with α = 35–15°. This transition, which occurred at ∼92 Ma, is accompanied by a shallowing of the lineation plunge observed also in other ∼88–84 Ma central Sierra Nevada plutons. Provided that the Cretaceous Sierra Nevada arc was constructed during overall dextral transpression, these transitions reflect significant changes in kinematics, where ∼107–92 Ma plutons were emplaced during pure shear‐dominated transpression, which was followed by a transition to wrench‐dominated transpression recorded in ∼92–84 Ma plutons. Such a transition in kinematics is explained as a result of progressively increasing obliquity of the relative convergence of the Farallon plate subducting beneath the North American continental margin, in agreement with most paleogeographic reconstructions.

Three-dimensional terminal angle constraint guidance law with class [formula omitted] function-based adaptive sliding mode control

This paper investigates the three-dimensional (3-D) interception guidance problem, where the missile is required to intercept the maneuvering target with the desired terminal angles. For the nonlinear relative kinematic model, a class K∞ function-based adaptive sliding mode guidance law is proposed, which ensures that the errors of terminal Line-of-Sight (LOS) angles converge to the small neighborhoods of origin at the time of interception, without relying on information about the target's acceleration. To overcome the challenges of large initial control input and chattering in existing sliding mode guidance laws, two improved control schemes are introduced. The first scheme is to directly impose saturation constraints into the adaptive gain. However, it is important to ensure that the unknown disturbance remains within the prescribed saturation bound. To avoid the limitation, another approach involves introducing auxiliary dynamics to eliminate the reaching phase and slow down the convergence of LOS angles by presetting the convergence time of the sliding mode variables, which helps mitigate excessive initial control inputs. Numerical simulations are conducted using a realistic missile model and considering a 3-DOF point-mass aircraft as the target to evaluate three different guidance laws. The results indicate that the proposed guidance law ensures interception accuracy while substantially reducing the control gain.

Nonlinear Dynamic Analysis of a Curved Sandwich Beam with a Time-Dependent Viscoelastic Core Using the Generalized Differential Quadrature Method (GDQM)

This paper focuses on the geometrically nonlinear dynamic analyses of a three-layered curved sandwich beam with isotropic face layers and a time-dependent viscoelastic core. The boundary conditions and equations of motion governing the forced vibration are derived by using Hamilton’s principle. The first-order shear deformation theory is used to obtain kinematic relations. The spatial discretization of the equations is achieved using the generalized differential quadrature method (GDQM), and the Newmark-Beta algorithm is used to solve the time variation of the equations. The Newton–Raphson method is used to transform nonlinear equations into linear equations. The validation of the proposed model and the GDQM solution’s reliability are provided via comparison with the results that already exist in the literature and finite element method (FEM) analyses using ANSYS. Then, a series of parametric studies are carried out for a curved sandwich beam with aluminum face layers and a time-dependent viscoelastic core. The resonance and cancellation phenomena for the nonlinear moving-load problem of curved sandwich beams with a time-dependent viscoelastic core are performed using the GDQM for the first time, to the best of the authors’ knowledge.

Palaeoseismological assessment for a seismic gap located very close to the epicentre of the 30 October 2020 Samos Earthquake (M6.9), western Anatolia, Turkey

AbstractThe Tuzla Fault (TF), considered one of the most important seismic sources in İzmir province, is defined as a strike–slip fault with N10E–N60E striking between Gaziemir and Doğanbey districts. A 50-km-long fault consists of three segments which are, from north to south Çatalca, Orhanlı, and Doğanbey segments. Recent studies claim that the part of the TF extending to Kuşadası Bay is also in a kinematic relationship with the Samos Fault that caused an earthquake on 30 October 2020 (Mw = 6.9). In this study, in order to analyse the historical behaviour of the fault, three trench-based palaeoseismology studies across the fault scarp were conducted on three geometric segments of the TF. Palaeoseismology findings show that seven historic/prehistoric earthquakes were generated by TF. According to Oxcal distribution using the Bayesian methods, the time of the events lie between 46.2 ± 6.1 and 1.6 ± 0.3 ka. When the events are compared with the historical earthquakes, the last event is correlated with the earthquakes of 47 AD and/or 177/178 AD on the Doğanbey segment. Moreover, the other events can be attributed to the late Pleistocene–Holocene earthquakes that are prehistorical periods. Our results provide a recurrence interval of an earthquake along the TF to between 0.7 and 4.3 ka for the Holocene period. The elapsed time since the most recent surface faulting earthquake on the TF is 1844 years. It is suggested that it is predicted that TF has the potential to produce destructive earthquakes in the near future, especially in Orhanlı and Çatalca segments which may be considered as a seismic gap.

Static analysis of a sandwich cylindrical panel composed of porous core sandwiched by graphene-reinforced copper matrix

A higher-order shear deformable model is extended in this paper for static analysis of a sandwich cylindrical panel composed of porous core sandwiched by graphene-reinforced copper matrix. Principle of virtual work is used to derive governing equations of static bending through the computation of strain energy and external work. A higher-order shear deformable model is used to develop the kinematic relations. The sandwich cylindrical panel is subjected to mechanical and thermal loads. The governing equations are solved using Eigenvalue–Eigenvector method for clamped–clamped boundary conditions. The eigenvalues of the characteristic equation are obtained, and the solution is obtained for real and complex roots. The boundary conditions are applied to obtain integration constants. The axial and radial variation of the displacement, strain, and stress components are presented in terms of significant input parameters such as volume fraction, and folding angle of the graphene origami, various distribution patterns, porosity coefficient, thermal and mechanical loads, and geometric parameters. The results indicate that the stress, strain, and deformation components are increased with an increase in porosity coefficient and folding angle of the graphene. Furthermore, an enhancement in the volume fraction of the graphene leads to a significant decrease in various stress, strain, and deformation components. The results of this work can be used in aerospace science and technology specially in airplanes.

Respiratory particles: from analytical estimates to disease transmission

Respiratory particles containing infectious pathogens are responsible for a large number of diseases. To define health politics and save lives, it is important to study their transmission mechanisms, namely the path of particles once expelled. This path depends on several driving factors as intrinsic properties of particles, environmental aspects and morphology of the scenario. Following physical arguments and taking into account the results of experimental works, we consider a mathematical drift model for the mixture composed by two phases: air and particles. The relative motion between the two phases is described by a kinematic constitutive relation. We prove the stability of the model for fixed times and establish an a priori estimate for the total number of infectious particles. The upper bound of this estimate exhibits sound physical dependencies on the driving factors, in agreement with the experimental literature and mounting epidemiological evidences. Namely, we establish that the amount of particles expelled and their emission rate can explain why some people are superspreaders. Several numerical simulations illustrate the theoretical results.

A quasi-3D hyperbolic formulation for the buckling study of metal foam microplates layered with graphene nanoplatelets-embedded nanocomposite patches with temperature fluctuations

The work analyzes the buckling behavior of size-dependent microplates with a metal foam core, covered by graphene nanoplatelets (GNPs)-embedded nanocomposite patches. Microplates rest on a bi-parameter elastic substrate, and they are immersed in a thermal environment to observe the effect of temperature fluctuations on their elastic buckling performance. All material properties for each layer of the microstructure are thickness-dependent. A novel quasi-3D shear and normal (Q-3D S-N) hyperbolic theory is here proposed to describe the kinematic relations, accounting for the transverse normal strain. At the same time, a modified couple stress theory (MCST) is employed to account for the size dependence of the mechanical behavior due to the presence of a material length-scale parameter. Using the energy method and virtual work principle, the differential equilibrium equations are derived and solved analytically, where solutions are verified against the existing literature. The study focuses on the impact of different parameters on the normalized critical buckling load (NCBL). Based on the results from the systematic investigation, it is found that the addition of GNPs to the microplate enhances its stiffness, leading to increased values of NCBL, which in turn reduce for an increased imperfection ratio.

A block diagram approach to characterize the kinematic and torque relationship of three-port transmission mechanism

ABSTRACT This paper presents a kinematic and dynamic modeling of a three-port transmission mechanism using the block diagram technique. By exploiting the simplicity of the block diagram technique, unlike the more complex conventional approaches, the three-port transmission mechanism is systematically characterized to obtain the velocity kinematics and torque relationship. This is achieved by establishing a feedback connection of the three-port transmission mechanism in block diagram form, and obtain the close-loop input/output relationship using techniques known in the control community, such as Mason’s rule. Two categories of the three-port transmission mechanism were investigated including, the 1D rotation type (planetary gear) and the 2D rotation type (differential). The kinematic and dynamic expressions of both categories were shown to be easily obtained, identifying the characteristic differences. The velocity kinematics, torque relationships, and power analysis were expressed to validate the proposed modeling. Further verification using MATLAB Simulink shows a good agreement of the analytical expressions and the proposed block diagram model. To demonstrate the effective use of the proposed approach, the block diagram technique is applied in the design analysis of a south-pointing chariot device.

Nonprehensile Manipulation for Rapid Object Spinning via Multisensory Learning from Demonstration.

Dexterous manipulation concerns the control of a robot hand to manipulate an object in a desired manner. While classical dexterous manipulation strategies are based on stable grasping (or force closure), many human-like manipulation tasks do not maintain grasp stability and often utilize the dynamics of the object rather than the closed form of kinematic relation between the object and the robotic hand. Such manipulation strategies are referred as nonprehensile or dynamic dexterous manipulation in the literature. Nonprehensile manipulation often involves fast and agile movements such as throwing and flipping. Due to the complexity of such motions and uncertainties associated with them, it has been challenging to realize nonprehensile manipulation tasks in a reliable way. In this paper, we propose a new control strategy to realize practical nonprehensile manipulation. First, we make explicit use of multiple modalities of sensory data for the design of control law. Specifically, force data are employed for feedforward control, while position data are used for feedback control. Secondly, control signals (both feedback and feedforward) are obtained through multisensory learning from demonstration (LfD) experiments designed and performed for specific nonprehensile manipulation tasks of concern. To prove the concept of the proposed control strategy, experimental tests were conducted for a dynamic spinning task using a sensory-rich, two-finger robotic hand. The control performance (i.e., the speed and accuracy of the spinning task) was also compared with that of classical dexterous manipulation based on force closure and finger gaiting.

Analitičko određivanje postupaka struganja sa velikim pomakom primenom konstruktivnog geometrijskog modeliranja

The development of different machining procedures requires the exact mathematical description of those. This is especially important in finishing procedures, where the final geometry and surface characteristics of the parts are produced. In this paper, three high-feed turning procedures are analysed: skiving turning, tangential turning, and rotational turning. All three promise the creation is ground-like surfaces with low roughness characteristics, while reaching high values of productivity. The analytical determination of these procedures is carried out by the application of constructive tool geometric modeling. After the analysis of the kinematic and geometric relations of each procedure, the proper coordinate systems are defined. The transformational equations are determined, which describe the geometric boundary conditions and the movement of the workpiece and the tool. In the next step, the equation of motion is defined for the three studied procedure. Finally, the one variable equation of the cut surface section in the base plane is determined. Experiments were also carried out, which validated the achieved results.

The effect of tectonic boudinage and folding in a subducted mélange of the Alpine orogenic belt (Zermatt–Saas Zone, Italian Western Alps)

The Zermatt–Saas Zone is an eclogite-facies meta-ophiolite unit representing the fossil oceanic lithosphere of the Jurassic Tethys. In the Italian Northwestern Alps, the Zermatt–Saas Zone includes a chaotic rock unit, or mélange, c. 40 m thick, interposed between serpentinites and calcschists. The mélange consists of decimetre-scale ultramafic layers and boudins embedded in a serpentine + carbonate-rich matrix showing a block-in-matrix fabric. The mélange has the same Alpine tectonometamorphic evolution as the surrounding rocks, starting with a prograde path developed under high-pressure (HP) conditions followed by a retrograde path during exhumation. The kinematic and metamorphic relations between inside- and outside-boudin foliations indicate that boudinage and shearing developed during the prograde HP path. Fluid–rock interaction enhanced shearing and focused ductile and brittle–ductile deformation along lithological contacts between rigid blocks and boudins and flowing carbonaceous matrix. Despite a pervasive orogenic evolution, the primary tectonosedimentary features of the mélange are still recognizable in some outcrops and are attributed to an intra-oceanic (Jurassic) setting characterized by mass-transport processes. The present-day fabric of the studied mélange unit thus results from the superimposition of the Alpine processes, responsible for fluid-assisted stratal disruption and mixing in the subduction channel, on the original stratigraphy formed during intra-oceanic gravitational processes. Supplementary material : Supplementary figures and tables are available at https://doi.org/10.6084/m9.figshare.c.6924080 Thematic collection: This article is part of the Ophiolites, melanges and blueschists collection available at: https://www.lyellcollection.org/topic/collections/ophiolites-melanges-and-blueschists

Автоматическая система позиционирования колёсных роботизированных технических средств, обслуживающих кормовой стол

The quality and availability of forage on the feed table increase cow productivity. Feed availability can be ensured by increasing the length of the feed table and using robotic tools. The use of a wheeled robotized device in feed distribution increases labour productivity and reduces the influence of the human factor on the feeding process. To improve the efficiency of the feed distribution process, the author has developed and tested an automatic positioning system and a robotic device for servicing the feed table. The article presents a mathematical description of the kinematic relationships of movement of wheeled robotic devices. The author has developed an algorithm of the automatic positioning system operation, which takes into account the algorithmic connection between the electric drive actuators of the driving wheels and the vision system, where the image is processed according to the intellectual algorithm of the feeding area recognition. The author has developed the principle of constructing the route travelled by the robotic device along the feed table. Tests have confirmed the conformity of output reactions of the robotic device actuators to the input commands of the automatic positioning system.

Kinematic Analysis of 3-PRPPS Spatial Parallel Manipulator with Circularly Guided Base for Singularity-Free Robotic Motions

Robot manipulators are classified as serial manipulators and parallel manipulators. Parallel manipulators are classified into planar and spatial parallel manipulators (SPMs). The parallel manipulators have moved and fixed platforms connected with serial chains. The parallel manipulators have many linkages, which create a singularity problem. The singular positions of SPMs have also gained substantial attention in various industrial applications due to their intrinsic advantages in precision, flexibility, and load-bearing capabilities. The 3-PRPPS SPM has three prismatic joints, one spherical joint, and one revolute joint. This work changed the fixed base with a circular guided base to avoid singularity issues. The manipulator was modeled with direct kinematic relations. The Jacobian matrix for position and orientation was derived. The workspace was taken as the common area of the three circles, whose radius was the maximum arm length. The position and orientation of the end effector were traced. In the form of the end effector traces, no singularities in the mechanism were observed. The path of the robot manipulator was observed in all the possible positions and orientations. The multi-body simulation was also conducted on the 3-PRPPS manipulator, the main findings of which are presented in this article.

Geometry and Kinematics of the Mecanum Wheel on a Plane and a Sphere

This article is devoted to a study of the geometry and kinematics of the Mecanum wheels, also known as Ilon wheels or the Swedish wheels. The Mecanum wheels are one of the types of omnidirectional wheels. This property is provided by peripheral rollers whose axes are deviated from the wheel one by 45 degrees. A unified approach to studying the geometry and kinematics of the Mecanum wheels on a plane and on the internal or external surface of a sphere is proposed. Kinematic relations for velocities at the contact point of the wheel and the supporting surface, and angular velocities of the roller relative to the supporting surface are derived. They are necessary to describe the dynamics of the Mecanum systems taking into account forces and moments of contact friction in the presence of slipping. From the continuous contact condition, relations determining the geometry of the wheel rollers on a plane and on the internal or external surface of a sphere are obtained. The geometric relations for the Mecanum wheel rollers could help to adjust the existing shape of the Mecanum wheel rollers of spherical robots and ballbots to improve the conditions of contact between the rollers and the spherical surface. An analytical study of the roller geometry was carried out, and equations of their generatrices were derived. Under the no-slipping condition, expressions for rotational velocities of the wheel and the contacting roller are obtained. They are necessary for analyzing the motion of systems within the framework of nonholonomic models, solving problems of controlling Mecanum systems and improving its accuracy. Using the example of a spherical robot with an internal three-wheeled Mecanum platform, the influence of the rollers on the robot movement was studied at the kinematic level. It has been established that the accuracy of the robot movement is influenced not only by the geometric parameters of the wheels and the number of rollers, but also by the relationship between the components of the platform center velocity and its angular velocity. Results of the numerical simulation of the motion of the spherical robot show a decrease in control accuracy in

A third-order shear deformation plate bending formulation for thick plates: first principles derivation and applications

A third-order shear deformation plate bending formulation is presented in this study from the first principles. The derivation assumed a displacement field constructed using third-order polynomial function of the transverse (z) coordinate; and made to apriori satisfy the linear three-dimensional (3D) kinematics relations as well as the transverse shear stress free boundary conditions at the top and bottom plate surfaces. The formulation thus has no need for shear stress correction factors of the first-order shear deformation plate theories. The domain equations of equilibrium are obtained as a set of three coupled differential equations in terms of three unknown displacements. The system of coupled equations is solved for simply supported rectangular and square plates subjected to four cases of loading distributions: sinusoidal loading, uniformly distributed loading, linearly distributed loading and point load at the plate center. Navier’s double trigonometric series method is used to construct trial solutions for the three displacement functions such that the boundary conditions are satisfied identically. The integration problem is thus reduced to an algebraic problem and is solved for each considered loading. It is found that the present formulation gives exact results for the normal stresses σxx for sinusoidal and uniformly distributed loads. The study further showed that the results for deflection and stresses agreed with Krishna Murty’s higher order shear deformation plate theory results. The present formulation gave accurate results because of the inclusion of transverse normal strain effects in the formulation. The formulation gives a quadratic variation of the transverse shear stresses across the thickness in consonance with the theory of elasticity method.

A limit analysis approach to uplift bearing capacity of shallow plate anchors in marine environments

AbstractOffshore oil and gas exploration activities involve the installation of various subsea infrastructures on the ocean floor, often supported by shallow foundations such as anchor plates or mudmats. These foundations must be designed to withstand applied service loads along the structure lifecycle, including decommissioning loads required for subsequent removal. In this context, this work is dedicated to the evaluation of uplift bearing capacity of shallow anchors within the theoretical framework of limit analysis and its related kinematic approach. Based on the implementation of 3D failure mechanisms, rigorous upper bound estimates for the uplift force viewed as ultimate load for the material system are derived from either total or effective stress analyses. In that respect, emphasis is given to the formulation of limit analysis problem in the context of effective stresses, showing how the effect of seepage flow may be accounted for by means of driving body forces derived from the gradient of excess pore pressure distribution and how suction forces arise from pore pressure difference between upper and lower anchor surfaces. Evaluation of suction forces developed during anchor lifting is addressed by resorting to a simplified modeling applied to circular and rectangular anchors. The accuracy of the upper bound predictions derived for uplift force is assessed by comparison with available experimental data. Several numerical results are also provided to investigate the effects of relevant problem parameters on the uplift bearing capacity.

Dynamic Oblique Towing Test (DOTT) to calculate the ship's hull maneuvering derivatives

An accurate and time-efficient numerical method is developed to find the hydrodynamic maneuvering derivatives with only a single simulation by computational fluid dynamics. The method is based on the oblique towing test by introducing an oscillatory variation to the model ship drift angle as time progress. The fluid flow velocity and direction are fixed during the simulation but the orientation of the model ship is changing sinusoidally with respect to the fluid flow with a certain amplitude and frequency. The velocity and acceleration of the model ship are calculated using the kinematic relationships and the forces and moment on the model ship are computed in a time period while the model ship drift angle is changing. The method is named dynamic oblique towing test (DOTT) and is applied to a container model ship and a surface combat model. The hydrodynamic maneuvering derivatives are obtained by an optimized curve fitting using Genetic Algorithms. The results of the computation in coefficient derivation and maneuver simulation indicate the accuracy and time efficiency of the method.