Kinematic Relations Research Articles

Research on the trajectory tracking method of aircraft towing systems based on nonlinear control

Abstract In this paper, for the towing problem of wheeled aircraft, an automatic control method is proposed based on the nonlinear control theory, which realizes the trajectory tracking of the aircraft by controlling the velocity of the towing point of the aircraft, so as to realize the aircraft’s outbound and inbound operations. Firstly, based on the nonholonomic constraint theory, the mathematical model of the aircraft towing system is established, and the kinematic relationship between the aircraft towing point and the aircraft is obtained. Then, a controller is designed based on the nonlinear control theory, and the stability analysis is carried out using the Lyapunov method to realize the trajectory tracking of the aircraft traction system. Finally, the effectiveness and accuracy of the control method are verified by the combination of MATLAB simulation analysis and scaled-down model experiment. The results show that the proposed control method can realize the trajectory control of the aircraft towing system.

Analytical and Experimental Study of the Start of the Chip Removal in Rotational Turning

The present challenges in the automotive industry require the development and practical implication of novel machining procedures, which will provide appropriate solutions. These procedures should still meet the requirements of productivity, surface quality and energy efficiency. The further development of novel machining procedures introduces new problems that did not occur (or occurred to a lesser extent) with traditionally applied procedures. Rotational turning has come to the attention of production engineers in the previous decade since it can be used to machine ground-like surfaces in an ecologically friendly and highly productive manner. However, the chip removal characteristic is slightly different from traditional turning due to the applied special kinematic relation and complex tool edge geometry. The run-in phase will take longer, which is the time period between the first contact of the tool and the formation of a constant chip cross-sectional area. The clarification of the chip formation is important in any machining procedure. To achieve this goal, the geometric parameters of the chip must be determined. Since the start of the chip removal is a crucial stage in rotational turning due to its length, the chip height, chip width and the cross-sectional area of the chip should be separately defined in the initial stage. Therefore, in this paper, the initial phase of chip removal in rotational turning is studied. The increasing cross-sectional area of the chip is determined analytically by the application of the previously elaborated equation of the cut surface. Calculating formulas are defined for the different stages of the start of the chip removal, which could be used in the forthcoming studies to analyze the chip formation. The effects of different determining parameters are analyzed theoretically by the deduced formulas of the run-in phase and practical experiments are also carried out. The analytical and experimental analyses showed that increasing feed also increases the dynamic load on the cutting edge, while the depth of cut lowers the growth of the characteristic parameters of the chip, which results in a lower dynamic load on the tool.

Structural evolution of the Handun salt diapir, Zagros fold and thrust belt, southern Iran

The Fars region, in the Zagros fold and thrust belt, hosts a wide range of diapirs piercing over 10 km of stratigraphic sequence. Comprising Precambrian to Early-Cambrian Hormuz Salt, these diapirs exhibit a prolonged history of evolution. Outcrop evidence for understanding the diapir deformation history is mostly limited to the Cenozoic contractive phase, and the seismic data lacks the necessary quality for an exhaustive understanding of the deepest structure's geometries. Through regional and field evidence we unravel the Handun salt structure evolution and propose a sequential restoration to describe the key deformational events. Our study presents a field-based novel regional balanced cross-section and a 3D-geological model, and addresses the role of structural inheritances and the position of the Handun diapir with respect to the decupled basement. The performed field studies describe folds and unconformities related to Cenozoic halokinetic sequences with exceptional clarity. It was possible to observe changes of the diapir activity along the structure and provide field evidence for the relative timing and kinematics of primary and secondary welding. Finally, our data suggest that the Handun diapir formed in the early Paleozoic above the shoulder of a basement extensional fault, and was partially translated above its southern hanging-wall during the shortening. In the Paleocene a sustained ratio of salt rise rate was enhanced by the Zagros/Oman contraction. In response to the Oligocene continental collision, the diapir was profusely supplied with salt, which flared upward to form overhangs. Since the middle Miocene the salt supply slowly depleted, with the diapiric walls remaining near the surface but tapering upward, probably due to primary welding or increased sedimentation. Secondary welding occurred post-Pliocene in the last stages of the diapir evolution with consequent development of a secondary minibasin.

There is no place like home – finding birth radii of stars in the Milky Way

ABSTRACT Stars move away from their birthplaces over time via a process known as radial migration, which blurs chemo–kinematic relations used for reconstructing the Milky Way (MW) formation history. To understand the true time evolution of the MW, one needs to take into account the effects of this process. We show that stellar birth radii can be derived directly from the data with minimum prior assumptions on the Galactic enrichment history. This is done by first recovering the time evolution of the stellar birth metallicity gradient, $\mathrm{ d}\mathrm{[Fe/H]}(R, \tau)/\mathrm{ d}R$, through its inverse relation to the metallicity range as a function of age today, allowing us to place any star with age and metallicity measurements back to its birthplace, R$_b$. Applying our method to a large high-precision data set of MW disc subgiant stars, we find a steepening of the birth metallicity gradient from 11 to 8 Gyr ago, which coincides with the time of the last massive merger, Gaia–Sausage–Enceladus (GSE). This transition appears to play a major role in shaping both the age–metallicity relation and the bimodality in the [$\alpha$/Fe]–[Fe/H] plane. By dissecting the disc into mono-R$_b$ populations, clumps in the low-[$\alpha$/Fe] sequence appear, which are not seen in the total sample and coincide in time with known star-formation bursts, possibly associated with the Sagittarius Dwarf Galaxy. We estimated that the Sun was born at $4.5\pm 0.4$ kpc from the Galactic centre. Our R$_b$ estimates provide the missing piece needed to recover the Milky Way formation history.

Recover a moving rotor UAV without ground–air communications: System and control of a dual-stage tracking device

Recovering a moving rotor unmanned aerial vehicle (UAV) using a single-stage dynamic tracking device poses a significant challenge, particularly without real-time communication between the two systems. This study presents a dual-stage tracking system comprising an unmanned ground vehicle (UGV) and a Stewart platform, aimed at dynamically tracking and recovering the UAV. Firstly, an observation algorithm combining Kalman filtering (KF) and curve fitting is designed to estimate and complete the drone’s states and predict its trajectory. Subsequently, a decoupled dual-stage tracking control structure is introduced, integrating two independent controlled subsystems. Specifically, in the UGV controller, the model predictive control (MPC) is employed to enhance dynamic tracking capabilities using absolute kinematics. A motion tracking algorithm based on relative kinematics was developed for the Stewart recovery platform to compensate for UGV tracking errors and improve tracking accuracy. Dynamic recovery simulations and experiments have been conducted to validate the feasibility and effectiveness of the proposed dual-stage tracking system. The results demonstrate the system’s capability to dynamically track and recover the drone without real-time communication in complex environments characterized by detection noise and target trajectory disturbances.

Pose-Constrained Control of Proximity Maneuvering for Tracking and Observing Noncooperative Targets with Unknown Acceleration

This paper proposes a pose control scheme of for proximity maneuvering for tracking and observing noncooperative targets with unknown acceleration, which is an important prerequisite for on-orbit operations in space. It mainly consists of a finite-time extended state observer and constraint processing procedures. Firstly, relative pose-coupled kinematics and dynamics models with unknown integrated disturbances are established based on dual quaternion representations. Then, a finite-time extended state observer is designed using the super-twisting algorithm to estimate the integrated disturbances. Both observation field of view and collision avoidance pose-constrained models are constructed to ensure that the service spacecraft continuously and safely observes the target during proximity maneuvering. And the constraint models are further incorporated into the design of artificial potential function with a unique minimum. After that, the proportional–derivative-like pose-constrained tracking control law is proposed based on the estimated disturbances and the gradient of the artificial potential function. Finally, the effectiveness of the control scheme is verified through numerical simulations.

Active disturbance rejection control for spacecraft relative motion in libration point orbits subject to actuator saturation and time-delays

This paper proposes a novel active disturbance rejection control (ADRC) scheme to achieve the spacecraft relative pose synchronization in the libration orbits under the constrations of the actuator saturation and time-delays. The relative kinematics and dynamics between two spacecraft are modeled using dual quaternions to avoid singularity. A set of dimensionless variables is introduced to improve computational accuracy. An extended state observer, consisting of a time-delay predictor and an anti-windup compensator, is designed to address actuator saturation and communication time delays. A composite controller is then proposed, based on the designed observer, to mitigate the impact of total disturbances. Finally, two illustrative numerical simulations, including a spacecraft close rendezvous and docking scenario and a formation flying scenario, are provided to verify the effectiveness of the proposed ADRC scheme.

Optimal strategies design of active target defense differential game

In this paper, the optimal strategies are investigated for the differential game of active target defense. Specifically, we describe a pursuitevasion game with three agents (namely, an attacker, a target and a defender). For the three agents engagement scenario, two different differential game guidance laws–pure pursuit (PP) and proportional navigation (PN)–are presented for defender. Firstly, the relative motion kinematic models of the three agents are established. We subsequently derive the coupled Hamilton-Jacobi (HJ) equations to design the optimal control strategies for the three agents. Through the construction of actor-critic neural networks, optimal solutions are obtained. Then, the stability of the three-agent system is ensured, and the convergence to the Nash equilibrium equations is demonstrated. Finally, we simulate the optimal strategies employed by the attacker and the defender-target team, thereby highlighting the contrasting outcomes and superiority of different defensive approaches.

Smart analysis of sandwich foldable cylinders as gymnastic accessories

A novel smart analysis of sandwich composite cylindrical shell is presented in this article. It is assumed that the sandwich shell is manufactured from the graphene origami reinforced copper core between two intelligent layers. The proposed structure in this article can be used as an idealized model for cylinder shapes in gymnastic sport and physical therapy units. The virtual work principle in the piezo elasticity framework and the cylindrical coordinate system is extended to derive governing equations. To arrive at more accurate results, a third order shear deformable model is extended for kinematic relations. The electro elastic responses are explored using the analytical method to seek impact of main parameters of the composite structure such as foldability parameter, graphene content percent, and applied electric potential on the electro elastic strain, deformation and stress results.

A new variational integrator for constrained mechanical system dynamics

A new variational integrator is proposed to solve constrained mechanical systems. The main distinguishing feature of the present integrator comes from the distinct discretization of Lagrangians based on the Hamilton's principle in its most general form. Specifically, Hermite interpolation is used for discrete positions, which provides at least C1 continuity for generalized coordinates. The velocities and momentums are interpolated using quadratic polynomials for the consistency, such that the kinematic relation between velocities and positions can be exactly satisfied. Meanwhile, the Gauss-Legendre quadrature rule is employed to guarantee the accuracy of discrete Lagrange equations. To tackle constrained mechanical systems, a coordinate partition approach is used to eliminate the constraint equations. The local incremental rotation vector is exploited to get rid of rotation singularities in spatial problems. Moreover, an adaptive stepsize strategy is implemented to improve the efficiency. The strengths of the new integrator lie in the accessible large step sizes in the simulation and its global second-order accuracy for positions as well as velocities. Several examples are performed and analyzed to validate its accuracy and capabilities.

A peridynamic formulation for planar arbitrarily curved beams with Timoshenko–Ehrenfest beam model

In this study, a peridynamic formulation is proposed for analysis of planar arbitrarily curved beams. Assumptions of Timoshenko–Ehrenfest beam model are considered such that linear kinematic relations are described by displacements of the beam axis and rotation of the cross-section. Equilibrium conditions and boundary conditions are derived by means of the principle of virtual work. Then, peridynamic functions are constructed, and incorporated with equilibrium conditions to develop a peridynamic formulation. Several examples are exhibited to examine the performance of the proposed formulation in some regards, i.e., numerical accuracy, convergence properties, and locking effects. It is delineated that the proposed formulation provides a good level of precision for the analysis of relatively thick beams. However, membrane and shear locking effects are present in the analysis of slender beams, and peridynamic functions of higher polynomial degree can be used to mitigate these unfavorable effects.

Active constraint control for the surgical robotic platform with concentric connector joints

Robotic minimally invasive surgery (MIS) has changed numerous surgical techniques in the past few years and enhanced their results. Haptic feedback is integrated into robotic surgical systems to restore the surgeon's perception of forces in response to interaction with objects in the surgical environment. The ideal exact emulation of the robot's interaction with its physical environment in free space is a very challenging problem to solve completely. Previously, we introduced the surgical robotic platform (SRP) with a novel concentric connector joint (CCJ). This study aims to develop a haptic control system that integrates an active constraint controller into a surgical robot platform. We have successfully established haptic feedback control for the surgical robot using constraint control and inverse kinematic relationships integrated into the overall positioning structure. A preliminary feasibility study, modelling, and simulation were presented.

Design and Simulation of an Innovative Modular Four-Bar Linkage Robotic Arm: Analysis and Applications

In response to the issues of traditional manipulators, such as difficulty in controlling the terminal posture during motion, low control precision, and complex structure, a modular mechanical arm based on a parallel four-bar terminal posture maintenance mechanism has been designed to meet the special requirements of terminal posture maintenance. By analyzing the motion mechanism of the manipulator, the shape space of the manipulator, the terminal position space, and the relationships of forward and inverse kinematics have been derived. A simulation model of the linkage manipulator was established in the Robotic Toolbook for Matlab environment, and structural simulation analysis and kinematic equation verification were conducted. The end positioning and attitude control of different manipulators are simulated by Matlab programming. The working space of the manipulators is calculated by Monte Carlo method, and compared with that of traditional planar manipulators. The results show the validity of the kinematics equation and the rationality of the end positioning control scheme of the linkage manipulator. Finally, the experiment verifies that the attitude retention rate of the modular decoupling manipulator is 97.78% under high load, which verifies the reliability of this scheme. In addition, the manipulator can simplify the complexity of the mechanical structure and complete the control requirements of the terminal attitude under the premise of increasing the working space as much as possible, which lays a foundation for the design and optimization of the manipulator in the field of modular terminal attitude.

Nonlinear dynamic response of a sandwich plate with negative Poisson’s ratio honeycomb-core layer under low-velocity collision impact

In this paper, a nonlinear analytical model is presented for the low-velocity collision impact of a sandwich plate with auxetic honeycomb-core layer. The auxetic feature of the honeycomb material is realized by mathematically expressing the effective material coefficients in terms of material property and cellular geometric parameters through a homogenization method. The higher order shear deformation theory, the von Kármán nonlinearity theory, and a modified Hertz contact law which accounts for the contact pressure distribution and indentation effect, are employed to establish the kinematic relations. The Newmark time integration scheme in conjunction with the direct iterative method is utilized to establish a solution procedure for the nonlinear dynamic governing equation. The verification of the presented model with the data in published literatures is carried out, followed by a series of numerical analyses for influences of cellular geometric features and impactor’s initial conditions (such as impactor’s initial velocity, mass, and nose curvature radius) on the nonlinear dynamic response. The results of numerical analyses show that the geometric features of the unit cell in the honeycomb-core and impactor’s initial conditions can cause significant influences on the nonlinear collision impact behaviors of the system.

Thermomechanical buckling and vibration of composite sandwich doubly curved shells with carbon nanotube‐reinforced face layers

AbstractIn this paper, the thermomechanical buckling and vibration analysis are investigated for carbon nanotube‐reinforced composite sandwich doubly curved shells (CNCSDS) under the action of both thermal loads and in‐plane compressive loads. Based on the von‐Karman non‐linear kinematic relations, First Order Shear Theory, and Hamilton's principle, the vibration and stability equations for CNCSDS under thermomechanical loads are deduced. For obtaining the critical thermomechanical buckling load and vibration frequency, an exact method is adopted. Subsequently, the results are validated by comparing with the finding in published literature and simulation results. At last, the influence of system parameters on critical thermomechanical buckling load and vibration frequency is studied and displayed graphically. Meanwhile, some new results about thermomechanical buckling and vibration analysis of CNCSDS are proposed for the first time.Highlights Thermomechanical buckling and vibration of carbon nanotube‐reinforced composite sandwich doubly curved shells was studied. Vibration and stability equations under thermomechanical loads was deduced. The change rules of thermomechanical buckling load and frequency were obtained.

Research on engine dynamic torque modeling for torsional vibration analysis of vehicle powertrain

In order to improve the accuracy of dynamic torque model of engine, a simulation model of quasi-transient engine dynamic torque under all operating conditions was established considering the influence of throttle opening. Firstly, the calculation model of engine output torque and cylinder pressure is established according to the kinematic relation of crank linkage mechanism. Secondly, BP neural network is used to establish the mapping relationship model of throttle opening, rotational speed, and cylinder pressure ratio data. In order to solve the contradiction between calculation accuracy and efficiency of engine cylinder pressure interpolation, a quadratic interpolation method is proposed, which refines data to improve interpolation accuracy, and improves calculation efficiency by online adjacent interpolation, and completes the construction of dynamic torque simulation model of engine in all working conditions. Finally, the experimental data of dynamic torque characteristics of the engine at different speeds are used to verify the accuracy of the model calculation. By using the verified engine model, the dynamic operating characteristics of variable valve opening and variable speed are simulated and analyzed. The results show that the model established in this paper can effectively reflect the dynamic characteristics of the engine, and the model is suitable for the simulation of the torsional vibration of the vehicle powertrain under steady and unsteady conditions.

Direct Closed-Loop Control Structure for the Three-Axis Satcom-on-the-Move Antenna

The traditional Satcom-on-the-Move (SOTM) mechanical structure consists of a dual-axis configuration with an azimuth axis and a pitch axis. In this structure, when the pitch angle is 90 degrees, the rotation of the azimuth axis cannot change the antenna’s direction. To solve this issue, a three-axis SOTM mechanical structure has been developed. The traditional three-axis SOTM servo control system adopts a closed-loop control scheme. In this scheme, due to the difficulty in directly obtaining the antenna’s rotation angle, the angles of rotation for each axis are typically selected to represent the antenna’s rotation angle. The closed-loop feedback includes the angles and angular velocities of the axes, which cannot completely capture the antenna’s motion state, essentially constituting an indirect closed-loop control. Addressing the shortcomings of this indirect closed-loop control, this paper first establishes the kinematic relations between the axes of the three-axis SOTM antenna using the Denavit–Hartenberg (DH) method. Subsequently, the relationship between antenna pointing and the rotational states of the three axes was derived using the Jacobian operator. Building upon this foundation, a direct closed-loop control structure for a three-axis SOTM antenna was designed. To enable the control system to achieve rapid convergence with minimal overshoot, an Active Disturbance Rejection Control (ADRC) algorithm based on smooth continuous functions is introduced as the inner and outer loop controller algorithms within the direct closed-loop control structure. To address the nonlinearity in the design scheme, a piecewise linearization method is proposed to reduce the demands on the microprocessor’s performance and enhance the engineering feasibility of the solution. Finally, the effectiveness of the proposed approach is validated through experiments. The experimental results demonstrate that compared to traditional indirect closed-loop control methods, utilizing the direct closed-loop control method for the three-axis SOTM antenna presented in this paper can lead to higher precision in pointing the antenna towards satellites and enhance communication effectiveness.

Effect of Roundness Error of the Grooves on the Inner Ring Runout of Angular Contact Ball Bearings

In this paper, a prediction model of the inner ring runout of angular contact ball bearings is established according to the geometric and kinematic relationships of the bearing, considering factors such as the roundness error of the inner and outer grooves, the dimensional error of the balls, and the change of the contact angle between the balls and the grooves. The correctness of the model is verified through experiments. The effects of the order and amplitude of the roundness error of the inner groove and the order and amplitude of the roundness error of the outer groove on the inner ring runout are analyzed. The coupling effect of the roundness error of the inner and outer grooves on the inner ring runout is further analyzed. The results show that the inner ring runout changes periodically with a change to the roundness error order of the grooves, which increases with an increase in the roundness error amplitude. Under the coupling of the roundness error of the inner and outer grooves, the magnification of the inner ring runout increases as a whole. When there are specific relationships between the roundness error orders of the grooves and the number of balls, the magnification of the axial or radial runout changes significantly.

Static bending analysis of pressurized cylindrical shell made of graphene origami auxetic metamaterials based on higher-order shear deformation theory

Static bending responses of a pressurized composite cylindrical shell made of a copper matrix reinforced with functionally graded graphene origami are studied in this paper. The kinematic relations are extended based on a new higher-order shear and normal deformation theory in the axisymmetric framework. The constitutive relations are extended for the composite cylindrical shell where the effective modulus of elasticity, Poisson's ratio, thermal expansion coefficient and density are estimated using the Halpin-Tsai micromechanical model and the rule of mixture. Some modified coefficients are employed for correction of the mentioned material properties in terms of the volume fraction and the folding degree of graphene origami, characteristics of copper and graphene nanoplatelets and thermal loads. The principle of virtual work is used to derive governing equations through computation of strain energy and external work. The static bending results including radial and axial displacements, circumferential strain and stress are presented along the longitudinal and radial directions in terms of volume fraction, folding degree and distribution of graphene origami. The results show an increase in radial displacement and circumferential strain with an increase in folding degree and a decrease in volume fraction of graphene origami. The main novelty of this work is investigating the effect of foldability parameter and various distribution of graphene origami on static results of short cylindrical shell.

Three-dimensional adaptive dynamic surface guidance law for missile with terminal angle and field-of-view constraints

In this paper, an adaptive dynamic surface (DSC) guidance law for missile is designed to intercept the maneuvering target with field-of-view (FOV) and terminal angle constraints in three-dimensional(3D) space, and the missile autopilot dynamics is considered. Firstly, the time-varying transformation function related to line of sight (LOS) is used to replace the FOV constraints, transforming the process-constrained control problem into the output-constrained control problem. Meanwhile, the 3D coupled relative kinematics model considering missile autopilot dynamics and maneuvering target acceleration is established. Secondly, a novel time-varying asymmetric barrier Lyapunov function (TABLF) with dead-zone characteristics is introduced to the adaptive dynamic surface guidance law design process to improve the robustness of parameter debugging. Thirdly, with the help of a nonlinear adaptive filter, the ‘explosion of complexity’ problem can be avoided effectively, which is caused by analytic computation of virtual signal derivatives. Furthermore, aiming at the problem of autopilot dynamic errors, target acceleration disturbances, and unmeasurable parameters in the model, a novel adaptive law is used to evaluate online. Then, the stability of the closed-loop system is rigorously proven using Lyapunov criteria. Ultimately, Numerical simulations with various constraints and comparison studies have been considered to show the feasibility and effectiveness of the proposed missile guidance law.