Momentum Preserving Simulation of Cooperative Multi-Rotors with Flexible-Cable Suspended Payload

In this paper, a momentum-preserving integration scheme is implemented for the simulation of single and cooperative multi-rotors with a flexible-cable suspended payload by employing a Lie group based variational integrator (VI), which provides the preservation of the configuration manifold and geometrical constraints. Due to the desired properties of the implemented VI method, e.g. sypmlecticity, momentum preservation, and the exact fulfillment of the constraints, exponentially long-term numerical stability and good energy behavior are obtained for more accurate simulations of aforementioned systems. The effectiveness of Lie group VI method with the corresponding discrete systems are demonstrated by comparing the simulation results of two example scenarios for the single and cooperative systems in terms of the preserved quantities and constraints, where a conventional fixed-step Runge-Kutta 4 (RK4) and Variable-Step integrators are utilized for the simulation of continuous-time models. It is shown that the implemented VI method successfully performs the simulations with a long-time stable behavior by preserving invariants of the system and the geometrical constraints, whereas the simulation of continuous-time models by RK4 and Variable Step are incapable of satisfying these desired properties, which inherently results in divergent and unstable behavior in simulations.

Large Deformation Dynamic Analysis of a Cable System by a New Hamiltonian Finite Element Method

This paper develops a new Hamiltonian nodal position finite element method for dynamic analysis of spatial flexible cable systems with large deformation. The dynamic governing equation is derived from finite elasticity theory. Logarithmic strain is applied to construct large deformation Hamiltonian canonical equations. An efficient second-order symplectic difference algorithm is built to solve the canonical equations numerically. A large strain conical pendulum system is analyzed numerically by the proposed method, and the numerical results are compared with those retracted from the existing Hamiltonian methods and Livermore Software Technology Corporation: dynamics (LS-DYNA). The proposed method is further verified by two tethered dynamic experiments involving large displacement motion and large deformation. The comparisons and verifications demonstrate that the proposed method is of symplectic conservation, has high accuracy and has stability for calculating flexible cable system dynamics with large deformation.

Section Optimization Design of a Flexible Cable-Bar Tensile Structure Based on Robustness

As the current literature lacks effective nonlinear robustness evaluation method and optimal design theory of the structural robustness for flexible cable-bar tensile structure, this paper aimed to conduct further studies. Based on the theory, a fundamental robustness analysis method and a detailed calculation way through the combination of induction of performance criterion and random theory for nonlinear structural robustness quantitative evaluation method were proposed. Following this, a real Geiger cable dome structure was studied as its research object, and the influences of structural robustness of simultaneous changes of all elements section and changes of every kind of element section were analysed, respectively. Finally, the genetic algorithm was applied through MATLAB and ANSYS software to achieve optimal section layout, with the goal of minimizing structural quality on the condition that the structural robustness indicator keep less than that of the initial structure. The result revealed that the increase of the section of elements can effectively enhance structural robustness and the section changes of various elements showed different sensitivities to the influence of structural robustness. Meanwhile, structural quality can be effectively reduced by optimizing measures such as increasing the section of elements with significant effect on structural robustness and reducing the section of elements with minor effects on structural robustness, while the structural robustness indicator keeps less than that of the initial structure. The optimization reveals that quality was reduced by 42.5% in this paper.

Finite-time stabilization of an overhead crane with a flexible cable submitted to an affine tension

The paper is concerned with the finite-time stabilization of a coupled PDE-ODE system describing the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is described by the wave equation with a variable coefficient which is an affine function of the curvilinear abscissa along the cable. Using several changes of variables, a backstepping transformation, and a finite-time stable second-order ODE for the dynamics of a conveniently chosen variable, we prove that a global finite-time stabilization occurs for the full system constituted of the platform and the cable. The kernel equations and the finite-time stable ODE are numerically solved in order to compute the nonlinear feedback law, and numerical simulations validating our finite-time stabilization approach are presented.

A Miniaturized High-Gain Flexible Antenna for UAV Applications

A miniaturized high-gain flexible unmanned aerial vehicle (UAV) antenna is presented in this study. The proposed antenna basically comprised of three parts of printed patch in series, etched on dielectric substrate. And, a flexible cable is loaded on the bottom of dielectric substrate. A coplanar waveguide (CPW) with asymmetric ground feeding structure is employed to provide good impedance matching. The surface current can achieve the same phase for the straight-line patch and the flexible cable, through adjusting the dimensions of the meander line patch, which increases radiation gain while maintaining the compact size. As an important merit to be highlighted, the flexible cable can greatly reduce the volume and aerodynamic drag of the antenna. It has a low-profile compact size of 196 × 15 × 0.8 mm3 (excluding flexible cable). The results show that the omnidirectional gain fluctuates within 4.5 ± 0.1 dBi in the desired band (902 MHz–928 MHz), which is high enough for the UAV application. Details of the antenna design and experimental results are presented and discussed.