Final Relative Position Research Articles

Prescribed-Time Network-Based Deployment of Nonlinear Multiagent Systems: A Discrete-Space PDE Method.

This article attempts to design the prescribed-time time-varying deployment schemes for first-order and second-order nonlinear multiagent systems (MASs). We assume that all agents can obtain the information of their current and final relative positions with their neighbors, and the final absolute velocities (as well as their current and final relative velocities, the final absolute accelerations for the second-order MASs) through a communication network, whereas two boundary agents are able to obtain their current and final absolute positions (as well as their current and final absolute velocities for the second-order MASs). The neighbor relationship of all agents is described by a spatial variable and two static-feedback controllers are introduced, which can be expressed as a second-order space difference of the spatial variable. Then, the deployment of MASs can be transformed into the stabilization of discrete-space partial differential equation (PDE) systems. Three virtual agents are introduced to constitute the Dirchlet and Neumann boundary conditions. Several algebraic inequality criteria are derived to guarantee that the prescribed-time time-varying deployment can be achieved within a prescribed time under the Dirchlet and mixed boundary conditions. Unlike the published results, our results are derived based on the discrete-space PDE systems instead of continuous-space PDE systems, which is consistent with the discrete spatial distribution of agents. Finally, two numerical examples are given to illustrate the effectiveness of our results.

Consensus and swarming behaviors for a proportional-derivative system with a cut-off interaction

Abstract This paper presents a proportional-derivative protocol for the consensus problem of a class of linear second-order multi-agent systems with local information transmission. The communication topology among the agents is switching and agents receive information within a critical bounded distance. As new observations, we show that the desired protocol system undergoes consensus and swarming behaviours when 1 is a simple eigenvalue of the adjacency matrix. In this case, both final velocity and final relative position are formulated. Simulation results show the effectiveness of the proposed protocol.

ASYMPTOTIC FLOCKING VELOCITY AND POSITION FORMULAS FOR THE DELAYED CUCKER-SMALE MODEL

<abstract> The Cucker-Smale (short for C-S) model was modified by introduced multiple time delays, and the flocking characteristics of the processing delay C-S model of systems was obtained. Based on the fixed point theorem, we present the existence and uniqueness of the flocking solution for our delayed C-S model when the influence function has the property of Lipschitz and the initial value satisfies certain conditions. At last, we present the asymptotic flocking velocity and the final relative position between agents of the unique flocking solution for such system. </abstract>

A comparative study on the migration of minor phase globule in different-sized droplets of Fe-58wt.%Sn immiscible alloy

The migration behaviors of minor-phase globules are comparatively studied inside (radius=) 200 μm and 400 μm droplets based on the model of Fe-58wt.%Sn alloy under reduced-gravity condition. It was found that the final relative positions of same-sized globules are not dependent on the droplet sizes, although the globule's migrating velocity and lifetime inside different-sized droplet alloys are different. This finding is contrary to the conventional understanding that the droplet size can exert great influence on the microstructures by controlling Marangoni motion, and moreover offers a new insight into how to design the desired structures in the droplet immiscible alloy.

Time and Covariance Threshold Triggered Optimal Uncooperative Rendezvous Using Angles-Only Navigation

A time and covariance threshold triggered optimal maneuver planning method is proposed for orbital rendezvous using angles-only navigation (AON). In the context of Yamanaka-Ankersen orbital relative motion equations, the square root unscented Kalman filter (SRUKF) AON algorithm is developed to compute the relative state estimations from a low-volume/mass, power saving, and low-cost optical/infrared camera’s observations. Multi-impulsive Hill guidance law is employed in closed-loop linear covariance analysis model, based on which the quantitative relative position robustness and relative velocity robustness index are defined. By balancing fuel consumption, relative position robustness, and relative velocity robustness, we developed a time and covariance threshold triggered two-level optimal maneuver planning method, showing how these results correlate to past methods and missions and how they could potentially influence future ones. Numerical simulation proved that it is feasible to control the spacecraft with a two-line element- (TLE-) level uncertain, 34.6% of range, initial relative state to a 100 m v-bar relative station keeping point, at where the trajectory dispersion reduces to 3.5% of range, under a 30% data gap per revolution on account of the eclipse. Comparing with the traditional time triggered maneuver planning method, the final relative position accuracy is improved by one order and the relative trajectory robustness and collision probability are obviously improved and reduced, respectively.

Solving the relative Lambert's problem and accounting for its singularities

A novel approach based on Lagrange's time equation and differential orbital elements is developed to solve the relative Lambert's problem for circular reference orbits. Compared with the conventional Clohessy–Wiltshire equation, the proposed method directly obtains differences of orbital elements between a transfer orbit and a reference orbit. This advantage enables us to account for singularities that occur in the relative Lambert's problem. The solved relative velocities depend on the five differential orbital elements. Accordingly, singularities can be attributed to any significant change in the semi-major axis, eccentricity, or orbital plane. Furthermore, appropriately adjusting initial and final relative positions eliminates some singularities. A numerical simulation based on the classic Lambert's formula for a rendezvous mission in closed range demonstrates the analytical results.

Two-Point Boundary Value Problem Solutions to Spacecraft Formation Flying

The two-point boundary value problem of a leader-follower spacecraft formation flying in unperturbed elliptical reference orbits is studied. The initial and final relative positions and times and the orbit of the leader are known, and the orbit of the follower must be determined. This problem will be called the relative Lambert's problem. First, we will show this relative Lambert's problem can be solved like the classical Lambert's problem. Then, a set of approximate analytic solutions are obtained through linearizing the Lagrange's time equation. Meanwhile, a simplified Newton-Raphson algorithm is applied to obtain numerical solutions, and the relevant quantities of the leader are used as initial conditions. Here, our special efforts are dedicated to the study of the periodic relative orbits of the follower. In particular, a set of first-order analytic solutions to the relative Lambert's problem are derived from the periodic solutions of Lawden's equations, and a constraint on the leader's true anomalies (implicitly in time) and relative positions is obtained. From that constraint on the radial/in-track plane of the leader local-vertical-local- horizontal frame, we found that, for specified initial and final times, the locus of final positions of the follower with fixed initial position is a straight line, and so is the locus of initial positions with fixed final position. Furthermore, for fixed initial and final positions, the transfer times with either specified initial time or final time can be expressed as the real roots of a cubic equation, for which there are at most three solutions. Several examples will be given to support these conclusions.

Adaptive control for autonomous rendezvous of spacecraft on elliptical orbit

A strategy for spacecraft autonomous rendezvous on an elliptical orbit in situation of no orbit information is developed. Lawden equation is used to describe relative motion of two spacecraft. Then an adaptive gain factor is introduced, and an adaptive control law for autonomous rendezvous on the elliptical orbit is designed using Lyapunov approach. The relative motion is proved to be ultimately bounded under this control law, and the final relative position error can achieve the expected magnitude. Simulation results indicate that the adaptive control law can realize autonomous rendezvous on the elliptical orbit with relative state information only.

Les limites de la chirurgie des modèles en chirurgie orthognathique : implications théoriques et pratiques

Orthognathic model surgery is a classical technique used to simulate orthognathic surgical cases. However, a detailed analysis of this technique demonstrates that theoretical errors and inaccuracies can occur in routine practice. 2D and 3D cephalometric analysis is the first source of inaccuracies. Then, during the occlusal plane transfer from the patient to the semi-adjustable dental articulator, errors can occur by inaccurate manipulation of the facial bow. Simulating the operation on the plaster cast is difficult due to the lack of a real link between the cephalometric analysis and the model surgery. Rotation and translation movements of the plaster casts are insufficiently controlled during the model surgery stage. Finally, the splint, which transfers the final relative position of maxilla to the mandible, summates all of the errors of the previous stages.

The influence of reactive-element coatings on the high-temperature oxidation of pure-Cr and high-Cr-content alloys

The influence of various reactive-element (RE) oxide coatings (Y2O3, CeO2, La2O3, CaO, HfO2, and Sc2O3) on the oxidation behavior of pure Cr, Fe−26Cr, Fe−16Cr and Ni−25Cr at 900°C in O2 at 5×10−3 torr has been investigated using the18O/SIMS technique. Polished samples were reactively sputtercoated with 4 nm of the RE oxide and oxidized sequentially first in16O2 and then in18O2. The effectiveness of each RE on the extent of oxidation-rate reduction varied with the element used. Y2O3 and CeO2 coatings were found to be the most beneficial, whereas Sc2O3 proved to be ineffective, for example, for the oxidation of Cr. SIMS sputter profiles showed that the maximum in the RE profile moved away from the substrate-oxide interface during the early stages of oxidation. After a certain time the RE maximum remained fixed in position with respect to this interface, its final relative position being dependent on the particular RE. The position of the RE maximum within the oxide layer also varied with the substrate composition. For all coatings18O was found to have diffused through the oxide to the substrate-oxide interface during oxidation, the amount of oxide at this interface increasing with increasing time. The SIMS data confirm that for coated substrates there has been a change in oxidegrowth mechanism to predominantly anion diffusion. The RE most probably concentrates at the oxide grain boundaries, generally as the binary oxide (RE) CrO3. Cr3+ diffusion is impeded, while oxygen diffusion remains unaffected.

Direct numerical simulations of round jets: Vortex induction and side jets

In this paper, a numerical investigation of three-dimensional round jets subjected to streamwise and azimuthal perturbations is reported. The main objective of the study is to give a consistent scenario for the breaking of rotational symmetry in such flows which may ultimately lead to the production of intense side jets. In particular it is shown that the development of the Widnall instability on the primary vortex rings and the evolution of the Bernal and Roshko [J. Fluid Mech. 170, 499 (1986)] streamwise vortices generated by the instability of the braid could be deeply intertwined. A comprehensive discussion of the vortex induction mechanisms leading to the reorientation of the initial vorticity both in the ring and braid regions and to the deformation of the rings is presented. The recent analysis by Monkewitz and Pfizenmaier [Phys. Fluids A 3, 1356 (1991)] is confirmed in the sense that strong radial ejection of fluid is not directly linked to the deformation of the vortex rings but rather to the occurrence of coherent streamwise vortex pairs. However, the final relative position of the streamwise vortex pairs with respect to the deformations of the vortex rings differs slightly from Monkewitz and Pfizenmaier’s proposition.