Free Trajectories Research Articles

Electric field makes Leidenfrost droplets take a leap.

Leidenfrost droplets, i.e. droplets whose mobility is ensured by a thin vapor film between the droplet and a hot plate, are exposed to an external electric field. We find that in a strong vertical electric field the droplet can start to bounce progressively higher, defying gravitational attraction. From the droplet's trajectory we infer the temporal evolution of the amount of charge on the droplet. This reveals that the charge starts high and then decreases in steps as the droplet slowly evaporates. After each discharge event the charge is in a fixed proportion to the droplet's surface area. We show that this behavior can be accurately modeled by treating the droplet as a conducting sphere that occasionally makes electrical contact with the hot plate, at intervals dictated by an electro-capillary instability in the vapor film. An analysis of the kinetic and potential energies of the bouncing droplet reveals that, while the overall motion is damped, the droplet occasionally experiences a sudden boost, keeping its energy close to the value for which the free fall trajectory and droplet oscillation are in sync. This helps the droplet to escape from the hot surface when finally the electrical surface forces overtake gravity.

Optimal Scheduling and Routing of Free-range AGVs at Large Scale Automated Container Terminals

This work tackles the problem of controlling operations at an automated container terminal. In the context of large supply chains, there is a growing trend for increasing productivity and economic efficiency. New optimization models and algorithms are provided for scheduling and routing equipment that is moving containers in a quay area, loading/unloading ships, transporting them via Automated Guided Vehicles (AGVs) to Automated Stacking Cranes (ASCs), organizing them in stacks. In contrast with the majority of the approaches in the related literature, this work tackles two dynamics of the system, a discrete dynamic, characteristic of the maximization of operations efficiency, by assigning the best AGV and operation time to a set of containers, and a continuous dynamic of the AGV that moves in a geographically limited area. As an assumption, AGVs can follow free range trajectories that minimize the error of the target time and increase the responsiveness of the system. A novel solution framework is proposed in order to tackle the two system dynamics. Various metaheuristic algorithms are tested to solve the problem in a near-optimal way. Computational experiments are presented in order to show the feasibility of the proposed framework on a practical case study, and to assess the performance of advanced scheduling and routing algorithms on numerous system settings.

Generation of Traffic/Terrain Conflict Free Trajectories and Their Analysis by Means of the On-board Model of the Airplane

In this paper an algorithm for formation of a set of conflict-free trajectories from current airplane position to the predetermined trajectory change point (TCP) to resolve traffic and terrain conflicts is proposed. Algorithm provides TCP arrival time synchronization with an airplane ahead and safe altitude clearance above terrain. An algorithm for calculation of velocity along those trajectories is described. This algorithm generates 4D trajectories that meet specified standards of longitudinal separation at the TCP. This technique can be implemented in on-board integrated surveillance system (ISS) to provide pilots with alerts and recommendations to prevent dangerous evolution of flight situation and increase flight safety.

View/state planning for three-dimensional object reconstruction under uncertainty

We propose a holistic approach for three-dimensional (3D) object reconstruction with a mobile manipulator robot with an eye-in-hand sensor; considering the plan to reach the desired view/state, and the uncertainty in both observations and controls. This is one of the first methods that determines the next best view/state in the state space, following a methodology in which a set of candidate views/states is directly generated in the state space, and later only a subset of these views is kept by filtering the original set. It also determines the controls that yield a collision free trajectory to reach a state using rapidly-exploring random trees. To decrease the processing time we propose an efficient evaluation strategy based on filters, and a 3D visibility calculation with hierarchical ray tracing. The next best view/state is selected based on the expected utility, generating samples in the control space based on an error distribution according to the dynamics of the robot. This makes the method robust to positioning error, significantly reducing the collision rate and increasing the coverage, as shown in the experiments. Several experiments in simulation and with a real mobile manipulator robot with 8 degrees of freedom show that the proposed method provides an effective and fast method for a mobile manipulator to build 3D models of unknown objects. To our knowledge, this is one of the first works that demonstrates the reconstruction of complex objects with a real mobile manipulator considering uncertainty in the controls.

Theorem of Optimal Image Trajectories in the Restricted Problem of Three Bodies

The restricted three-body problem represents the dynamical framework employed for spacecraft mission analysis, in the presence of two attracting bodies, since the 1950s. In this context, orbital motion is often chaotic, although several special solutions (equilibrium points, periodic orbits, and quasiperiodic trajectories) exist, and can be--or have already been--profitably employed in space missions. The theorem of image trajectories, proven five decades ago by Miele, states that for a given path in the restricted problem of three bodies (with primaries in mutual circular orbits), there exists a mirror trajectory (in two dimensions) and three mirror paths (in three dimensions). This theorem regards feasible trajectories and proved extremely useful for investigating the natural dynamics in the restricted problem of three bodies, by identifying special solutions, such as symmetric periodic orbits and free return trajectories. This work extends the theorem of image trajectories to optimal paths, which minimize either the propellant consumption or the time of flight, by determining the relations between the optimal thrust sequence, magnitude, and direction of an outgoing path and a symmetrical returning trajectory. This means that while the theorem of image paths revealed extremely useful for investigating natural dynamics, the theorem of optimal image trajectories can be profitably employed for powered orbital motion, i.e., in the context of impulsive and finite-thrust orbit transfers and rendezvous, as well as for the purpose of analyzing artificial periodic orbits that use very low thrust propulsion.

An algorithm for multi-robot collision-free navigation based on shortest distance

This paper presents a new approach for multi-robot navigation in dynamic environments, called the shortest distance algorithm. This approach uses both the current position and orientation of other robots to compute the collision free trajectory. The algorithm suggested in this paper is based on the concept of reciprocal orientation that guarantees smooth trajectories and collision free paths. All the robots move either in a straight line or in a circular arc using the Bresenham algorithms. The current approach is tested on three simulation scenarios.

Near-optimal trajectory generation, using a compound B-spline interpolation and minimum distance criterion with dynamical feasibility correction

Trajectory generation for robotic vehicles tries to provide real time computing of a collision free path from one point to another, which usually involves minimizing a performance measure, to accomplish a desired task. A novel hierarchical method for generating near-optimal and collision free trajectories is proposed here to be used on-line in three-dimensional space. At the top level, the off-line optimal trajectory problem is solved in a complex environment, using B-spline interpolation and genetic algorithm, while considering the dynamic constraints of the vehicle. At the intermediate level, the path is modified for any possible on-line intersections with unexpected obstacles, using a minimum distance correction technique. The feasibility of the generated path is assessed at the lowest level by considering dynamic constraints of the vehicle. A novel method is presented at this level for correcting the path and obtaining near-optimal and dynamically feasible trajectories. Each part is assessed by a separate robotic vehicle to ensure the capability and performance. Lastly, the consistency between the levels of hierarchy is evaluated by presenting a differential-drive robot example. The final path is also verified with two commercial software codes for path planning and optimal trajectory generation.

Asymptotically free scaling solutions in non-Abelian Higgs models

We construct asymptotically free renormalization group trajectories for the generic nonabelian Higgs model in four-dimensional spacetime. These ultraviolet-complete trajectories become visible by generalizing the renormalization/boundary conditions in the definition of the correlation functions of the theory. Though they are accessible in a controlled weak-coupling analysis, these trajectories originate from threshold phenomena which are missed in a conventional perturbative analysis relying on the deep Euclidean region. We identify a candidate three-parameter family of renormalization group trajectories interconnecting the asymptotically free ultraviolet regime with a Higgs phase in the low-energy limit. We provide estimates of their low-energy properties in the light of a possible application to the standard model Higgs sector. Finally, we find a two-parameter subclass of asymptotically free Coleman-Weinberg-type trajectories that do not suffer from a naturalness problem.

High-latitude-landing circumlunar free return trajectory design

Purpose The purpose of this paper is to design free return trajectories launching at lower-latitude launch site Wenchang and landing at relatively high-latitude landing site Siziwang Banner tailored to human lunar missions for China, and in general demonstrate the feasibility of high-latitude landings with acceptable entry range.

Generation of launch windows for high-accuracy lunar trajectories

The purpose of this paper is to systematically establish in arbitrary timespan a full set of instantaneous ground launch windows for certain accurate three-dimensional asymmetric free return circumlunar trajectories tailored to human lunar missions for China, and in general propose a novel methodology useful for determining ground launch windows for other Earth-to-Moon trajectories.Using time-varying spherical trigonometry, an analytical design method for finding ground launch windows is developed with two-body model assumption. Windows appear when the Moon at arrival time and the Earth parking orbit nodes on lunar orbit plane have similar right ascensions. The numerical first guesses obtained almost instantly are within minutes of accurate solutions and refined to highly accurate trajectories by differential corrections of only one phase. A translunar launch window plot visualizing all monthly and daily launch windows differentiating two types of translunar injections is created.The method proposed can be used for automated generation of complete trajectory sets, and provide the basis for the preparation of launch timetables satisfying lunar mission requirements.

Spatiotemporal properties of nanoshell plasmonic response for strong-field experiments

Field enhancement behavior of a ${\mathrm{SiO}}_{2}$/Au nanoshell is studied in the framework of strong-field physics. Localized plasmonic fields induce local electric field enhancement with the potential to lead to the strong-field regime without the use of costly amplified lasers. In this framework, electrons are tunnel ionized from the nanoshell and accelerated by the local field being spatially inhomogeneous in terms of spectral and polarization properties. These processes are happening within a single laser shot, and thermal effects are therefore neglected. We show that the localized response to ultrashort femtosecond pulses can be investigated by extending Mie theory to multilayer spherical particles. Nanoshell plasmonic resonances can be easily tuned depending on the volume ratio between core and whole particle. Optimum geometric parameters of the nanoshell are selected for use with ultrashort pulses centered at 800 nm where most femtosecond oscillators operate. It is shown that phase and amplitude reshaping of the incident pulse by the plasmonic resonance can be partially corrected using active shaping leading to ultrashort response of the medium. Finally, free electron classical trajectories are calculated to highlight the inhomogeneous nature of the local enhancement in a strong-field picture.

Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape.

Broadband ultrashort terahertz (THz) pulses can be produced using plasma generation in a noble gas ionized by femtosecond two-color pulses. Here we demonstrate that, by using multiple-frequency laser pulses, one can obtain a waveform which optimizes the free electron trajectories in such a way that they acquire the largest drift velocity. This allows us to increase the THz conversion efficiency to 2%, an unprecedented performance for THz generation in gases. In addition to the analytical study of THz generation using a local current model, we perform comprehensive 3D simulations accounting for propagation effects which confirm this prediction. Our results show that THz conversion via tunnel ionization can be greatly improved with well-designed multicolor pulses.

Circumlunar free return trajectories design and validation for high-speed moon-to-earth reentry mission

This paper introduces the trajectory design method used in CE-5T1 mission and the flight results. Firstly, the design method and analysis of circumlunar trajectory is studied. Secondly, circumlunar trajectory correction maneuver (TCM) strategy is discussed, including full target strategy, reduced-order target strategy and bias target strategy. In the end, the flight data is compared with predicted value.

Spectral self-action of THz emission from ionizing two-color laser pulses in gases

The spectrum of terahertz (THz) emission in gases via ionizing two-color femtosecond pulses is analyzed by means of a semi-analytic model and numerical simulations in 1D, 2D and 3D geometries taking into account propagation effects of both pump and THz fields. We show that produced THz signals interact with free electron trajectories and thus significantly influence further THz generation upon propagation, i.e., make the process inherently nonlocal. This self-action contributes to the observed strong spectral broadening of the generated THz field. We show that diffraction of the generated THz radiation is the limiting factor for the co-propagating low frequency amplitudes and thus for the self-action mechanism in 2D and 3D geometries.

C-19 セット・フォーム習得支援RTがフリースロー軌道のばらつきを与える影響の検証(投げ)

C-19 セット・フォーム習得支援RTがフリースロー軌道のばらつきを与える影響の検証(投げ)

Rozmyte generowanie bezkolizyjnej trajektorii MRK z zastosowaniem laserowego skanera przestrzeni

Rozmyte generowanie bezkolizyjnej trajektorii MRK z zastosowaniem laserowego skanera przestrzeni

Trajectory Planning with Negotiation for Maritime Collision Avoidance

The problem of vessel collisions or near-collision situations on sea, often caused by human error due to incomplete or overwhelming information, is becoming more and more important with rising maritime traffic. Approaches to supply navigators and Vessel Traffic Services with expert knowledge and suggest trajectories for all vessels to avoid collisions, are often aimed at situations where a single planner guides all vessels with perfect information. In contrast, the authors suggest a two-part procedure which plans trajectories using a specialised A* and negotiates trajectories until a solution is found, which is acceptable for all vessels. The solution obeys collision avoidance rules, includes a dynamic model of all vessels and negotiates trajectories to optimise globally without a global planner and extensive information disclosure. The procedure combines all components necessary to solve a multi-vessel encounter and is tested currently in simulation and on several test beds. The first results show a fast converging optimisation process which after a few negotiation rounds already produce feasible, collision free trajectories.

Підготовка майбутніх учителів до суб’єкт-суб’єктної взаємодії з учнями

This article describes a theoretical grounding for prospective teacher training system to subject-subjective interaction with pupils. The system is based on the next principles: humanization of education and professional environment, free trajectory evolution choice, relationship of fields of activity, cultural correspondence, value attitude to collaboration and cooperation of subjects in all fields of activity. The process of teacher training consists of four stages.

Efficient time-optimal two-corner trajectory planning algorithm for differential-driven wheeled mobile robots with bounded motor control inputs

We propose an efficient time-optimal trajectory planning algorithm for differential-driven wheeled mobile robots with bounded motor control inputs in the environment with cranked road where two corners with arbitrary angles exist. Based on dynamics for differential-driven wheeled mobile robots including actuating motors as well as on the bang–bang principle for time-optimality, we plan the time-optimal free path trajectory which unifies path planning and trajectory generation. Thus it improves total time significantly while handling obstacle avoidance. We divide our trajectory into three sections and then divide each section into an appropriate number of subsections to make five subsections in total. We introduce the concept of transition angle to solve the problem with formulating search loops efficiently. Numerical results are provided to validate the effectiveness of the proposed algorithm.

Trajectory Modulated Arc Therapy: A Fully Dynamic Delivery With Synchronized Couch and Gantry Motion Significantly Improves Dosimetric Indices Correlated With Poor Cosmesis in Accelerated Partial Breast Irradiation

Trajectory modulated arc therapy (TMAT) is a novel treatment technique using an optimized trajectory combining synchronized dynamic gantry rotation, translational and rotational couch movement, and MLC motion during continuous beam delivery. The purpose of this work is to develop a tool for planning deliverable TMAT on a collision free coronal trajectory and evaluate its benefit for accelerated partial breast irradiation (APBI) in a prone position. The TMAT algorithm was largely based on a VMAT progressive sampling approach with the following modifications: (1) physical constraints on couch movement and couch angle dependent efficiency constraints for MU weight changes and MLC leave motion were defined; (2) collimator rotation was fixed to minimize the impact of greater BEV target motion on MLC modulation; and (3) the pencil beam dose calculation engine was modified to support extended SSDs. A commercial computer algorithm software environment for TMAT optimization and dose calculation was created allowing for user specified dynamic motions that support any motion axis. TMAT delivery was implemented and demonstrated on a medical linear accelerator via custom XML scripts. TMAT was evaluated in 10 cases for prone breast irradiation through comparison to a 6 field non-coplanar IMRT plan. Patient selection/exclusion criteria and structure contouring were in compliance with NSABP B-39/RTOG 0413 protocol. A total of 251.5° ± 7.88° (standard deviation) couch arc can be achieved by the optimized trajectory with 180-210 control points at 1°-2° rotational increments. An XML file of the TMAT plan defining the optimized trajectory, MLC aperture shape and accumulative MU per control point was delivered in the developer mode on a solid water phantom with a delivery time of 4.5 min. Compared with IMRT, TMAT achieved significantly reductions on V50%, V80% and V100% of irradiated non-target breast tissue. The ratios of normal breast tissue volume receiving 50%, 80% and 100% of the prescription dose for TMAT relative to IMRT were: V50% (TMAT/IMRT) = 78.38% ± 13.03%, V80% (TMAT/IMRT) = 44.19% ± 9.04% and V100% (TMAT/IMRT) = 9.96% ± 7.55%, all p ≤ 0.01 (paired two sample t-test). The ratios of whole breast reference volume receiving 50%, 80%, and 100% of the prescription dose for TMAT versus IMRT were: V50% (TMAT/IMRT) = 85.18% ± 9.67%, V80% (TMAT/IMRT) = 72.19% ± 7.39% and V100% (TMAT/IMRT) = 89.19% ± 6.91%, all p ≤ 0.01. For a first time the study demonstrated the planning and delivery implementation of a fully dynamic APBI TMAT with continuous couch motion. When applied to APBI in the prone breast setup, TMAT showed prominent dosimetric advantages over non-coplanar IMRT on dose volume parameters correlated to cosmetic outcome of APBI, and hence implicates the potential to reduce toxicity.