Optimal midcourse trajectory cluster generation and trajectory modification for hypersonic interceptions

The hypersonic interception in near space is a great challenge because of the target’s unpredictable trajectory, which demands the interceptors of trajectory cluster coverage of the predicted area and optimal trajectory modification capability aiming at the consistently updating predicted impact point(PIP) in the midcourse phase. A novel midcourse optimal trajectory cluster generation and trajectory modification algorithm is proposed based on the neighboring optimal control theory. Firstly, the midcourse trajectory optimization problem is introduced; the necessary conditions for the optimal control and the transversality constraints are given.Secondly, with the description of the neighboring optimal trajectory existence theory(NOTET), the neighboring optimal control(NOC)algorithm is derived by taking the second order partial derivations with the necessary conditions and transversality conditions. The revised terminal constraints are reversely integrated to the initial time and the perturbations of the co-states are further expressed with the states deviations and terminal constraints modifications.Thirdly, the simulations of two different scenarios are carried out and the results prove the effectiveness and optimality of the proposed method.

Effect of laser intensity on quantum trajectories in the macroscopic high-order harmonic generation

We macroscopically investigate the effect of the laser intensity and gas density on quantum trajectories in the highorder harmonic generation of Ne atoms irradiated by few-cycle, 800-nm laser pulses. The time–frequency profile of the harmonics shows that the long quantum trajectory is dominant at both lower and higher gas densities for a low laser intensity. At high laser intensities, the long quantum trajectory plays an important role for lower gas densities, while the short quantum trajectory is dominant at higher gas densities. An analysis of the phase mismatch for high-order harmonic generation shows that the primary emission of the quantum trajectories is determined by dynamic changes in the laser electric field during the propagation process.

High-order harmonic generation in a two-color strong laser field with Bohmian trajectory theory

We theoretically study the high-order harmonic generation （HHG） in a two-color laser field using the Bohmian mechanics. Our results show that, for tile case of a weak second-color laser field, the simulation of the HHG with only one central Bohmian trajectory is in a good agreement with the ab initio time-dependent Schrodinger equation （TDSE） results. In contrast, with the increase of the amplitude of the second-color laser field, the HHG spectra from the single central Bohmian trajectory deviate from the TDSE results more and more significantly. By analyzing the Bohmian trajectories, we find that the significant deviation is due to the fact that the central Bohmian trajectory leaves the core quickly in the two-color laser field with the breaking of inversion symmetry. Interestingly, we find that another Bohmian trajectory with different initial position, which keeps oscillating around the core, could qualitatively well reproduce the TDSE results. Furthermore, we study the HHG spectrum in a two-color laser field with inversion symmetry and find that the HHG spectrum in TDSE can be still well simulated with the central Bohmian trajectory. These results indicate that, similar to the case of one color laser field, the HHG spectra in a two-color laser field can be also reproduced with a single Bohmian trajectory, although the initial position of the trajectory is dependent on the symmetry of the laser field. Our work thus demonstrates that Bohmian trajectory theory can be used as a promising tool in investigating the HHG process in a two-color laser field.

TRAJECTORY GENERATION AND CONTROL FOR NON-CIRCULAR CNC TURNING

A trajectory generation method which is based on NURBS interpolation is studied to improve the fitting accuracy and smoothness of non-circular cross section and obtain higher accuracy of the final non-circular profile control. After using the NURBS, the most optimized and smooth trajectory for the linear actuator can be obtained. For the purpose of machining the non-circular cross section by CNC turning, the fast response linear actuator has been used. The control algorithm which is compound control of proportional-integral-differential （PID） and iterative learning control has been developed for non-circular profile generation. By using the NURBS interpolation and the compound control of PID and iterative learning control, the final motion accuracy of linear actuator has been improved, therefore, the machining accuracy of the non-circular turning can be improved.

On-line trajectory generation of midcourse cooperative guidance for multiple interceptors

The cooperative interception trajectories generation of multiple interceptors to hypersonic targets is studied.First,to solve the problem of on-line trajectory generation of the single interceptor,a generation method based on neighborhood optimal control is adopted.Then,when intercepting the strong maneuvering targets,the single interceptor is insufficient in maneuverability,therefore,an on-line multiple trajectories generation algorithm is proposed,which uses the multiple interceptors intercept area(IIA)to cover the target's predicted intercept area(PIA)cooperatively.Through optimizing the interceptors'zero control terminal location,the trajectories are generated on-line by using the neighborhood optimal control method,these trajectories could make the IIA maximally cover the PIA.The simulation results show that the proposed method can greatly improve the interception probability,which provides a reference for the collaborative interception of multiple interceptors.

Probing dynamic interference in high-order harmonic generation from long-range molecular ion:Bohmian trajectory investigation

Using Bohmlan trajectory （151） method, we investigate the dynamic interference in nlgn-orcter narmonlc generauon from diatomic molecular ions. It is demonstrated that the main characteristics of the molecular harmonic spectrum can be well reproduced by only two BTs which are located at the two ions. This haiapens because these two localized trajectories can receive and store the whole collision information coming from all of the other re-collision trajectories. Therefore, the amplitudes and frequencies of these two trajectories represent the intensity and frequency distribution of the harmonic generation. Moreover, the interference between these two trajectories shows a dip in the harmonic spectrum, which reveals the molecular structure information.

An automatic grid generation approach over free-form surface for architectural design

An essential step for the realization of free-form surface structures is to create an efficient structural gird that satisfies not only the architectural aesthetics,but also the structural performance.Employing the main stress trajectories as the representation of force flows on a free-form surface,an automatic grid generation approach is proposed for the architectural design.The algorithm automatically plots the main stress trajectories on a 3D free-form surface,and adopts a modified advancing front meshing technique to generate the structural grid.Based on the proposed algorithm,an automatic grid generator named "St-Surmesh" is developed for the practical architectural design of free-form surface structure.The surface geometry of one of the Sun Valleys in Expo Axis for the Expo Shanghai 2010 is selected as a numerical example for validating the proposed approach.Comparative studies are performed to demonstrate how different structural grids affect the design of a free-form surface structure.

Role of potential on high-order harmonic generation from atoms irradiated by bichromatic counter-rotating circularly polarized laser fields

We investigate high-order harmonic generation from atoms irradiated by bichromatic counter-rotating circularly polarized laser pulses by numerically solving the time-dependent Schrödinger equation.It is found that the minimum energy position of the harmonic spectrum and the non-integer order optical radiation are greatly discrepant for different atomic potentials.By analyzing the quantum trajectory of the harmonic emission,discrepancies among the harmonic spectra from different potentials can be attributed to the action of the potential on the ionized electrons.In addition,based on the influence of the driving light intensity on the overall intensity and ellipticity of higher order harmonics,the physical conditions for generating a high-intensity circularly polarized harmonic can be obtained.

Weightlifting Motion Generation for a Stance Robot with Repeatedly Direct Kinematics

This research focuses on how to control the robot easily and how to generate the better trajectories of the robot with multiple joints to implement weightlifting motion. The purpose of this research is to develop a multijoint robot can stand up successfully with an object. This research requires the operations with two items. First, when the object is lifted up slowly, the robot could stand up as easily as possible and does not tumble down. Second, the load applied on each joint should be as small as possible. In this article, a motion control method is proposed to evaluate the variations of the load torque and rotated angle of each joint with the geometrical constraints in the procedure and find the best algorithm to generate the trajectory of a weightlifting motion by a stance robot with repeatedly direct kinematics.

Bohmian trajectory perspective on strong field atomic processes

The interaction of an atom with an intense laser field provides an important approach to explore the ultrafast electron dynamics and extract the information of the atomic and molecular structures with unprecedented attosecond temporal and angstrom spatial resolution. To well understand the strong field atomic processes, numerous theoretical methods have been developed, including solving the time-dependent Schr ?dinger equation(TDSE), classical and semiclassical trajectory method, quantum S-matrix theory within the strong-field approximation, etc. Recently, an alternative and complementary quantum approach, called Bohmian trajectory theory, has been successfully used in the strong-field atomic physics and an exciting progress has been achieved in the study of strong-field phenomena. In this paper, we provide an overview of the Bohmian trajectory method and its perspective on two strong field atomic processes, i.e., atomic and molecular ionization and high-order harmonic generation, respectively.

Extension of high-order harmonic cutoff frequency by synthesizing the waveform of a laser field via the optimization of classical electron trajectory in the laser field

We theoretically investigate high-order harmonic generation by employing strong-field approximation （SFA） and present a new approach to the extension of the high-order harmonic cutoff frequency via an exploration of the dependence of high-order harmonic generation on the waveform of laser fields. The dependence is investigated via detailed analysis of the classical trajectories of the ionized electron moving in the continuum in the velocity-position plane. The classical trajectory consists of three sections （Acceleration Away, Deceleration Away, and Acceleration Back）, and their relationship with the electron recollision energy is investigated. The analysis of classical trajectories indicates that, besides the final （Acceleration Back） section, the electron recollision energy also relies on the previous two sections. We simultaneously optimize the waveform in all three sections to increase the electron recollision energy, and an extension of the cutoff frequency up to Ip ＋ 20.26Up is presented with a theoretically synthesized waveform of the laser field.

Bio-inspired Collision-free 4D Trajectory Generation for UAVs Using Tau Strategy

Inspired by the general tau theory in animal motion planning, a collision-free four-dimensional （4D） trajectory generation method is presented for multiple Unmanned Aerial Vehicles （UAVs）. This method can generate a group of optimal or near-optimal collision-free 4D trajectories, the position and velocity of which are synchronously planned in accordance with the arrival time. To enlarge the shape adjustment capability of trajectories with zero initial acceleration, a new strategy named intrinsic tau harmonic guidance strategy is proposed on the basis of general tau theory and harmonic motion. In the case of multiple UAVs, the 4D trajectories generated by the new strategy are optimized by the bionic Particle Swarm Optimization （PSO） algorithm. In order to ensure flight safety, the protected airspace zone is used for collision detection, and two collision resolution approaches are applied to resolve the remaining conflicts after global trajectory optimization. Numerous simulation results of the simultaneous arrival missions demonstrate that the proposed method can effectively provide more flyable and safer 4D trajectories than that of the existing methods.

Trajectory generation of heat load test based on gauss pseudospectral method

A new trajectory generation for heat load test is proposed based on gauss pseudospectral method within limit range. Firstly,with multiple path constraints and flight task requirements taken into consideration, heat load parameters are introduced into the dynamics equations. In order to solve the problem of generating such a trajectory within limit range rapidly, the dynamics equations have been normalized by Earth related parameters. Secondly, since the gauss pseudospectral method is just employed to solve the discrete nonlinear programming problem, transformations are developed, which can relate the Lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem. In addtion, another approach of trajectory generation by tracking the given heat rate is also presented. Finally, simulation results with common aero vehicle(CAV-H) show that the trajectories obtained by both methods can well perform the heat load test with high stagnation heating rate and the large total aeroheating amount; meanwhile, gauss pseudospectral method is better than the compared one in the given range. Furthermore, the 3-D trajectory states and control variables, angle of attack and bank, which are generated by gauss pseudospectral method, can change smoothly.

Bioinspired 4D Trajectory Generation for a UAS Rapid Point-to-Point Movement

A bioinspired trajectory generation approach for Unmanned Aerial System （UAS） rapid Point-to-Point （PTP） movement was presented. The approach was based on general tau theory developed by biologists from observing and studying the behavior of birds and some other animals. We applied the bioinspired approach to the rapid PTP movement problem of a rotary UAS and derived two different trajectory planning strategies, namely, the tau coupling strategy and the intrinsic tau gravity guidance strategy. Based on general tau theory, according to the dynamic model of UAS, we presented a new strategy named intrinsic tau jerk guidance which can fit the movement that the initial acceleration of the UAS is zero. With new strategies, flight trajectory generation examples with a UAS were presented. The kinematics and dynamics analyses of the UAS for rapid PTP movement were presented with simulation results which show that the generated trajectories were feasible.

Axis-coupled trajectory generation for chains of integrators through smoothing splines

Integrator based model is used to describe a wide range of systems in robotics. In this paper, we present an axis-coupled trajectory generation algorithm for chains of integrators with an arbitrary order. Special notice has been given to problems with pre-existing nominal plans, which are common in robotic applications. It also handles various type of constraints that can be satisfied on an entire time interval, including non-convex ones which can be transformed into a series of convex constraints through time segmentation. The proposed approach results in a linearly constrained quadratic programming problem, which can be solved effectively with off-the-shelf solvers. A closed-form solution is achievable with only the boundary constraints considered. Finally, the proposed method is tested in real experiments using quadrotors which represent high-order integrator systems.

Reference Trajectory Generation for 3-Dimensional Walking of a Humanoid Robot

Humanoid walking planning is a complicated task because of the high number of degrees of freedom （DOFs） and the variable mechanical structure during walking. In this paper, a planning method for 3- dimensional （3-D） walking movements was developed based on a model of a typical humanoid robot with 12 DOFs on the lower body. The planning process includes trajectory generation for the hip, ankle, and knee joints in the Cartesian space. The balance of the robot was ensured by adjusting the hip motion. The angles for each DOF were obtained from 3-D kinematics calculation. The calculation gave reference trajectories of all the DOFs on the humanoid robot which were used to control the real robot. The simulation results show that the method is effective.

Integrated Entry Guidance for Reusable Launch Vehicle

A method for the implementation of integrated three-degree-of-freedom constrained entry guidance for reusable launch vehicle is presented. Given any feasible entry conditions, terminal area energy management interface conditions, and the reference trajectory generated onboard then, the method can generate a longitudinal guidance profile rapidly, featuring linear quadratic regular method and a proportional-integral-derivative tracking law with time-varying gains, which satisfies all the entry corridor constraints and meets the requirements with high precision. Afterwards, by utilizing special features of crossrange parameter, establishing bank-reversal corridor, and determining bank-reversals according to dynamically adjusted method, the algorithm enables the lateral entry guidance system to fly a wide range of missions and provides reliable and good performance in the presence of significant aerodynamic modeling uncertainty. Fast trajectory guidance profiles and simulations with a reusable launch vehicle model for various missions and aerodynamic uncertainties are presented to demonstrate the capacity and reliability of this method.

Obstacle Avoidance Method for a Redundant Manipulator Based on a Configuration Plane

This paper presents a novel approach of obstacle avoidance for redundant manipulators, which is challenging with the considerations of the building of universal kinematics, the formation of dynamics, and the generation of trajectories. A universal approach to deal with obstacle avoidance for the redundant manipulator, that is based on the configuration plane, is presented. The paper also examines common serial robot configurations and introduces a method for classification, partitioning, simplification, and forms of expression used in the workspace to define the configuration plane. This relatively new method is combined with a weighted space vector method to match the configuration plane and solve the inverse kinematics problem. The proposed planner is demonstrated with examples, in which the proposed planner is shown to be capable of providing a smoother trajectory.

Possible source and migration pathway for early-summer immigrants of the oriental armyworm, Mythimna separata, arriving in northern Japan

The first generation of the oriental armyworm, Mythimna separata(Walker), arrives every year in northern Japan in mainly late May to early June. Analyses of weather maps suggested that this moth’s immigration source could be eastern China, but the accuracy of those analyses was very limited due to the lack of a current standard trajectory analysis. The management of migratory insect pests such as M. separata benefits from the identification of the migration source(s)and pathway(s) of the pests. The present study provides a trajectory analysis for M. separata. Backward trajectories from trap sites in northern Japan were calculated with the HYSPLIT System developed by the U.S. National Oceanic and Atmospheric Administration, taking the flight speed of M. separata and the limitation of low ambient temperature at flight height into account. The ending times of the moth’s short and long trajectories were set at dusk on the day before and two days before the possible arrival date, respectively. The results suggested two types of possible migration pathway: a multi-step pathway from Northeast China, the Korean Peninsula, and eastern Russia, which are destination areas of the first-generation’s migration, and a direct pathway from seasonal main emigration areas in eastern China such as Jiangsu and Shandong provinces. These findings contribute to our understanding of the migration ecology of M. separata and can be used for the development of methods to predict the migration of this insect.

Adaptive Walking Control of Biped Robots Using Online Trajectory Genera- tion Method Based on Neural Oscillators

This work concerns biped adaptive walking control on irregular terrains with online trajectory generation. A new trajectory generation method is proposed based on two neural networks. One oscillatory network is designed to generate foot trajectory, and another set of neural oscillators can generate the trajectory of Center of Mass （CoM） online. Using a motion engine, the characteristics of the workspace are mapped to the joint space. The entraining property of the neural oscillators is exploited for adaptive walking in the absence of a priori knowledge of walking conditions. Sensory feedback is applied to modify the gen- erated trajectories online to improve the walking quality. Furthermore, a staged evolutionary algorithm is developed to tune system parameters to improve walking performance. The developed control strategy is tested using a humanoid robot on ir- regular terrains. The experiments verify the success of the presented strategy. The biped robot can walk on irregular terrains with varying slopes, unknown bumps and stairs through autonomous adjustment of its walking patterns.