Trajectory Design and Flight Result of Gravity-1 Launch Vehicle

Gravity-1(YL-1) launch vehicle completed its maiden flight from the Yellow Sea near Haiyang City, Shandong Province, on January 11, 2024, this mission successfully launched three Yunyao satellites into their 500 km orbit. The YL-1 has a performance of 4.2 tons for 500 km sun-synchronous orbit and 6.5 tons for low Earth orbit. The success of YL-1 has further enriched China's launch vehicle spectrum, and will facilitate the launch of medium and large satellites and satellite constellations. In this paper, the flight ballistic solution of YL-1 is introduced. The flight trajectory consists of seven flight segments. The trajectory design comprehensively considered the characteristics and safety requirements of the vehicle to achieve effective utilization of the performance. Through comparative analysis of the flight trajectory and the predicted trajectory, the result confirmed that the flight trajectory was consistent with the design results, the design methodology was correct, and the flight test met the expected requirements. Subsequently, the vehicle will be employed for commercial application launch services.

Inverse Kinematics Analysis of a 7-DOF Space Manipulator for Trajectory Design

To solve the inverse kinematics problem for redundant degrees of freedom（DOFs）manipulators has been and still continues to be quite challenging in the field of robotics.Aiming at trajectory planning for a 7-DOF space manipulator system,joint rotation trajectories are obtained from predetermined motion trajectories and poses of the end effector in Cartesian space based on the proposed generalized inverse kinematics method.A minimum norm method is employed to choose the best trajectory among available trajectories.Numerical simulations with the7-DOF manipulator show that the proposed method can achieve the planned trajectory and pose under the circumstances of minimum angular velocities.Moreover,trajectory results from the proposed kinematics model and inverse kinematics method has the advantages of simple modelling,low computation cost,easy to solve and plan trajectory conveniently.The smooth and continuous joint rotation functions obtained from the proposed method are suitable for practical engineering applications.

Optimal design of near-Earth asteroid sample-return trajectories in the Sun–Earth–Moon system

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-kin-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.

Mobile Jammer-Aided Secure UAV Communications via Trajectory Design and Power Control

To further promote the achievable average secrecy rate for UAV-ground communications, a UAV-aided mobile jamming strategy was proposed in this paper. Specifically, an additional cooperative UAV is employed as a mobile jammer to transmit the jamming signal to help keep the source UAV closer to the ground destination, thus establishing more favorable legitimate link and enhancing the secrecy performance. We aimed to maximize the achievable secrecy rate by jointly optimizing the trajectories and transmit power of both source UAV and jammer UAV. To solve the considered non-convex optimization problem, we presented a block coordinate descent based iterative algorithm to address a sequence of approximated convex problems for the optimized parameter block by block to find a local optimal solution. Numerical results verify that the proposed algorithm can achieve significant secrecy rate gain compared to all the benchmark schemes.

Energy-Efficient UAV Trajectory Design for Backscatter Communication: A Deep Reinforcement Learning Approach

Recently,backscatter communication(BC)has been introduced as a green paradigm for Internet of Things(IoT).Meanwhile,unmanned aerial vehicles(UAVs)can serve as aerial base stations(BSs)to enhance the performance of BC system thanks to their high mobility and flexibility.In this paper,we investigate the problem of energy efficiency(EE)for an energy-limited backscatter communication(BC)network,where backscatter devices(BDs)on the ground harvest energy from the wireless signal of a flying rotary-wing quadrotor.Specifically,we first reformulate the EE optimization problem as a Markov decision process(MDP)and then propose a deep reinforcement learning(DRL)algorithm to design the UAV trajectory with the constraints of the BD scheduling,the power reflection coefficients,the transmission power,and the fairness among BDs.Simulation results show the proposed DRL algorithm achieves close-to-optimal performance and significant EE gains compared to the benchmark schemes.

Robust Trajectory and Communication Design for Angle-Constrained Multi-UAV Communications in the Presence of Jammers

This paper studies a multi-unmanned aerial vehicle(UAV)enabled wireless communication system,where multiple UAVs are employed to communicate with a group of ground terminals(GTs)in the presence of potential jammers.We aim to maximize the throughput overall GTs by jointly optimizing the UAVs’trajectory,the GTs’scheduling and power allocation.Unlike most prior studies,we consider the UAVs’turning and climbing angle constraints,the UAVs’three-dimensional(3D)trajectory constraints,minimum UAV-to-UAV(U2U)distance constraint,and the GTs’transmit power requirements.However,the formulated problem is a mixed-integer non-convex problem and is intractable to work it out with conventional optimization methods.To tackle this difficulty,we propose an efficient robust iterative algorithm to decompose the original problem be three sub-problems and acquire the suboptimal solution via utilizing the block coordinate descent(BCD)method,successive convex approximation(SCA)technique,and S-procedure.Extensive simulation results show that our proposed robust iterative algorithm offers a substantial gain in the system performance compared with the benchmark algorithms.

Trajectory design and simulation in injection phase for hyper-velocity kinetic energy missile

A movement law of laser beam facula is designed for the injection trajectory of hyper-ve- locity kinetic energy missile to eliminate the influence of motor exhaust smoke on laser signal trans mission. Taking guidance loop of hyper velocity kinetic energy missile as plant, a closed loop control system with desired step response characteristics is constructed and the movement law of laser beam facula for the missile injection trajectory is designed based on the output signal of the closed loop controller under a step input. Six degree of freedom trajectory simulations show that by the guidance of the laser beam facula moving with designed law, the missile can finish transition from the initial trajectory to a stable tracking trajectory without overshoot within the required time.

Ivar asteroid rendezvous mission system scenario and trajectory design

The asteroid exploration opportunities are searched and calculated with launch dates in 2006 to2010, and with asteroid Ivar 1627 as the target, the spacecraft and its subsystems are designed and analyzed,and the transfer trajectory is designed using △VEGA technology for the asteroid rendezvous. The design resultssatisfied the energy requirements for small explorers.

Design of MGA trajectories for main belt asteroid

Asteroid exploration is one of the most sophisticated missions currently being investigated. Gravity-assist trajectories have proven valuable in interplanetary missions such as the Pioneer, Voyager and Galileo. In this paper, we design interplanetary trajectory for main belt asteroid exploration mission with the Mars gravity-assist (MGA) using “pork chop” plots and patched-conic theory and give some initial valuable trajectory parameters on main belt asteroid exploration mission with MGA.

Design and optimization in multiphase homing trajectory of parafoil system

In order to realize safe and accurate homing of parafoil system,a multiphase homing trajectory planning scheme is proposed according to the maneuverability and basic flight characteristics of the vehicle.In this scenario,on the basis of geometric relationship of each phase trajectory,the problem of trajectory planning is transformed to parameter optimizing,and then auxiliary population-based quantum differential evolution algorithm(AP-QDEA)is applied as a tool to optimize the objective function,and the design parameters of the whole homing trajectory are obtained.The proposed AP-QDEA combines the strengths of differential evolution algorithm(DEA)and quantum evolution algorithm(QEA),and the notion of auxiliary population is introduced into the proposed algorithm to improve the searching precision and speed.The simulation results show that the proposed AP-QDEA is proven its superior in both effectiveness and efficiency by solving a set of benchmark problems,and the multiphase homing scheme can fulfill the requirement of fixed-points and upwind landing in the process of homing which is simple in control and facile in practice as well.

Multi-Agent Few-Shot Meta Reinforcement Learning for Trajectory Design and Channel Selection in UAV-Assisted Networks

Unmanned aerial vehicle(UAV)-assisted communications have been considered as a solution of aerial networking in future wireless networks due to its low-cost, high-mobility, and swift features. This paper considers a UAV-assisted downlink transmission,where UAVs are deployed as aerial base stations to serve ground users. To maximize the average transmission rate among the ground users, this paper formulates a joint optimization problem of UAV trajectory design and channel selection, which is NP-hard and non-convex. To solve the problem, we propose a multi-agent deep Q-network(MADQN) scheme.Specifically, the agents that the UAVs act as perform actions from their observations distributively and share the same reward. To tackle the tasks where the experience is insufficient, we propose a multi-agent meta reinforcement learning algorithm to fast adapt to the new tasks. By pretraining the tasks with similar distribution, the learning model can acquire general knowledge. Simulation results have indicated the MADQN scheme can achieve higher throughput than fixed allocation. Furthermore, our proposed multiagent meta reinforcement learning algorithm learns the new tasks much faster compared with the MADQN scheme.

REVERSE DESIGN APPROACH FOR MECHANISM TRAJECTORY BASED ON CODE-CHAINS MATCHING

Aiming at the problem of reverse-design of mechanism, a method based on the matching of trajectory code-chains is presented. The motion trajectory of mechanism is described with code-chain, which is normalized to simplify the operation of geometric transformation. The geometric transforma-tion formulas of scale, mirror and rotation for trajectory code-chain are defined, and the reverse de-sign for mechanism trajectory is realized through the analysis and solution of similarity matching between the desired trajectory and the predefined trajectory. The algorithm program and prototype system of reverse design for mechanism trajectory are developed. Application samples show that the method can break the restriction of trajectory patterns in matching, meet the demand of partial match-ing, and overcome the influence of geometric transformation of trajectory on the reverse design for mechanism.

Modified shape-based method for three-dimensional trajectory design

Although the shape-based method has been proven to be useful for low-thrust trajectory design,and be capable to provide near-optimal solution for a more accurate trajectory optimization method,it is slightly non-effective when used in some 3D cases.In this paper,a modified 3D shape-based method is proposed for earth trajectory design.In this approach,in consideration of the sinusoidal periodic variation in z direction of actual trajectory,a new exponential sinusoid model is chosen for the out-of-plane motion,with four coefficients such that four scalar out-of-plane boundary conditions can be satisfied.After deriving the 3D shape-based procedure,low-thrust trajectory design example with modest inclination change is given.The results demonstrate that this modified approach is feasible for the transfer trajectory design,and comparing to the former shape-based method,the z direction solution is more coincident with the actual situation,furthermore,the solution may be used for further mission planning,trajectory evaluation and optimization.

Departure Trajectory Design Based on Pareto Ant Colony Algorithm

Due to the ever-increasing air traffic flow,the influence of aircraft noise around the airport has become significant.As most airlines are trying to decrease operation cost,stringent requirements for more simple and efficient departure trajectory are on a rise.Therefore,a departure trajectory design was established for performancebased navigation technology,and a multi-objective optimization model was developed,with constraints of safety and noise influence,as well as optimization targets of efficiency and simplicity.An improved ant colony algorithm was then proposed to solve the optimization problem.Finally,an experiment was conducted using the Lanzhou terminal airspace operation data,and the results showed that the designed departure trajectory was feasible and efficient in decreasing the aircraft noise influence.

Short Range Top Attack Trajectory Optimum Design Based on Genetic Algorithm

A flying-body is considered as the reference model, the optimized mathematical model is established. The genetic operators are designed and algorithm parameters are selected reasonably. The scheme control signal in short range top attack flight trajectory is optimized by using genetic algorithm. The short range top attack trajectory designed meets the design requirements, with the increase of the falling angle and the decrease of the minimum range. The application of genetic algorithm to top attack trajectory optimization is proved to be feasibly and effectively according to the analyses of results.

Method of suspender line trajectory design

Based on the mechanical model of an elastic rod,a new trajectory design method was established.The advantages of the suspender line trajectory in reducing drag and torsion were compared,and the main controlling factors of drag and torque and their influence rules were analyzed.Research shows that the suspender line trajectory reduces drag and torque more effectively than the conventional trajectory in a certain parameter interval and has more controllable parameters than that of the catenary trajectory.The main factors affecting the drag reduction and torque reduction of the suspender line trajectory include the friction coefficient,vertical distance,horizontal distance,and deviation angle at the initial point in the suspended section.The larger the friction coefficient and deviation angle,the less the drag reduction and torque reduction.The suspender line trajectory has the best drag reduction effect when the horizontal and vertical distances are more than 3000 m and the ratio is close to 1.5.The drag in sliding drilling can be reduced up to 60%,and the torque in rotary drilling can be reduced by a maximum of 40%.Therefore,the trajectory design of the suspender line has unique application prospects in deep extended-reach wells.

Research on and Design of Mechanical System with Optimal Cutting Movement Trajectory of Energy-Saving Stone-Sawing Machine

The technique of cutting slabstone with stone-sawi ng machine is analyzed completely. A new kind of cutting movement trajectory is gi ven whose actual cutting efficiency is near to 100%. It can reduce the energy w earing greatly, and the surface quality of the product is improved to the utmost extent. The design mechanism of the optimal cutting movement trajectory system structure is analyzed incisively. At the same time, the principle of the complex movement of horizontal movement and swing is researched. The optimal design scheme of th e cutting movement trajectory system structure is set up. The choice method to g et the superior value of the movement system structure is found. The mathematics function formula is established which exhibits the relationship between the par ameter of the complex movement structure and that of the system movement structu re. By the formula, the precision value of the offset can be figured out. The r ule is adapted to different types of energy-saving stone-sawing machines. The complex movement structure of horizontal movement and swing is designed to f ulfill the cutting movement. It can make the saw frame move up with the hanging pod deviating from the vertical direction. At the same time, the saw frame have a down-movement. Then the sum of the two movements is near to zero, and the saw blade and the stone can keep in touch during the whole horizontal cutting. The result is that the actual cutting efficiency is 100%. Also, when the hanging pod moves to the limited position, the saw frame can keep the original inertia, and continue to swing up. It makes the back-cutting have high energy-storing. The optimal design of the eccentricity balance wheel is done. The mathematics fo rmula for expressing the movement system structure is deduced. The calculation m ethod and formula is set up which is used to get the value of important componen ts such as offset. The choice method and formula of elasticity distortion coeffi cient is set up when the saw frame moves smoothly. It is concluded that the offs et is the key dimension to actualize the optimal cutting movement trajectory. The resolving of the technical problems discussed above offers a theoretic and technical basis for optimal design of energy-saving stone-sawing machines.

Trajectory Design for UAV-Enabled Maritime Secure Communications:A Reinforcement Learning Approach

This paper investigates an unmanned aerial vehicle(UAV)-enabled maritime secure communication network,where the UAV aims to provide the communication service to a legitimate mobile vessel in the presence of multiple eavesdroppers.In this maritime communication networks(MCNs),it is challenging for the UAV to determine its trajectory on the ocean,since it cannot land or replenish energy on the sea surface,the trajectory should be pre-designed before the UAV takes off.Furthermore,the take-off location of the UAV and the sea lane of the vessel may be random,which leads to a highly dynamic environment.To address these issues,we propose two reinforcement learning schemes,Q-learning and deep deterministic policy gradient(DDPG)algorithms,to solve the discrete and continuous UAV trajectory design problem,respectively.Simulation results are provided to validate the effectiveness and superior performance of the proposed reinforcement learning schemes versus the existing schemes in the literature.Additionally,the proposed DDPG algorithm converges faster and achieves higher utilities for the UAV,compared to the Q-learning algorithm.

Trajectory Design and Optimization for LEO Satellites in Formation to Observe GEO Satellites’ Beams

This paper presents the methods and results for the trajectory design and optimization for the low earth orbit (LEO) satellites in formation to observe the geostationary orbit (GEO) satellites’ beams. The background of the trajectory design mission is the 9th China Trajectory Optimization Competition (CTOC9). The formation is designed according to the observation demands. The flying sequence is determined by a reference satellite using a proposed improved ephemeris matching method (IEMM). The formation is changed, maintained and transferred following the reference satellite employing a multi-impulse control method (MICM). Then the total observation value is computed by propagating the orbits of the satellites according to the sequence and transfer strategies. Based on the above methods, we have obtained a fourth prize in the CTOC9. The proposed methods are not only fit for this competition, but can also be used to fulfill the trajectory design missions for similar multi-object explorations.

Torpedo's Search Trajectory Design Based on Acquisition and Hit Probability Calculation

Taking aim at light torpedo search trajectory characteristic of warship, by analyzing common used torpedo search trajectory, a better torpedo search trajectory is designed, a mathematic model is built up, and the simulation calculation taking MK46 torpedo for example is carried out. The calculation results testify that this method can increase acquisition probability and hit probability by about 10%-30% at some situations and becomes feasible for the torpedo trajectory design. The research is of great reference value for the acoustic homing torpedo trajectory design and the torpedo combat efficiency research.