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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Trajectory Design of Launch Vehicle with the Argument of Perigee Constraint for Highly Eccentric Orbit Mission

For the final stage of a launch vehicle which cannot start multiple times,the main constraint of a highly eccentric orbit launch mission is the argument of perigee,which is conditioned by the range.This paper studies the payload capacity at different launch sites for a highly eccentric orbit(e.g.GTO)and gives a method to improve the payload capacity with an argument of perigee constraint by increasing the sliding time before the final ignition and simultaneously adjusting the launch azimuth and yaw at the final stage.An example of launching to GTO orbit on a rocket from Hainan is given,which proves that the method has strong engineering value.

Trajectory design for the Moon departure libration point mission in full ephemeris model

The lunar probe may still have some remaining fuel after completing its predefined Moon exploration mission and is able to carry out some additional scientific or technological tasks after escaping from the Moon orbit.The Moon departure mission for the lunar probe is the focus of this paper.The possibility of the spacecraft orbiting the Moon to escape the Moon's gravitational pull is analyzed.The trajectory design for the Earth-Moon system libration point mission is studied in a full ephemeris dynamical model,which considers the non-uniform motion of the Moon around the Earth,the gravity of the Sun and planets and the finite thrust of the onboard engine.By applying the Particle Swarm Optimization algorithm,the trajectory design for the transfer from the Moon-centered orbit to the L1 halo orbit,the station-keeping strategies for the Earth-Moon halo orbit and the construction of homoclinic and heteroclinic orbits are investigated.Taking the tracking conditions and engineering constraints into account,two feasible schemes for the Moon departure libration point mission for the lunar probe are presented.

Trajectory design for a solar-sail mission to asteroid 2016 HO_(3)

This paper proposes the use of solar-sail technology currently under development at NASA Langley Research Center for a CubeSat rendezvous mission with asteroid 2016 HO_(3),a quasi-satellite of Earth.Time-optimal trajectories are sought for within a 2022–202_(3) launch window,starting from an assumed launcher ejection condition in the Earth-Moon system.The optimal control problem is solved through a particular implementation of a direct pseudo-spectral method for which initial guesses are generated through a relatively simple and straightforward genetic algorithm search on the optimal launch date and sail attitude.The results show that the trajectories take 2.16–4.21 years to complete,depending on the assumed solar-sail reflectance model and solar-sail technology.To assess the performance of solar-sail propulsion for this mission,the trajectory is also designed assuming the use of solar electric propulsion.The resulting fuel-optimal trajectories take longer to complete than the solar-sail trajectories and require a propellant consumption that exceeds the expected propellant capacity onboard the CubeSat.This comparison demonstrates the superior performance of solar-sail technology for this mission.

Leveraging quasi-periodic orbits for trajectory design in cislunar space

Incorporating quasi-periodic orbits into the preliminary design process offers a wide range of options to meet mission constraints and address the challenges in a complex trade space.In this investigation,linear stability and quasi-periodic orbit family continuation schemes are examined to meet various types of constraints.Applications in eclipse avoidance and transfer design are examined by leveraging quasi-periodic orbits and their associated hyperbolic manifolds in the lunar region.Solutions are transitioned to an ephemeris model to validate that geometries are maintained in higher-fidelity models.When the natural dynamical structures associated with quasi-periodic orbits are leveraged,novel trajectory solutions can emerge.

Optimized Trajectory Design in UAV Based Cellular Networks for 3D Users: A Double Q-Learning Approach

In this paper,the problem of trajectory de-sign of unmanned aerial vehicles(UAVs)for maximizing the number of satisfied users is studied in a UAV based cellular network where the UAV works as a flying base station that serves users,and the user indicates its satis-faction in terms of completion of its data request within an allowable maximum waiting time.The trajectory design is formulated as an optimization problem whose goal is to maximize the number of satisfied users.To solve this problem,a machine learning framework based on double Q-learning algorithm is proposed.The algorithm enables the UAV tofind the optimal trajectory that maximizes the number of satisfied users.Compared to the traditional learning algorithms,such as Q-learning that selects and evaluates the action using the same Q-table,the proposed algorithm can decouple the selection from the evaluation,therefore avoid overestimation which leads to sub-optimal policies.Simulation results show that the proposed algorithm can achieve up to 19.4% and 14.1% gains in terms of the number of satisfied users compared to random algorithm and Q-learning algorithm.

Joint 3D Trajectory and Resource Optimization for A UAV Relay-Assisted Cognitive Radio Network

In this paper,we consider a new spectrum sharing scenario for a cognitive relay network,where a secondary unmanned aerial vehicle(UAV)relay receives information from the ground secondary base station(SBS)and transmits information to the ground secondary user(SU),coexisting with the primary users(PUs)at the same wireless frequency band.We investigate the optimization of the UAV relay’s three-dimensional(3D)trajectory to improve the communication throughput performance of the secondary network subject to the interference constraints of the PUs.The information throughput maximization problem is studied by jointly optimizing the UAV relay’s 3D trajectory and the transmit power of the SBS and the UAV,subject to the constraints on the velocity and elevation of the UAV relay,the maximum and average transmit power,and the information causality,as well as a set of interference temperature(IT)constraints.An efficient algorithm is proposed to solve the admittedly challenging non-convex problem by using the path discretization technique,the successive convex approximation technique and the alternating optimization method.Finally,simulation results are provided to show that our proposed design outperforms other benchmark schemes in terms of the throughput。

Joint Trajectory and Power Optimization for Securing UAV Communications Against Active Eavesdropping

Due to both of jamming and eavesdropping,active eavesdroppers can induce more serious security threats to unmanned aerial vehicle(UAV)-enabled communications.This paper considers a secure UAV communication system including both the downlink(DL)and uplink(UL)transmissions,where the confidential information is transmitted between a UAV and a ground node in the presence of an active eavesdropper.We aim to maximize the average secrecy rates of the DL and UL communications,respectively,by jointly optimizing the UAV trajectory and the UAV/ground node’s transmit power control over a given flight period.Due to the non-convexity of the formulated problems,it is difficult to obtain globally optimal solutions.However,we propose efficient iterative algorithms to obtain high-quality suboptimal solutions by applying the block coordinate descent and successive convex optimization methods.Simulation results show that the joint optimization algorithms can effectively improve the secrecy rate performance for both the DL and UL communications,as compared with other baseline schemes.The proposed schemes can be considered as special cases of UAV-assisted non-orthogonal multiple access(NOMA)networks.

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.

Multi-objective reentry trajectory optimization method via GVD for hypersonic vehicles

In the constrained reentry trajectory design of hypersonic vehicles, multiple objectives with priorities bring about more difficulties to find the optimal solution. Therefore, a multi-objective reentry trajectory optimization (MORTO) approach via generalized varying domain (GVD) is proposed. Using the direct collocation approach, the trajectory optimization problem involving multiple objectives is discretized into a nonlinear multi-objective programming with priorities. In terms of fuzzy sets, the objectives are fuzzified into three types of fuzzy goals, and their constant tolerances are substituted by the varying domains. According to the principle that the objective with higher priority has higher satisfactory degree, the priority requirement is modeled as the order constraints of the varying domains. The corresponding two-side, single-side, and hybrid-side varying domain models are formulated for three fuzzy relations respectively. By regulating the parameter, the optimal reentry trajectory satisfying priorities can be achieved. Moreover, the performance about the parameter is analyzed, and the algorithm to find its specific value for maximum priority difference is proposed. The simulations demonstrate the effectiveness of the proposed method for hypersonic vehicles, and the comparisons with the traditional methods and sensitivity analysis are presented.