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The combination of unmanned aerial vehicles (UAVs) and mobile edge computing (MEC) is considered as a promising approach to tackle soaring computing requirements. The broadcast nature of air‐to‐ground (A2G) links makes UAV communications vulnerable to eavesdroppers, so secure UAV communications remain an open question. This paper proposes a secure communication scheme for reconfigurable intelligent surface (RIS)‐assisted UAV‐MEC systems, in which the RIS assists the user in offloading data to the legitimate UAV, and the legitimate UAV provides computing services to the user. To fully expand the security computing capacity of the system, the communication link is improved by introducing RIS, and the jammer interferes with the eavesdropper. The secure computing capability of the system is maximized by optimizing communication resources and trajectories. Since the proposed problem is non‐convex, successive convex approximation (SCA) technique and block coordinate descent (BCD) technique is combined to solve the problem. The simulation results show that the proposed scheme in this paper can effectively improve the system secure computing bits compared with the benchmark scheme. [ABSTRACT FROM AUTHOR]

Due to their flexible deployment and movement capability, unmanned aerial vehicles (UAVs) are being utilized as flying mobile edge computing (MEC) platforms, offering real-time computational resources and low-latency data processing for a wide range of applications. This article aims to explore a UAV-assisted MEC system where multiple UAVs provide MEC services to mobile devices (MDs) using an ellipsoidal trajectory. Depending on the position, size, and orientation of the ellipsoidal trajectories, the coverage area of the UAV, the energy consumption, and the task transmission latency of MDs change. This has rarely been investigated in the existing works. Furthermore, unlike other studies, we consider that each MD has varying task offloading rates, which, together with varying user densities, makes the problem more challenging. Therefore, we formulate an optimization problem that finds the center position, major radius, minor radius, and rotation angle of the ellipsoidal trajectory of UAV-assisted MEC servers, to minimize the total transmission latency and energy consumption of mobile devices while taking into account the required data transmission rate, task transmission time, and energy consumption constraints. Then, we transform this optimization problem into a Markov decision process and propose a deep Q-learning-based ellipsoidal trajectory optimization (DETO) algorithm, to resolve it. The results from our simulations demonstrate that DETO efficiently computes the optimal position and trajectory for each UAV, and can achieve better performance compared to other baselines, leading to the reduced data transmission latency and energy consumption of mobile devices across a range of simulation scenarios. [ABSTRACT FROM AUTHOR]

In general, optimal motion planning can be performed both locally and globally. In such a planning, the choice in favor of either local or global planning technique mainly depends on whether the environmental conditions are dynamic or static. Hence, the most adequate choice is to use local planning or local planning alongside global planning. When designing optimal motion planning, both local and global, the key metrics to bear in mind are execution time, asymptotic optimality, and quick reaction to dynamic obstacles. Such planning approaches can address the aforementioned target metrics more efficiently compared to other approaches, such as path planning followed by smoothing. Thus, the foremost objective of this study is to analyze related literature in order to understand how the motion planning problem, especially the trajectory planning problem, is formulated when being applied for generating optimal trajectories in real-time for multirotor aerial vehicles, as well as how it impacts the listed metrics. As a result of this research, the trajectory planning problem was broken down into a set of subproblems, and the lists of methods for addressing each of the problems were identified and described in detail. Subsequently, the most prominent results from 2010 to 2022 were summarized and presented in the form of a timeline. [ABSTRACT FROM AUTHOR]

In space mission design, an important operational constraint is planned periodic coast arcs during which various mission-critical tasks such as navigation or ground communications are performed. These constraints, typically implemented as thruster duty cycles, can be characterized as discrete coast arcs enforced periodically during intervals of deterministic thrusting. A typical approach to incorporate duty cycles is by enforcing maximum thrust levels that are less than a nominal value. This work presents an embedded homotopy indirect optimization method for a smooth enforcement of discrete duty-cycle constraints for low-thrust trajectory optimization. The complexity of enforcing such discrete constraints is two-fold: (1) a precise event-detection strategy is needed to determine the beginning of deterministic thrust arcs, which must be successively updated along the trajectory and (2) a smooth modeling of the discrete coast events occurring on the order of 10s or even 100s depending on the duration of deterministic thrust arcs. Duty cycle constraints are enforced at the level of the Hamiltonian using a Composite Smooth Control (CSC) method, producing high-resolution optimal control solutions conscious of planned duty cycle coast arcs. Numerical solutions are presented for the heliocentric transfer phases of three space missions. The results are then validated against the Evolutionary Mission Trajectory Generator (EMTG), one of NASA's global trajectory optimization tools used for interplanetary mission design and capable of the explicit enforcement of periodic duty cycle coasting. The proposed indirect method is suitable for obtaining high-resolution trajectory solutions with realistically enforced thruster duty cycle, which could then be used as high-quality initial guesses in flight-fidelity mission planning tools. The proposed smooth modeling of discrete coast arcs can also be customized to enforce periodic and non-periodic thrust shutdown constraints. • Duty-cycle aware, multi-revolution, low-thrust, minimum-fuel trajectories. • A novel smooth switching function for embedding forced coast arcs. • Composite Smooth Control (CSC) is used to embed the discrete duty-cycle constraints. • Comparison with NASA's Evolutionary Mission Trajectory Generator (EMTG). • Julia programming language is used for solution of the boundary-value problems. [ABSTRACT FROM AUTHOR]

This paper investigates the trajectory design for landing on a small celestial body with a flexible lander. The flexible lander features a flexible structure that increases surface contact area and facilitates the dissipation of residual kinetic energy. Compared with rigid landing, flexible landing, which utilizes a flexible lander to execute the landing process, offers enhanced safety during the landing operation. However, the introduced nonlinear flexible force will degrade the convergence of landing trajectory optimization. To address this challenge, the homotopic approach is employed to smoothly connect the trajectory optimization problem from rigid landing to flexible landing. Then, the connection between the optimal solution of the rigid problem and the flexible problem is revealed in detail with the presented theorem. Based on this theorem, the flexible landing fuel optimal trajectory is generated by iteratively solving a sequence of convexified and discretized homotopic problems. The effectiveness of the proposed algorithm is demonstrated through 433 Eros flexible landing mission based numerical simulations. • A novel convex programming method for flexible landing trajectory design is proposed. • The proposed method is proved to converge to the optimal solution of the flexible landing problem. • The optimal thrust magnitude profile for the flexible landing problem is of bang–bang structure. [ABSTRACT FROM AUTHOR]

For the first time in spaceflight history the flight of a fully reusable launch system with rocket propulsion appears possible within the next couple of years. Apart from the implications for the orbital launch market, a fully reusable system could also enable an entirely new class of commercial point-to-point transport on Earth. Rocket propelled point-to-point systems promise the ability to transport passengers or cargo to any suitable landing site on Earth with extremely short travel times (typically less than 90 min). In this study the primary focus is on DLR-SART's SpaceLiner 7 vehicle concept with an initial comparison to Starship, currently being developed by SpaceX. The trajectories are identified using multi-objective optimization with evolutionary algorithms. These allow the identification of a solution space with regard to multiple objectives, in this case minimal overflight of populated areas and minimal peak heat flux, while still respecting other constraints (e.g. structural loads). The population disturbance is computed by using a global population density database and integrating the number of people along the flight track. Ideally, the solution space consists of a pareto-front which correlates to the most optimal solutions possible for all objectives. The mission analysis identifies various feasible trajectories around the world. Primarily, these routes are going along less populated areas such as the oceans and the polar regions. Especially the latter enable large longitudinal changes during the flight and consequently connecting distant places on Earth. The critical routes are large longitudinal crossings around the equator where land masses must be overflown. These shall be reconsidered and/or improved in the future. Comparing SpaceLiner to Starship, it is found that the mission profiles vary significantly. While SpaceLiner uses its high lift-to-drag ratio in the higher atmosphere to manoeuvre around large land masses, Starship can only follow the direct route. In contrast, Starship flies higher into space and thereby might avoid having large population disturbances on ground. Only the re-entry and landing are critical as it does not have significant cross range capability. As a design option for the next iteration of the SpaceLiner development, SpaceLiner 8, it is planned to assess the possibility of using a smaller wing to follow a similar coast through space like Starship and have a steep re-entry at the end of the flight instead of a prolonged glide. • SpaceLiner trajectory optimization using evolutionary algorithms. • Hypersonic point-to-point trajectories between major population centres on Earth. • Analysis and minimization of overflown population to avoid sonic boom disturbance. • Comparison of flight characteristics between SpaceLiner and SpaceX Starship. [ABSTRACT FROM AUTHOR]

This study investigated the time-optimal low-thrust interplanetary transfer problem, and proposes a fast estimation method for guessing the initial costate and optimal transfer time based on a surrogate model, and applied it to the problem of the 11th Global Trajectory Optimization Competition (GTOC 11). Two core methods are proposed in this paper: (1) a fast generation method called the neighbor point iteration algorithm (NPIA) is presented for rapidly generating low-thrust databases with high efficiency and accuracy; and (2) deep neural networks (DNNs) are adopted to learn the state–costate pairs of low-thrust databases, and the surrogate network can quickly estimate the initial costate and optimal transfer time of the low-thrust interplanetary problem. Experiments verified the proposed method and investigated the influence of network structure, learning rate, and loss function on the accuracy of network estimation. The effects of database generation and network estimation were compared based on three transfer scenarios: coplanar, non-coplanar, and arbitrary orbital transfer. In addition, the application case study showed that the proposed method can quickly obtain the time-optimal low-thrust solution to GTOC 11's interplanetary transfer, which achieves high precision and meets the terminal constraints. [ABSTRACT FROM AUTHOR]

This study proposes a Gaussian-discretization control vector parametrization (CVP) algorithm to improve the reentry trajectory optimization accuracy of a hypersonic vehicle (HV) with a complex path and terminal state constraints. First, the reentry trajectory optimization problem (TOP) of the HV is established by analyzing the equations of motion and constraints. Second, a Gaussian distribution strategy is derived to obtain a suitable control parametrization time grid for improving control quality. By combining the handling strategies for path and terminal constraints, an efficient, non-uniform control parametrization trajectory optimization method is established, and the HV trajectory optimization algorithm framework is provided in detail. Lastly, the proposed algorithms are implemented on a widely studied common aero vehicle model. Numerical simulation tests are conducted on terminal-time-free and terminal-time-fixed TOPs to optimize the reentry downrange. Test results show that the proposed method has a stable solving ability with high satisfaction of terminal constraints. Simulation results reveal that the proposed method efficiently increases the downrange compared with other CVP methods under the tested scenario, thus showing the effectiveness of the proposed distribution strategy. [ABSTRACT FROM AUTHOR]

Recently, advanced in-vehicle technologies have led to the emergence of connected and automated vehicles (CAVs). CAVs are supposed to improve traffic efficiency and safety by coordinating the vehicles based on the communication among vehicles. This study addresses the trajectory optimization of CAVs in the drop-off area of the departure curbside, which consists of many conflict points. We first propose a centralized control method to optimize the trajectories of CAVs and then propose an implementation procedure to deal with the dynamic features and reduce the problem scales for practical instances. Contrast experiments are conducted to test the performance of the proposed control method. Results under various scenarios (different volumes, safety gaps, and desired speeds) demonstrate that CAVs controlled by the proposed method significantly outperform human-driven vehicles without control concerning mean travel time in the drop-off area. [ABSTRACT FROM AUTHOR]

Aiming at the perturbation of motion capability and the deviation of end effector from its desired trajectory caused by joint effectiveness partial loss failure, a fault-tolerant control strategy considering motion capability optimization is proposed to ensure that the faulty space manipulator can carry on-orbit operation tasks. Firstly, the joint effectiveness partial loss failure model is established, and the kinematic and dynamic model of the faulty manipulator is established based on the failure model. The kinematic and dynamic coupling relationship of the faulty manipulator is also analyzed. Then based on sliding mode control, the fault-tolerant control strategy that ensures the end effector trajectory tracking and base orientation deflection attenuation is designed. Meanwhile, the motion capability optimization model is designed based on the redundancy characteristic of the manipulator and combined with the fault-tolerant control system. This combined system can realize end effector trajectory tracking, base orientation deflection attenuation, and motion capability optimization at the same time. Finally, simulation experiment is carried out to verify the proposed fault-tolerant control strategy for the faulty manipulator. The result shows that the proposed fault-tolerant control strategy can realize end effector trajectory tracking, base orientation deflection attenuation, and motion capability optimization with high control accuracy, high convergence rate, and significant motion capability optimization effect. For both joint velocity partial loss and joint torque partial loss failure, the duration of convergence is less than 0.5 s, the steady-state error is less than 1 × 10 - 4 m for end effector position and less than 1 × 10 - 5 degree for base orientation deflection, and the motion capability indexes have been raised by over 40%. [ABSTRACT FROM AUTHOR]

• The mathematical model of the reachable domain of the contingency return trajectories. • Reachable domain calculation method of the contingency return trajectories based on interval analysis. • Parameter characteristic analysis of reachable domain. The investigation on reachable domain based on interval analysis is performed, which is aimed for the contingency return trajectories during the circumlunar flight stage in manned lunar landing engineering. First, the issue of contingency return trajectory, which adopts a non-coplanar maneuver during the circumlunar flight phase, is expounded upon. The mathematical model of the reachable domain of contingency return trajectories is established. Second, the contingency return trajectory is designed. An improved interval branch and bound algorithm is introduced and a reachable domain calculation method of the contingency return trajectories is proposed. Third, in numerical simulations, by comparing the reachable domain obtained by the traditional brute force method, the accuracy of the method presented in this paper is verified. It also indicates that this method has a higher calculation efficiency. Finally, numerous simulations are conducted to discuss the parameter characteristic of reachable domain by adopting this method. The study conclusions can serve as an important reference for the selection and decision of contingency return trajectory plans in the future manned lunar landing engineering. [ABSTRACT FROM AUTHOR]

This paper proposes a linear programming approach for onboard optimization of rocket trajectories, motivated by the need for reliable and computationally efficient trajectory optimization methods in real-time applications. To reformulate rocket trajectory optimization problems within a linear programming framework, a polytopal approximation method is developed. The polytopal approximation method approximates the thrust magnitude constraint using a set of artificial variables and linear constraints. Compared with a state-of-the-art approximation method, the polytopal approximation method demonstrates a higher accuracy-to-size ratio, enabling rocket trajectory optimization problems to be cast into linear subproblems without significantly increasing problem sizes. As linear subproblems can be readily solved by linear programming solvers, the proposed trajectory optimization approach inherits the solver's reliability and computational efficiency, making it potentially useful for critical onboard applications. An ascent trajectory optimization problem is provided as an illustrative example to demonstrate the effectiveness of the proposed linear programming approach. [ABSTRACT FROM AUTHOR]

Optimal entry flight of hypersonic vehicles requires achieving specific mission objectives under complex nonlinear flight dynamics constraints. The challenge lies in rapid generation of optimal or near-optimal flight trajectories with significant changes in the initial flight conditions during entry. Deep Neural Networks (DNNs) have shown the capability to capture the inherent nonlinear mapping between states and optimal actions in complex control problems. This paper focused on comprehensive investigation and evaluation of a DNN-based method for three-dimensional hypersonic entry flight trajectory generation. The network is designed using cross-validation to ensure its performance, enabling it to learn the mapping between flight states and optimal actions. Since the time-consuming training process is conducted offline, the trained neural network can generate a single optimal control command in about 0.5 milliseconds on a PC, facilitating onboard applications. With the advantages in mapping capability and calculating speed of DNNs, this method can rapidly generate control action commands based on real-time flight state information from the DNN model. Simulation results demonstrate that the proposed method maintains a high level of accuracy even in scenarios where the initial flight conditions (including altitude, velocity, and flight path angle) deviate from their nominal values, and it has certain generalization ability. [ABSTRACT FROM AUTHOR]

Electroaerodynamic unmanned aerial vehicles (EAD-UAVs) are innovative UAVs that use high-voltage asymmetric electrodes to ionize air molecules and Coulomb force to push these ions to produce thrust. Unlike fixed-wing and rotor UAVs, EAD-UAVs contain no moving surfaces and have the advantages of very low noise, low mechanical fatigue, and no carbon emissions. This paper proposes an EAD-UAV configuration with an orthogonal arrangement of multiple EAD thrusters to adjust the EAD-UAV attitude and flight trajectory through voltage distribution control alone. Based on a one-dimensional dynamic model of an EAD thruster, the attitude–path coupling dynamics of the EAD-UAV were derived. To achieve EAD-UAV flight control for a specified target, the Bezier shaping approach (BSA) was implemented to realize rapid trajectory optimization considering the coupling dynamic constraints. The numerical simulation results indicate that the BSA can quickly procure an optimized flight trajectory that satisfies the dynamic and boundary constraints. Compared with the Gaussian pseudospectral method (GPM), the BSA changes the optimization index of the objective function by nearly 1.14% but demands only nearly 1.95% of the computational time on average. Hence, the improved integrative Bezier shaping approach (IBSA) can overcome the poor convergence issue of the BSA under the continuous acceleration constraint of multi-target flight trajectories. [ABSTRACT FROM AUTHOR]

Landing of supersonic transport (SST) suffers from a large uncertainty due to its highly sensitive aerodynamic properties in the subsonic domain, as well as the wind gusts around runways. At the vehicle design stage, a landing trajectory optimization under wind uncertainty in a multi-objective solution space is desired to explore the possible trade-off in its key flight performance metrics. The proposed algorithm solves this robust constrained multi-objective optimal control problem by integrating non-intrusive polynomial chaos expansion into a constrained evolutionary algorithm. The computationally tractable optimization is made possible through the conversion of a probabilistic problem into an equivalent deterministic representation while maintaining a form of the multi-objective problem. The generated guidance trajectories achieve a significant reduction of the uncertainty in their terminal states with a marginal modification in the control history of the deterministic solutions, validating the importance of the consideration of robustness in trajectory optimization. [ABSTRACT FROM AUTHOR]

This paper proposes a control system to address the efficiency and pollutant emissions of heterogeneous traffic flow composed of human-operated vehicles (HVs) and connected and automated vehicles (CAVs). Based on the comprehensive collection of information on the flow of heterogeneous traffic, the control system uses a two-layer optimization model for signal duration calculation and CAV trajectory planning. The upper model optimizes the phase duration in real time based on the actual total number and type of vehicles entering the control adjustment zone, while the lower model optimizes CAV lane-changing strategies and vehicle acceleration optimization curves based on the phase duration optimized by the upper model. The target function accounts for reducing fuel usage, carbon emission lane-changing costs, and vehicle travel delays. Based on the Webster optimal cycle formula, an improved cuckoo algorithm with strong search performance is created to solve the model. The numerical data confirmed the benefits of the suggested signal control and CAV trajectory optimization method based on pre-signal lights and dedicated CAV lanes for heterogeneous traffic flow. Intersection capacity was significantly enhanced, CAV average fuel consumption, carbon emission and lane-changing frequency were significantly reduced, and traffic flow speed and delay were significantly improved. [ABSTRACT FROM AUTHOR]

In order to improve the safety and efficiency of inspection robots for solar power plants, the Rapidly Exploring Random Tree Star (RRT*) algorithm is studied and an improved method based on an adaptive target bias and heuristic circular sampling is proposed. Firstly, in response to the problem of slow search speed caused by random samplings in the traditional RRT* algorithm, an adaptive target bias function is applied to adjust the generation of sampling points in real-time, which continuously expands the random tree towards the target point. Secondly, to solve the problem that the RRT* algorithm has a low search efficiency and stability in narrow and long channels of solar power plants, the strategy of heuristic circular sampling combined with directional deviation is designed to resample nodes located on obstacles to generate more valid nodes. Then, considering the turning range of the inspection robot, our method will prune nodes on the paths that fail to meet constraint of the minimum turning radius. Finally, the B-spline curve is used to fit and smooth the path. A simulation experiment based on the environment of solar power plant is conducted and the result demonstrates that, compared with the RRT*, the improved RRT* algorithm reduces the search time, iterations, and path cost by 62.06%, 45.17%, and 1.6%, respectively, which provides a theoretical basis for improving the operational efficiency of inspection robots for solar power plants. [ABSTRACT FROM AUTHOR]

After the completion of the launch mission, the soft landing recovery and reuse of the carrier rocket's first-stage can effectively control the landing area to ensure safety and significantly reduce the cost of space launch transportation. The trajectory optimization of the whole process from the first section to the landing site is significant to fuel saving. In the entire process, the first-stage needs to go through three startup ignitions of course adjustment, power deceleration, and vertical landing. For this segmented fuel optimization problem, optimizing the thrust size and direction during three sections and the switching time between each section is necessary. Optimizing the vertical landing section is essential to ensure the accuracy of landing position and speed, which greatly complicates the whole process's optimization. Therefore, the optimization process of the vertical landing is substituted by a neural network predictor, which is used to obtain the mapping relationship between the initial state of the vertical landing section and the fuel consumption of the segment. Besides, the thrust profiles of the first two startup sections are reasonably handled based on physical cognition. The combination of convex optimization and neural network successfully converted the multi-stage optimal control problem into a parameter optimization problem and solved it by a genetic algorithm. Optimization results were compared with the conventional method, which indicated its superiority. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new optimal trajectory planning method for the manipulator to optimize its operating efficiency and ensure the smoothness of the motion process. The position sequences in joint space corresponding to a specified trajectory in task space are obtained by using the inverse kinematic algorithm, and the seventh-degree B-spline curve interpolation method is used to construct the joint trajectory with controllable start–stop kinematic parameters, and continuous velocity, acceleration and jerk. The kinematic constraints of the manipulator are transformed into the control point constraints of the B-spline curve, the sequential quadratic programming method is used to solve the optimal motion time node, and then the time-optimal continuous jerk trajectory satisfying the nonlinear kinematic constraints is planned. Simulation results show that the proposed trajectory planning method provides the ideal trajectory for the joint controller, ensuring the manipulator can smoothly track any specified trajectory in the task space in the shortest time. [ABSTRACT FROM AUTHOR]

This paper presents an innovative approach to optimize the trajectories of a robotic surveillance system, employing three different optimization methods: genetic algorithm (GA), particle swarm optimization (PSO), and pattern search (PS). The research addresses the challenge of efficiently planning routes for a LiDAR-equipped mobile robot to effectively cover target areas taking into account the capabilities and limitations of sensors and robots. The findings demonstrate the effectiveness of these trajectory optimization approaches, significantly improving detection efficiency and coverage of critical areas. Furthermore, it is observed that, among the three techniques, pattern search quickly obtains feasible solutions in environments with good initial trajectories. On the contrary, in cases where the initial trajectory is suboptimal or the environment is complex, PSO works better. For example, in the high complexity map evaluated, PSO achieves 86.7% spatial coverage, compared to 85% and 84% for PS and GA, respectively. On low- and medium-complexity maps, PS is 15.7 and 18 s faster in trajectory optimization than the second fastest algorithm, which is PSO in both cases. Furthermore, the fitness function of this proposal has been compared with that of previous works, obtaining better results. [ABSTRACT FROM AUTHOR]

When humanoid robots work in human environments, falls are inevitable due to the complexity of such environments. Current research on humanoid robot falls has mainly focused on falls on the ground, with little research on humanoid robots falling from the air. In this paper, we employ an extended state variable formulation that directly maps from the high-level motion strategy space to the full-body joint space to optimize the falling trajectory in order to protect the robot when falling from the air. In order to mitigate the impact force generated by the robot's fall, during the aerial phase, we employ simple proportion differentiation (PD) control. In the landing phase, we optimize the optimal contact force at the contact point using the centroidal dynamics model. Based on the contact force, the changes to the end-effector positions are solved using a dual spring–damper model. In the simulation experiments, we conduct three comparative experiments, and the simulation results demonstrate that the robot can safely fall 1.5 m from the ground at a pitch angle of 45°. Finally, we experimentally validate the methods on an actual robot by performing a side-fall experiment. The experimental results show that the proposed trajectory optimization and motion control methods can provide excellent shock absorption for the impact generated when a robot falls. [ABSTRACT FROM AUTHOR]

Building upon the recent development of solar sailing primer vector theory and its successful applications, we propose a new formulation for indirect solar-sail trajectory optimization, which minimizes solar angle (cone angle between the sail normal and sunlight vectors) over a trajectory. The minimum solar-angle objective is introduced to address a typical demand in mission design: having the ability to design trajectories with fixed time-of-flight, which is especially crucial when the mission involves time-sensitive events, such as scientific observations with specific lighting conditions, gravity assists at specific epochs, to name a few. We derive an analytical optimal control law for minimum solar-angle sail transfers by applying Pontryagin's optimality principle. Our theoretical results illuminate that a quantity termed solar sailing primer vector characterizes the optimal solar-sail control law for both minimum-time and minimum solar-angle transfers, as is the case in Lawden's primer vector theory for conventional low-thrust transfers. We numerically demonstrate these theoretical results by applying them to asteroid rendezvous transfers for NASA's NEA Scout mission. The numerical examples also reveal the numerical advantage of using the minimum solar-angle objective over the minimum-time one for solar-sail trajectory design because of the smoother optimal control profile. Solar sailing primer vector theory provides a tool to characterize the optimal control law independent of particular state representations or solution methods, enabling mission designers to combine it with a wealth of techniques developed for low-thrust trajectory optimization. • Propose an indirect trajectory optimization formulation based on solar sail primer vector theory. • The formulation minimizes the solar angle over a transfer with fixed time-of-flight. • The formulation derives an analytical optimal control law via Pontryagin's minimum principle. • Numerical examples demonstrate the analytical results in a NASA's NEA Scout exploration scenario. [ABSTRACT FROM AUTHOR]

In this paper, Particle Swarm Optimization with energy-to-fuel continuation is proposed for initializing the co-state variables for low-thrust minimum-fuel trajectory optimization problems in the circular restricted three-body problem. Particle Swarm Optimization performs a search of the solution space by minimizing the weighted sum of squares of the two-point boundary-value problem final boundary condition residuals for the minimum-energy problem. Next, an energy-to-fuel homotopy is employed to transition the minimum-energy trajectory to a minimum-fuel trajectory, starting from the generated guess. The proposed methodology is applied to two low-thrust transfer problems in the Earth–Moon system: a transfer from a geostationary transfer orbit to an L1 halo orbit, and a transfer from an L2 halo orbit to an L1 halo orbit. The resulting minimum-fuel trajectories are validated with the literature. It is demonstrated that the methodology can successfully generate guesses for the initial co-state variables which converge to a solution for both scenarios. A strategically chosen particle swarm size is shown to improve the efficiency of the methodology. The proposed approach is of simple implementation, can be easily extended to other trajectory optimization problems, facilitates the discovery of multiple candidate trajectories, and does not require a user-provided guess, all of which are advantageous features for the preliminary phase of mission design. • Particle Swarm Optimization is proposed to guess the Lagrange co-states variables. • PSO initialization is paired with homotopy continuation for trajectory optimization. • The proposed algorithm facilitates discovery of multiple unique optimal trajectories. • Two minimum-fuel trajectory optimization problems are solved. • The effect of the particle swarm size on successful convergence is analyzed. [ABSTRACT FROM AUTHOR]

A rendezvous mission with a tumbling space object has been studied by developing a novel three-phase mission design architecture which includes model and state uncertainties by utilizing Ensemble Optimal Control and warm-start Bellman Pseudospectral Optimal Control. Ensemble optimal control problem is solved via in-house developed Stochastic-Collocation based Ensemble Pseudospectral Optimal Control Software (SC-EPOCS) by modeling the uncertainties via samples generated by Conjugate Unscented Transformation based on the initial statistical distributions. Then, a new concept called checkpoints has been introduced to decide a feasible and optimal transition trajectory from uncertainty-aware trajectories to a deterministic optimal trajectory. This is achieved by conducting a reachability analysis for all ensembles and uncertainties. As a result, two Deep Neural Networks (DNNs), one for translational and other for the rotational motion, have been trained by utilizing initial costate values that correspond to optimal trajectories, starting from the checkpoints. By deriving costate dynamics for optimal trajectories, a warm-start algorithm is developed by applying Covector Mapping Theorem. Finally, Bellman Pseudospectral Optimal Control is applied in a Caratheodory- Π sense by recursively solving an optimal control problem, subjected to state estimation errors. Results prove the feasibility, robustness, and optimality of the approach. • A novel robust trajectory optimization framework for rendezvous is proposed. • A robust trajectory database is generated via Conjugate Unscented Transformation. • Two Deep Neural Networks are trained for optimal transition trajectories. • Framework has demonstrated optimality, safety, robustness, and flexibility. [ABSTRACT FROM AUTHOR]

Numerous process architectures for fabric molding are investigated because fiber braided structure is closely related to the performance of fiber‐reinforced composites. However, existing methods for calculating process architectures have to deal with the coordinates of each fiber when modeling the three‐dimensional braiding method without individually controlled switches. The amount of data grows geometrically as the number of fibers and braiding steps increases. A methodology that enables simple and efficient computation of a model of the relationship between braiding parameters and fiber structure is urgently needed. This paper proposes a novel algorithm to trace the yarn carrier trajectories through machine simulation with Euler rotation‐matrix operations. To predict the real fabric architecture, a contraction factor is introduced to optimize the yarn trajectory while considering the volume of the yarn. The optimized fabric architecture is explored and the braiding process architecture with different braiding parameters is simulated according to the algorithm. Based on the exploration of the relationship between the braiding parameters and the process structure, a hexagonal‐annular braiding machine was established, which can fabricate fabrics with different cross‐sectional shapes. The simulation results were verified by the braiding experiments. [ABSTRACT FROM AUTHOR]

This article investigates a new autonomous mobile fog computing (MFC) system empowered by multiple unmanned aerial vehicles (UAVs) in order to serve medical Internet of Things devices (MIoTDs) efficiently. The aim of this article is to reduce the energy consumption of the UAVs-empowered MFC system by designing UAVs' trajectories. To construct the trajectories of UAVs, we need to consider not only the order of SPs but also the association among UAVs, SPs, and MIoTDs. The above-mentioned problem is very complicated and is difficult to be handled via applying traditional techniques, as it is NP-hard, nonlinear, non-convex, and mixed-integer. To handle this problem, we propose a novel simulated annealing trajectory optimization algorithm (SATOA), which handles the problem in three phases. First, the deployment (i.e., number and locations) of stop points (SPs) is updated and produced randomly using variable population sizes. Accordingly, MIoTDs are associated with SPs and extra SPs are removed. Finally, a novel simulated annealing algorithm is proposed to optimize UAVs' association with SPs as well as their trajectories. The performance of SATOA is demonstrated by performing various experiments on nine instances with 40 to 200 MIoTDs. The simulation results show that the proposed SATOA outperforms other compared state-of-the-art algorithms in terms of saving energy consumption. [ABSTRACT FROM AUTHOR]

• Multi-target Active Debris Removal missions are necessary to reduce the proliferation of debris. • Using of simulated annealing optimization groups debris in an efficient way for removal missions. • Proposed missions have an average delta-V budget of 2.41 km/s and an average duration of 1 years. The proliferation of debris in Low Earth Orbit raises increasing challenges about the sustainability of the space environment. The current international recommendations to deorbit satellites at the end of their life are not sufficient to ensure this sustainability. To accelerate the process, it would be necessary to remove hazardous debris and thus de-congest the high-risk orbits. However, active debris removal missions are very expensive, and still in their early stages. One way to reduce its costs is to remove several pieces of debris per removal mission, which corresponds to a global optimization problem, with the objective of optimizing the number of debris removed while minimizing the cost in mission time and in propellant. In our study, the trajectory optimization is performed using a simulated annealing algorithm. The tool classifies the targets in groups gathered by similarities of orbital parameters, with the objective for each mission not to exceed a total Δ V = 4 km/s for a mission time lower than 3 years. To achieve this, a weighting is made between out-of-plane maneuvers, costly in propellant, and the use of the orbital parameter Ω drift, costly in time, to allow the spacecraft to pass from one debris to another. A criterion is set up to determine from which threshold it is more interesting to carry out a maneuver on Ω rather than to let the gravitational drift act. As a result, applied on the 50 most hazardous debris established by the International Astronautical Federation, we obtain a classification of the 50 pieces of debris into 11 optimal groups, with an average Δ V of 3.05 km/s and an average mission time of 1.5 years, which corresponds to the imposed criteria and validates the feasibility of such ADR missions. [ABSTRACT FROM AUTHOR]

• A generic non-linear post-capture detumble trajectory optimization formulation capable of including joint, base, and end-effector wrench limits. • A quaternion-based linearization of free-floating multibody system for trajectory tracking and stabilization. • A Lyapunov-based Region of Attraction analysis of the tracking controller. Recent increase in space debris combined with the increase in the number of satellites launched has created an increased risk of collisions. The effects of the increased risk can be seen in the form of an increased number of near misses in recent years. The use of robotic manipulators has been suggested for Active Debris Removal (ADR) to reduce the risk of potential future collisions that generate more debris in the orbits around Earth. Compared to other ADR methods, robotic manipulators provide increased versatility as they can be reused for On-Orbit Servicing as well as On-Orbit Assembly missions. A robotic ADR operation consists of three phases: Approach, Capture, and Detumble. This paper provides a method for performing feedback-based stabilization of post-capture detumble trajectories of the chaser-debris system. The approach presented here uses Time-Varying Linear Quadratic Regulator (TVLQR) for stabilization along the detumble trajectory. The contributions of this paper are as follows: A quaternion-based linearization method for multibody systems with a free-floating base, TVLQR for stabilizing the optimal detumble trajectory, and a probabilistic Region of Attraction analysis of the resulting closed-loop system. The estimated Region of Attraction could serve as the goal for the capture controller thus allowing for controller composition through ADR phases while guaranteeing stability and successful detumble. [ABSTRACT FROM AUTHOR]

An adaptive control arc length-based trajectory optimisation approach, which combines the control vector parameterisation (CVP) method with Gauss time grid distribution and adaptive grid refinement strategy, is proposed to further improve the downrange of unmanned hypersonic vehicles. Firstly, the Gauss time grid strategy is introduced to obtain a nonuniform Gauss time grid to calculate the original control profiles. By employing the curve integral formula to analyse the control arc length, an adaptive time grid refinement concept is proposed and the refinement process is derived in detail. The initial time grid nodes are then adaptively subdivided and combined. Finally, the control arc length-based nonuniform time grid refinement optimisation method is implemented. Numerical tests are carried out on common aero hypersonic vehicles and comparisons are made with other CVP methods. The test results reveal that the proposed approach can efficiently improve the downrange and decrease the path constraint oscillation. [ABSTRACT FROM AUTHOR]

This paper derives the dynamic equations of a reduced-order race-car model using Lie-group methods. While these methods are familiar to computational dynamicists and roboticists, their adoption in the vehicle dynamics community is limited. We address this gap by demonstrating how this framework integrates smoothly with the Articulated-Body Algorithm (ABA) and provides a fresh and systematic formulation of vehicle dynamics. For the first time, we model the car body as the end effector of a serial robot with a floating base connected to the track via virtual revolute and prismatic joints. Our formulation also accounts for the effects of 3D track geometry, providing a natural embedding of the car into the 3D track. We rigorously reconcile the ABA steps with key aspects of vehicle dynamics, including road-tire interactions, aerodynamic forces, and load transfers. The resulting model, simple yet accurate, is a powerful tool to efficiently solve Minimum-Lap-Time Planning problems. To demonstrate the effectiveness of our approach, we show numerical results obtained on the Nürburgring circuit. Our optimization problem is formulated via a direct collocation method and solved using the CasADi optimization suite. To validate the results, we test our reduced-order model against a full-fledged multi-body model recently developed by the same authors. The comparison confirms the validity of our reduced-order model, proving both the accuracy of the solution and the computational efficiency achieved. [ABSTRACT FROM AUTHOR]

It is a new application of the high-altitude balloon system to launch multiple small folding wing unmanned aerial vehicles (UAVs). Based on the design of the launching system, we conduct numerical simulations of the ejection process from the balloon platform and the subsequent UAV wing deployment with trajectory leveling operation. We use the Kane method to establish the dynamic model of the balloon launching platform in the inertial coordinate system (ICS). By introducing the degree of freedom of UAV sliding along the sliding track, we realize the dynamic simulation of eight UAV launching processes and obtain the instantaneous separated states. The folding wing UAV first deploys its wings after ejection, which has the coupling characteristics between structural deformation and attitude adjustment. It is regarded as a multi-rigid body connecting structure composed of the fuselage and four wings. We establish the dynamic simulation model by the Kane method in the UAV body coordinate system (BCS). The Radau pseudo-spectral method is used to calculate the flight trajectory of each UAV. This paper is an engineering application research and can provide a simulation reference for the launching test of the balloon-borne folding wing UAV program. [ABSTRACT FROM AUTHOR]

This paper presents a fast trajectory optimization method combining the hp-Legendre pseudospectral method and convex optimization for the 6-Degree-of-Freedom rocket-powered landing problem. To accelerate calculations, this paper combines the Legendre pseudospectral method with a linearization method for convexification, and an hp method that can divide the mesh is introduced to reduce the computational workload. In terms of accuracy, a trust region update strategy that can control the solution process is presented to approximate the original problem iteratively. Convergence analysis is provided as evidence, substantiating that any solution produced by the hp-Legendre pseudospectral convex method is not only feasible but potentially optimal for the original problem. The effectiveness of the proposed method is demonstrated by numerical experiments. When compared, the proposed method achieves higher calculation accuracy in solving the 6-Degree-of-Freedom rocket-powered landing trajectory problem, while taking into account rocket attitude control. [ABSTRACT FROM AUTHOR]

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To improve the insufficient adaptability of single degree-of-freedom (DOF) closed-chain legs to unknown surroundings, this paper studies a novel adjustable closed-chain leg mechanism. Based on the traditional six-bar Stephenson-III leg mechanism, we add one degree-of-freedom to realize the adjustment of frame rod position, by which different shapes of foot trajectory curves are obtained. The height of the foot trajectory can be adjusted longitudinally to enhance the obstacle-surmounting ability, and the length of the walking stride can be changed in the transverse direction to achieve the landing point placement of the swing leg. The structure optimization, gait analysis and obstacle-surmounting simulation in different scenarios are carried out. The test results of walking ability and obstacle surmounting performance in specific surrounding show that the designed closed-chain leg mechanism can increase the maximum obstacle-crossing height and walking stability, which proves the promising characteristics of the proposed leg mechanism in the application of multi-legged robots. [ABSTRACT FROM AUTHOR]

Flexible manipulators capable of high speed operations with low energy consumption have high potential uses for large-scale deployment in industrial works. However, for such systems, simultaneous control of trajectory and vibration still remains a challenge. This paper describes the development of a controller that enables trajectory and vibration control. The controller performance was tested and verified through simulations and actual experiments with a laboratory grade 3D 2-link, flexible manipulator. As a baseline, trajectory tracking using inverse kinematics was observed to have poor tracking due to selfweight deflection. Inverse kinematics results was used to acquire a model of the manipulator using canonical variate analysis system identification. Further, an inverse system was modeled for simultaneous trajectory and vibration control. Compared against the inverse kinematic and the traditional direct strain feedback (DSFB) controller, the inverse system model was found to have 9-fold decrease in trajectory error tracking as well as vibration suppression. The validation experiments on the actual manipulator showed that the inverse system based controller was superior to the inverse kinematics and DSFB method of tracking as it followed the ideal trajectory by overcoming the gravitational pull, and suppressed the link vibrations. [ABSTRACT FROM AUTHOR]

To improve the generality and computational efficiency of robust trajectory optimization technology under multi parameter uncertainty, a robust trajectory optimization method based on stochastic response surface method and polynomial chaos is designed. Firstly, non-intrusive polynomial chaos is combined with stochastic response surface, and a Latin hypercube sampling strategy is introduced to establish a multi-dimensional uncertainty quantification model, which realizes the effective and accurate transformation of the uncertain optimization problem. Secondly, combining the model with the convex optimization method, a trajectory optimization solution strategy based on the sequential convex optimization algorithm is designed to realize the rapid solution of the high-dimensional deterministic optimization problem. Finally, a hypersonic glide trajectory optimization problem considering multi parameter uncertainty such as initial state and process parameters is simulated and compared with the existing methods. The results show that compared with the traditional deterministic trajectory optimization algorithm, the proposed method can obtain the hypersonic glide trajectory with both reliability and robustness. Compared with the existing robust trajectory optimization methods, the proposed method has considerable accuracy and significant computational efficiency, which can ensure the efficiency and reliability of the robust trajectory optimization trajectory generation when the dimension of random variables increases. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Xinyang Normal University Natural Science Edition is the property of Journal of Xinyang Normal University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract A novel system for human following using a differential robot, including an accurate 3‐D human position tracking module and a novel planning strategy that ensures safety and dynamic feasibility, is proposed. The authors utilise a combination of gimbal camera and LiDAR for long‐term accurate human detection. Then the planning module takes the target's future trajectory as a reference to generate a coarse path to ensure the following visibility. After that, the trajectory is optimised considering other constraints and following distance. Experiments demonstrate the robustness and efficiency of our system in complex environments, demonstrating its potential in various applications.

Unmanned aerial vehicles (UAVs) have been generally applied in the field of communication due to their small size, flexible mobility, and convenient deployment. As a mobile base station, the UAV node can quickly establish a line-of-sight link with the ground node, thereby improving communication performance. In this paper, we study a multi-UAV assisted data collecting system. Specifically, in the case of limited system energy consumption, UAV flight energy consumption and ground node data transmission energy consumption are considered as an general limitation, and considering the channel interference between nodes, a multi-UAV assisted data collection model is studied. An non-convex problem that maximizes the minimum amount of data collected from ground nodes is further formulated. Since the original optimization problem is non-convex that difficult to solve directly, the problem is first decomposed into four sub-problems, and then the solution of each sub-problem is obtained by using successive convex approximation and block coordinate descent method. Finally, based on the solution of the four subproblems, an iterative algorithm for joint optimization of data transmission planning, transmission power, UAV trajectory and mission time is proposed. Simulation experiments show that the proposed algorithm can obtain more transmission data than the baseline algorithms.

The ability of a robot to navigate through a dynamic environment, avoid obstacles, and reach its destination is crucial for safety and a major technological challenge in autonomous navigation, especially in crowded environments involving hospitals, hotels, and restaurants. Most prominent methods use distance metrics as a safety constraints in their planning algorithms, which leads to overly cautious navigation. Thus, a velocity obstacle guided motion planning method for mobile robots in moving obstacle environments is proposed. The approach automatically negotiates dynamic obstacles combining velocity obstacle (VO) and trajectory generating. First, a dynamic perception algorithm is developed to track and predict obstacles using only point cloud input. Subsequently, to obtain an initial trajectory that satisfies kinodynamic and the VO-based safety metric (VOSM), VO is applied to search the kinodynamic path to verify the safety of the extended motion primitives. Finally, the smoothness and safety of the robot trajectory are enhanced by nonlinear optimization, which incorporates the proposed safety constraints based on VO. Extensive simulations in challenging environments demonstrate a 40.0% success rate increase and a 44.8% trajectory smoothness improvement over obstacle distance-based methods. Practical testing prove our technology is reliable and can safely avoid dynamic obstacles.