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Accepted by: Konstantinos Nikolopoulos We propose solving non-linear optimization problems by a trajectory method. A parameter is introduced into the optimization problem. For example, a variable in the original formulation is replaced by its squared value. The parameter is the power at which the variable is raised. For a particular value of the parameter (power of 2), the optimal solution is easily obtained. The original optimization problem is defined for another value of the parameter (power of 1). As another example, the means and standard deviations of a function based on a set of variables can be calculated. We multiply the standard deviations by a factor (the parameter) between 0 and 1. Suppose that the problem is easily solvable for zero standard deviations (factor of 0). If we 'slowly' increase the factor, the solution moves to the desired solution for a factor of 1. A trajectory connects the easily obtained solution to the desired solution. We trace the trajectory and the solution for the optimization problem is at the end of the trajectory. The procedure is applied for solving the single facility Weber location problem, and a competitive location problem with good results. [ABSTRACT FROM AUTHOR]

With the development of the Internet of Things (IoT) technology, massive amounts of sensor data in applications such as fire monitoring need to be transmitted to edge servers for timely processing. However, there is an energy-hole phenomenon in transmitting data only through terrestrial multi-hop networks. In this study, we focus on the data collection task in an unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) network, where a UAV is deployed as the mobile data collector for the ground sensor nodes (SNs) to ensure high information freshness. Meanwhile, the UAV is equipped with an edge server for data caching. We first establish a rigorous mathematical model in which the age of information (AoI) is used as a measure of information freshness, related to both the data collection time and the UAV's flight time. Then a mixed-integer non-convex optimization problem is formulated to minimize the peak AoI of the collected data. To solve the problem efficiently, we propose an iterative two-step algorithm named the AoI-minimized association and trajectory planning (AoI-MATP) algorithm. In each iteration, the optimal SN–collection point (CP) associations and CP locations for the parameter ε are first obtained by the affinity propagation clustering algorithm. The optimal UAV trajectory is found using an improved elite genetic algorithm. Simulation results show that based on the optimized ε , the AoI-MATP algorithm can achieve a balance between data collection time and flight time, reducing the peak AoI of the collected data. [ABSTRACT FROM AUTHOR]

Apple tree branches have the physical characteristics of high cellulose content and high elasticity, and the use of traditional soft straw pickers will miss a large number of branches. It is necessary to design a picking mechanism that adapts to the physical characteristics of fruit tree branches. In the treatment of branches in modern orchards, the picking mechanism is an important part of the picking device. The success rate of picking directly affects the processing performance of the whole machine. To improve the picking rate, the roller branch picking mechanism is studied. The trajectory of the roller picking and the stress state of the branches are analyzed, and five main factors affecting the picking effect are obtained, i.e. the position relationship between the rotation center of the picking roller and the feeding roller, inclination angle of the steel teeth, the effective working length, the speed and the forward speed of the machine. A mathematical model is established to obtain the static and dynamic motion trajectories of the roller picking mechanism are obtained by using Matlab. Taking the analysis results of influencing factors as the optimization goal, the picking trajectory of the mechanism is simulated to obtain a set of non-inferior solutions. A roller branch picker is manufactured according to the parameter values and tested in the field, and the picking rate can reach 91%. [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]

Motion blur in dynamic scenes is an important yet challenging research topic. Recently, deep learning methods have achieved impressive performance for dynamic scene deblurring. However, the motion information contained in a blurry image has yet to be fully explored and accurately formulated because: (i) the ground truth of dynamic motion is difficult to obtain; (ii) the temporal ordering is destroyed during the exposure; and (iii) the motion estimation from a blurry image is highly ill-posed. By revisiting the principle of camera exposure, motion blur can be described by the relative motions of sharp content with respect to each exposed position. In this paper, we define exposure trajectories, which represent the motion information contained in a blurry image and explain the causes of motion blur. A novel motion offset estimation framework is proposed to model pixel-wise displacements of the latent sharp image at multiple timepoints. Under mild constraints, our method can recover dense, (non-)linear exposure trajectories, which significantly reduce temporal disorder and ill-posed problems. Finally, experiments demonstrate that the recovered exposure trajectories not only capture accurate and interpretable motion information from a blurry image, but also benefit motion-aware image deblurring and warping-based video extraction tasks. Codes are available on https://github.com/yjzhang96/Motion-ETR. [ABSTRACT FROM AUTHOR]

In this article, we present an optimization-based framework for multicopter trajectory planning subject to geometrical configuration constraints and user-defined dynamic constraints. The basis of the framework is a novel trajectory representation built upon our novel optimality conditions for unconstrained control effort minimization. We design linear-complexity operations on this representation to conduct spatial–temporal deformation under various planning requirements. Smooth maps are utilized to exactly eliminate geometrical constraints in a lightweight fashion. A variety of state-input constraints are supported by the decoupling of dense constraint evaluation from sparse parameterization and the backward differentiation of flatness map. As a result, this framework transforms a generally constrained multicopter planning problem into an unconstrained optimization that can be solved reliably and efficiently. Our framework bridges the gaps among solution quality, planning efficiency, and constraint fidelity for a multicopter with limited resources and maneuvering capability. Its generality and robustness are both demonstrated by applications to different flight tasks. Extensive simulations and benchmarks are also conducted to show its capability of generating high-quality solutions while retaining the computation speed against other specialized methods by orders of magnitude. [ABSTRACT FROM AUTHOR]

This article considers the problem of estimating the trajectory of a ballistic target in the reentry phase using 2-D measurements (azimuth and elevation angles) from a moving passive sensor. Previous works investigated the estimation problem of an object in the thrusting and initial ballistic phase from a single fixed passive sensor. This article shows that the 3-D trajectory in the reentry phase can be obtained by estimating the target's state at the end of the observation interval. The 7-d motion parameter vector (velocity azimuth angle, velocity elevation angle, drag coefficient, target speed, and 3-D position) is estimated by the maximum likelihood (ML) estimator with numerical search. Then we can predict the future position at an arbitrary time and the impact point of the target. The observability of the system for a sensor on a fast aircraft moving with constant velocity or maneuvering is verified via the invertibility of the Fisher information matrix. This is a major extension of the applicability of the recent observability proof for a stationary passive sensor observing a target in a gravitational field. The Cramer–Rao lower bound for the estimated parameters is evaluated and it shows that the estimates are statistically efficient. The angle estimation performance for the ML estimator is also compared with that of the polynomial fitting method. Simulation results illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Optimizing k-space sampling trajectories is a promising yet challenging topic for fast magnetic resonance imaging (MRI). This work proposes to optimize a reconstruction method and sampling trajectories jointly concerning image reconstruction quality in a supervised learning manner. We parameterize trajectories with quadratic B-spline kernels to reduce the number of parameters and apply multi-scale optimization, which may help to avoid sub-optimal local minima. The algorithm includes an efficient non-Cartesian unrolled neural network-based reconstruction and an accurate approximation for backpropagation through the non-uniform fast Fourier transform (NUFFT) operator to accurately reconstruct and back-propagate multi-coil non-Cartesian data. Penalties on slew rate and gradient amplitude enforce hardware constraints. Sampling and reconstruction are trained jointly using large public datasets. To correct for possible eddy-current effects introduced by the curved trajectory, we use a pencil-beam trajectory mapping technique. In both simulations and in- vivo experiments, the learned trajectory demonstrates significantly improved image quality compared to previous model-based and learning-based trajectory optimization methods for $10\times $ acceleration factors. Though trained with neural network-based reconstruction, the proposed trajectory also leads to improved image quality with compressed sensing-based reconstruction. [ABSTRACT FROM AUTHOR]

Placing robotsoutside controlled conditions requires versatile movement representations that allow robots to learn new tasks and adapt them to environmental changes. The introduction of obstacles or the placement of additional robots in the workspace and the modification of the joint range due to faults or range-of-motion constraints are typical cases, where the adaptation capabilities play a key role for safely performing the robot’s task. Probabilistic movement primitives (ProMPs) have been proposed for representing adaptable movement skills, which are modeled as Gaussian distributions over trajectories. These are analytically tractable and can be learned from a small number of demonstrations. However, both the original ProMP formulation and the subsequent approaches only provide solutions to specific movement adaptation problems, e.g., obstacle avoidance, and a generic, unifying, probabilistic approach to adaptation is missing. In this article, we develop a generic probabilistic framework for adapting ProMPs. We unify previous adaptation techniques, for example, various types of obstacle avoidance, via-points, and mutual avoidance, in one single framework and combine them to solve complex robotic problems. Additionally, we derive novel adaptation techniques such as temporally unbound via-points and mutual avoidance. We formulate adaptation as a constrained optimization problem, where we minimize the Kullback–Leibler divergence between the adapted distribution and the distribution of the original primitive,while we constrain the probability mass associated with undesired trajectories to be low. We demonstrate our approach on several adaptation problems on simulated planar robot arms and seven-degree-of-freedom Franka Emika robots in a dual-robot-arm setting. [ABSTRACT FROM AUTHOR]

In the manufacturing industry, spray painting is often an important part of the manufacturing process. Especially in the automotive industry, the perceived quality of the final product is closely linked to the exactness and smoothness of the painting process. For complex products or low batch size production, manual spray painting is often used. But in large scale production with a high degree of automation, the painting is usually performed by industrial robots. There is a need to improve and simplify the generation of robot trajectories used in industrial paint booths. A novel method for spray paint optimization is presented, which can be used to smooth out a generated initial trajectory and minimize paint thickness deviations from a target thickness. The smoothed out trajectory is found by solving, using an interior point solver, a continuous non-linear optimization problem. A two-dimensional reference function of the applied paint thickness is selected by fitting a spline function to experimental data. This applicator footprint profile is then projected to the geometry and used as a paint deposition model. After generating an initial trajectory, the position and duration of each trajectory segment are used as optimization variables. The primary goal of the optimization is to obtain a paint applicator trajectory, which would closely match a target paint thickness when executed. The algorithm has been shown to produce satisfactory results on both a simple 2-dimensional test example, and a non-trivial industrial case of painting a tractor fender. The resulting trajectory is also proven feasible to be executed by an industrial robot. Note to Practitioners—The work is motivated by the need to generate well performing robot trajectories in robotized spray-painting booths. The described method applies to cases where robotic spray painting is to be used for painting a surface with an even layer of paint at a specified thickness. The method generates and optimizes robot trajectories and is shown to be able to generate a satisfactory paint cover for simple test cases as well as more realistic industrial cases. For a user it could be implemented as is, or be obtained as a standalone service, but there are some prerequisites that need to be fulfilled to make use of the optimization method. It is assumed that the surface to be painted is available as a CAD-model and that physical testing has been performed to determine the characteristics of the paint and nozzle. These physical tests amount to spraying paint on a flat piece of material at a few different distances from the surface and measuring the cross section of the paint thickness. The resulting trajectory can be executed on any industrial painting robot that can handle linear motion commands. [ABSTRACT FROM AUTHOR]

In the field of sculptured surfaces machining, the robot trajectory planning, under high-order complex constraints, aiming at minimizing energy or time, is always a challenge. The complexity of curvature characteristics of sculptured surfaces and the nonlinearity of relevant constraints are the main reasons. This article proposes an efficient planning method of minimum-energy robot trajectory, for high-speed machining of sculptured surfaces. First, the energy characteristic model of the robot machining system (RMS) is established, to acquire the energy-optimal feedrate, under velocity constraints, to use in the subsequent trajectory planning. Next, a trajectory planning model, with complex constraints, is developed. The proposed method transforms the original trajectory planning into a minimal modification of the initial objective-optimal B-spline feedrate curve (BFC). Furthermore, two main coupling problems, which influence the minimal change of curves, in the direct evolution-based BFC modification, are addressed. Based on the derived solutions, a novel modification algorithm of BFC, with a callback mechanism (CBM), is proposed. Finally, the performance of the proposed method and the specific algorithm is validated by two case studies. Results show that the proposed method can significantly improve the efficiency of robot trajectory planning, aiming at minimum energy, while exhibiting excellent performance. Note to Practitioners—This work was motivated by how to automatically and effectively acquire the energy-saving trajectory of a robotic system, executing sculptured surface machining. This article suggests a new approach that transforms the original trajectory optimization into a minimal modification of the initial energy-optimal BFC, obtained under velocity constraints. This approach calculates the complex energy formula only once. A CBM, for constraint-based BFC modification, is proposed, to revise the redundant reduction of the feedrate. The proposed modification algorithm significantly decreases the detrimental effect of two coupling problems, on the adjustment of the BFC. Results show that the computational efficiency of the proposed method is significantly superior to the one of the direct optimization method. The performance of the proposed modification algorithm is obviously advanced compared to the existing B-spline evolution algorithm. In blade machining, after optimizing the trajectory using the proposed method and algorithm, both energy and time decrease by more than 45% compared to the conservative feed. The proposed algorithm improves significantly the trajectory compared to the prior art algorithm. Technologists benefit from reduced planning time and improved machining performance. However, incorporation into a CAM or manufacturing system has not yet been realized and remains a significant work to be done in the future. [ABSTRACT FROM AUTHOR]

Previous deep learning-based video stabilizers require a large scale of paired unstable and stable videos for training, which are difficult to collect. Traditional trajectory-based stabilizers, on the other hand, divide the task into several sub-tasks and tackle them subsequently, which are fragile in textureless and occluded regions regarding the usage of hand-crafted features. In this paper, we attempt to tackle the video stabilization problem in a deep unsupervised learning manner, which borrows the divide-and-conquer idea from traditional stabilizers while leveraging the representation power of DNNs to handle the challenges in real-world scenarios. Technically, DUT is composed of a trajectory estimation stage and a trajectory smoothing stage. In the trajectory estimation stage, we first estimate the motion of keypoints, initialize and refine the motion of grids via a novel multi-homography estimation strategy and a motion refinement network, respectively, and get the grid-based trajectories via temporal association. In the trajectory smoothing stage, we devise a novel network to predict dynamic smoothing kernels for trajectory smoothing, which can well adapt to trajectories with different dynamic patterns. We exploit the spatial and temporal coherence of keypoints and grid vertices to formulate the training objectives, resulting in an unsupervised training scheme. Experiment results on public benchmarks show that DUT outperforms state-of-the-art methods both qualitatively and quantitatively. The source code is available at https://github.com/Annbless/DUTCode. [ABSTRACT FROM AUTHOR]

The control objective of the vertical plane underactuated manipulator (VPUM) is generally to swing up the end point (EP) from the vertical down equilibrium point (VDEP) to the vertical up equilibrium point (VUEP), and finally, to stabilize it at the VUEP. The zone control methods are usually used to achieve this control objective, but the problem of these methods is that they cannot find a unified zone range, and it is easy to appear singularity in the motion process. In this article, for two-link VPUMs, we propose a control strategy based on trajectory planning and optimization, which does not need to divide the zone range, avoids the singularity problem, and can achieve the control objective quickly and smoothly. We design the trajectory by using the time scale method for the active link according to the initial and target states. Then, we obtain the trajectory parameters by employing differential evolution algorithm to ensure that the passive link can also move from the initial states to the target states simultaneously. We design a sliding mode tracking controller to make the active link move along the designed trajectory, so the EP is moved to VUEP. Meantime, we design a sliding mode stabilization controller to ensure that the system is stable at VUEP. Finally, the universality and robustness of the proposed method are proved by simulations. [ABSTRACT FROM AUTHOR]

Intelligent reflecting surface (IRS) cooperated with the simultaneous wireless information and power transfer (SWIPT) can reinforce the desired signal and deal with the energy supply problem effectively. By leveraging the on-demand mobility of unmanned aerial vehicles (UAVs), the IRS cooperated SWIPT can be deployed in more flexible and reliable scenarios. In this article, we investigate the UAV-mounted IRS-assisted SWIPT for Internet of Things (IoT) networks. In particular, a UAV-mounted IRS is deployed to assist the information transmission and power transfer from the access point to several IoT devices simultaneously. Taking full advantage of the UAV-mounted IRS in attending multiple IoT devices flexibly, a time division multiple access (TDMA)-based scheduling protocol is proposed to serve different IoT devices alternatively during the UAV flying along an optimized trajectory with the information and power transfer executed. Then, an optimization problem of maximizing the minimum average achievable rate of multiple devices is formulated with the specific energy harvesting requirement guaranteed. To solve the nonconvex problem, we leverage the successive convex approximation and block coordinate descent methods to develop an iterative algorithm. Simulation results demonstrate that with the help of the more flexible and reliable UAV-mounted IRS, the minimum achievable rate of the IoT network can be significantly improved. [ABSTRACT FROM AUTHOR]

Due to their promising applications and intriguing characteristics, Unmanned Aerial Vehicles (UAVs) can be dispatched as flying base stations to serve multiple energy-constrained Internet-of-Things (IoT) sensors. Moreover, to ensure fresh data collection while providing sustainable energy support to a large set of IoT devices, a required number of UAVs should be deployed to carry out these two tasks efficiently and promptly. Indeed, the data collection requires that UAVs first make Wireless Energy Transfer (WET) to supply IoT devices with the necessary energy in the downlink. Then, IoT devices perform Wireless Information Transmission (WIT) to UAVs in the uplink based on the harvested energy. However, it turns out that when the same UAV performs WIT and WET, its energy usage and the data collection time are severely penalized. Worse yet, it is difficult to efficiently coordinate between UAVs to improve the performance in terms of WET and WIT. This work proposes to divide UAVs into two teams to behave as data collectors and energy transmitters, respectively. A Multi-Agent Deep Reinforcement Learning (MADRL) method, called TEAM, is leveraged to jointly optimize both teams’ trajectories, minimize the expected Age of Information (AoI), maximize the throughput of IoT devices, minimize the energy utilization of UAVs, and enhance the energy transfer. Simulation results depict that TEAM can effectively synchronize UAV teams and adapt their trajectories while serving a large-scale dynamic IoT environment. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicle (UAV)-enabled communication has emerged as an irreplaceable technology in military, disaster relief and emergency scenarios. This correspondence investigates the average throughput in a UAV-enabled cognitive radio network, where the UAV is regarded as a dedicated secondary user to enhance the network coverage and spectral efficiency. Based on the probabilistic line-of-sight channel, we exploit the joint design of UAV trajectory and resource allocation to maximize the average throughput under the constraints of co-channel interference and completion time. The original problem is a mixed integer non-convex problem which is generally NP-hard. We first decompose the primal problem into a bilevel programming problem, and then propose an efficient high-quality algorithm based on the particle swarm optimization approach. The optimized trajectory reveals the trade-off between throughput and co-channel interference. Numerical results verify the superiority of the proposed algorithm as compared to other benchmark schemes. [ABSTRACT FROM AUTHOR]

3D human trajectory reconstruction in an indoor scene is critical in various applications, such as indoor navigation and human activity recognition. This task is challenging due to occlusion and clutters of indoor scenes, flexible human body joints, and severe lack of relevant datasets. Although several methods have been proposed to reconstruct a 3D human trajectory, they either can recover only 2D positions or require human initiative cooperation. In this paper, we propose a novel framework for 3D human trajectory reconstruction in an indoor scene using monocular surveillance videos and static point clouds without any initiative cooperation. The proposed framework consists of three modules: 3D pose estimation, depth regression, and trajectory reconstruction. We first estimate 3D pose from videos. Especially, we reconstruct a half-body 3D pose to deal with the occlusion problem. Then, we propose a depth regression approach to iteratively regress the depth of a 3D pose. Unlike data-driven approaches, our depth regression approach does not require training data and can be integrated into any 3D pose model. Finally, we exploit the geometric constraints from the point cloud to optimize the 3D trajectory. We evaluated the 3D pose estimation and depth regression modules on the H3.6M datasets. Due to the lack of evaluation datasets, we also built a trajectory dataset to evaluate the trajectory reconstruction performance. Empirical evaluation shows that our framework achieves accurate trajectory reconstruction results on real-world videos. [ABSTRACT FROM AUTHOR]

Planning high-speed trajectories for UAVs in unknown environments requires algorithmic techniques that enable fast reaction times to guarantee safety as more information about the environment becomes available. The standard approaches that ensure safety by enforcing a “stop” condition in the free-known space can severely limit the speed of the vehicle, especially in situations where much of the world is unknown. Moreover, the ad-hoc time and interval allocation scheme usually imposed on the trajectory also leads to conservative and slower trajectories. This work proposes FASTER (Fast and Safe Trajectory Planner) to ensure safety without sacrificing speed. FASTER obtains high-speed trajectories by enabling the local planner to optimize in both the free-known and unknown spaces. Safety is ensured by always having a safe back-up trajectory in the free-known space. The MIQP formulation proposed also allows the solver to choose the trajectory interval allocation. FASTER is tested extensively in simulation and in real hardware, showing flights in unknown cluttered environments with velocities up to 7.8 m/s, and experiments at the maximum speed of a skid-steer ground robot (2 m/s). [ABSTRACT FROM AUTHOR]

This article describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2-D and 3-D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g., closed-loop linkages), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly defined manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium configurations of the biped often belong to such manifolds, we use equilibria as “templates” from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2-D and 3-D biped walkers. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicle (UAV)-enabled wireless power transfer (WPT) is a viable solution to remotely charge several energy receivers (ERs) in areas with intermittent access to a source of energy. However, given the limited available energy in the on-board battery of the UAV, which is mainly required to suffice propulsion energy consumption, the UAV struggles to roam seamlessly for long intervals. A key challenge is thus to efficiently use the limited battery energy, and accordingly prolong the UAV’s endurance, via controlling the underlying associated parameters such as cruising velocity. To further extend the battery lifetime, the UAV can also harness other sources of sustainable energy, such as sunlight, via solar energy harvesting. This paper studies a UAV-enabled WPT system, where a rotary-wing UAV transfers radio frequency (RF) wireless energy to several ERs at known locations. To offer uninterrupted seamless service, the UAV also harvests solar energy using solar panels. Considering the propulsion energy consumption of the UAV, we maximize the minimum average power received among all ERs over a finite cycle duration by jointly optimizing the UAV’s time allocation between harvesting and charging, flight trajectory as well as velocity, and transmit power allocation. Due to the non-convexity of the problem, we utilize the block coordinate descent (BCD) and successive convex approximation (SCA) methods. Numerical results show that the proposed solution outperforms benchmark schemes. [ABSTRACT FROM AUTHOR]

Satellite and unmanned aerial vehicle (UAV) networks have been introduced as enhanced approaches to provide dynamic control, massive connections and global coverage for future wireless communication systems. This paper considers a coordinated satellite-UAV communication system, where the UAV performs the environmental reconnaissance task with the assistance of satellites in a hostile jamming environment. To fulfill this task, the UAV needs to realize autonomous trajectory control and upload the collected data to the satellite. With the aid of the uploading data, the satellite builds the environment situation map integrating the beam quality, jamming status, and traffic distribution. Accordingly, we propose a closed-loop anti-jamming dynamic trajectory optimization approach, which is divided into three stages. Firstly, a coarse trajectory planning is made according to the limited prior information and preset points. Secondly, the flight control between two adjacent preset points is formulated as a Markov decision process, and reinforcement learning (RL) based automatic flying control algorithms are proposed to explore the unknown hostile environment and realize autonomous and precise trajectory control. Thirdly, based on the collected data during the UAV’s flight, the satellite utilizes an environment situation estimating algorithm to build an environment situation map, which is used to reselect the preset points for the first stage and provide better initialization for the RL process in the second stage. Simulation results verify the validity and superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

Despite the wide utilization of unmanned aerial vehicles (UAVs), UAV communications are susceptible to eavesdropping due to air-ground line-of-sight channels. Intelligent reflecting surface (IRS) is capable of reconfiguring the propagation environment, and thus is an attractive solution for integrating with UAV to facilitate the security in wireless networks. In this paper, we investigate the secure transmission design for an IRS-assisted UAV network in the presence of an eavesdropper. With the aim at maximizing the average secrecy rate, the trajectory of UAV, the transmit beamforming, and the phase shift of IRS are jointly optimized. To address this sophisticated problem, we decompose it into three sub-problems and resort to an iterative algorithm to solve them alternately. First, we derive the closed-form solution to the active beamforming. Then, with the optimal transmit beamforming, the passive beamforming optimization problem of fractional programming is transformed into corresponding parametric sub-problems. Moreover, the successive convex approximation is applied to deal with the non-convex UAV trajectory optimization problem by reformulating a convex problem which serves as a lower bound for the original one. Simulation results validate the effectiveness of the proposed scheme and the performance improvement achieved by the joint trajectory and beamforming design. [ABSTRACT FROM AUTHOR]

This article presents MADER, a 3-D decentralized and asynchronous trajectory planner for UAVs that generates collision-free trajectories in environments with static obstacles, dynamic obstacles, and other planning agents. Real-time collision avoidance with other dynamic obstacles or agents is done by performing outer polyhedral representations of every interval of the trajectories and then including the plane that separates each pair of polyhedra as a decision variable in the optimization problem. MADER uses our recently developed MINVO basis to obtain outer polyhedral representations with volumes 2.36 and 254.9 times, respectively, smaller than the Bernstein or B-Spline bases used extensively in the planning literature. Our decentralized and asynchronous algorithm guarantees safety with respect to other agents by including their committed trajectories as constraints in the optimization and then executing a collision check-recheck scheme. Finally, extensive simulations in challenging cluttered environments show up to a 33.9% reduction in the flight time, and a 88.8% reduction in the number of stops compared to the Bernstein and B-Spline bases, shorter flight distances than centralized approaches, and shorter total times on average than synchronous decentralized approaches. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicle (UAV)-aided two-way relay networks with multiple terrestrial user pairs is investigated, where a fix-wing UAV is served as a two-way relay to assist information transmission. We aim to maximize the total rate of the two-way relay networks while the quality of service (QoS) being guaranteed. A novel relay strategy, namely time-slots pairing, is proposed by exploiting physical-layer network coding (PNC) protocol. Specifically, the UAV receives and buffers the signals from the scheduled user pair when the UAV approaches one of them, then forwards the modulated signal when the UAV is close to the other. As a result, a non-convex total rate maximization problem is formulated by joint trajectory design and resource optimization. To solve this problem, we first decompose it into three sub-problems, and then a three-step iterative algorithm that can effectively handle the non-convex problem with no worse than a polynomial complexity is developed leveraging the block coordinate descent (BCD) technique and successive convex approximation (SCA) method. Simulation results finally illustrate that: 1) Compared with amplify-and-forward (AF) or decode-and-forward (DF) protocols, the proposed design based on PNC protocol can significantly improve the total rate of the two-way relay networks; 2) the time-slots pairing relay strategy always achieves a significant enhancement on performance than the traditional non-time-slots pairing relay strategy; 3) the time-slots pairing relay strategy is more favorable for the mobile PNC relay networks since it can well resist the degradation of the entire networks caused by users’ increased service quality requirements. [ABSTRACT FROM AUTHOR]

Direct optimization of many-revolution spacecraft trajectories is performed using an unconstrained formulation with many short-arc, embedded Lambert problems. Each Lambert problem shares its terminal positions with neighboring segments to implicitly enforce position continuity. Use of embedded boundary value problems (EBVPs) is not new to spacecraft trajectory optimization, including extensive use in primer vector theory, flyby tour design, and direct impulsive maneuver optimization. Several obstacles have prevented their use on problems with more than a few dozen segments, including computationally expensive solvers, lack of fast and accurate partial derivatives, unguaranteed convergence, and a non-smooth solution space. Here, these problems are overcome through the use of short-arc segments and a recently developed Lambert solver, complete with the necessary fast and accurate partial derivatives. These short arcs guarantee existence and uniqueness for the Lambert solutions when transfer angles are limited to less than a half revolution. Furthermore, the use of many short segments simultaneously approximates low-thrust and eliminates the need to specify impulsive maneuver quantity or location. For preliminary trajectory optimization, the EBVP technique is simple to implement, benefiting from an unconstrained formulation, the well-known Broyden–Fletcher–Goldfarb–Shanno line search direction, and Cartesian coordinates. Moreover, the technique is naturally parallelizable via the independence of each segment's EBVP. This new, many-rev EBVP technique is scalable and reliable for trajectories with thousands of segments. Several minimum fuel and energy examples are demonstrated, including a problem with 6143 segments for 256 revolutions, found within 5.5 h on a single processor. Smaller problems with only hundreds of segments take minutes. [ABSTRACT FROM AUTHOR]

In maritime wireless communications, unmanned surface vehicles (USVs) can improve coverage and transmission performance due to their agile maneuverability and flexible deployment. This paper considers a USV-enabled maritime wireless network, where a USV is employed to assist the communication between the terrestrial base station and ships. Considering the maritime environment characteristics and earth curvature, we establish the systematic USV kinetics and information transmission models. To guarantee fairness, we aim to maximize the minimum expected throughput overall ships by jointly optimizing the trajectory and communication resource allocation, subject to the constraints of the USV kinetics, safe sailing, breakpoint distances, line-of-sight links, resource allocation, and information-causality. Due to the complexity of the maritime two-ray signal propagation model, we propose a channel approximation method to find an upper bound of the throughput for the original problem. By the problem decomposition, two sub-problems are derived and solved iteratively using successive convex approximation and interior-point methods. Simulation results confirm the effectiveness of the proposed method and show that USV can significantly improve transmission performance in maritime wireless networks. [ABSTRACT FROM AUTHOR]

In the article, we present an efficient optimization framework that solves trajectory optimization problems by decoupling state variables from timing variables, thereby decomposing a challenging nonlinear programming (NLP) problem into two easier subproblems. With timing fixed, the state variables can be optimized efficiently using convex optimization, and the timing variables can be optimized in a separate NLP, which forms a bilevel optimization problem. The challenge of obtaining the gradient of the timing variables is solved by sensitivity analysis of parametric NLPs. The exact analytic gradient is computed from the dual solution as a by-product, whereas existing finite-difference techniques require additional optimization. The bilevel optimization framework efficiently optimizes both timing and state variables which is demonstrated on generating trajectories for an UAV. Numerical experiments demonstrate that bilevel optimization converges significantly more reliably than a standard NLP solver, and analytical gradients outperform finite differences in terms of computation speed and accuracy. Physical experiments demonstrate its real-time applicability for reactive target tracking tasks. [ABSTRACT FROM AUTHOR]

Recent advances in trajectory replanning have enabled quadrotor to navigate autonomously in unknown environments. However, high-speed navigation still remains a significant challenge. Given very limited time, existing methods have no strong guarantee on the feasibility or quality of the solutions. Moreover, most methods do not consider environment perception, which is the key bottleneck to fast flight. In this article, we present RAPTOR, a robust and perception-aware replanning framework to support fast and safe flight, which addresses these issues systematically. A path-guided optimization approach that incorporates multiple topological paths is devised, to ensure finding feasible and high-quality trajectories in very limited time. We also introduce two perception-aware planning approaches to actively observe and avoid unknown obstacles. A risk-aware trajectory refinement ensures that unknown obstacles which may endanger the quadrotor can be observed earlier and avoid in time. The motion of yaw angle is planned to actively explore the surrounding space that is relevant for safe navigation. The proposed methods are tested extensively through benchmark comparisons and challenging indoor and outdoor aggressive flights. We release our implementation as an open-source package1 for the community. [ABSTRACT FROM AUTHOR]

Unmanned Aerial Vehicles (UAVs) have attacted much attention in the field of wireless communication due to its agility and altitude. UAVs can be used as low-altitude aerial base stations (UAV-BSs) to provide communication services for ground devices (GDs) in various scenarios, such as emergency communication and traffic offloading in hotspots. However, due to the limited communication ranges and high prices of commercial UAV-BSs, covering a target area all the time with sufficient UAVs is quite challenging, especially under dynamic environment. We need to design the trajectory of the UAV-BSs to optimize system performance. Most existing works focus on the energy-efficient coverage and throughput maximization but ignore the fairness of communication service, especially the fairness at user-level. Besides, reinforcement learning is suitable for solving decision problems in dynamic environments. However, most existing works use centralized deep reinforcement learning (DRL) approaches. Due to the scalability and low time complexity, a distributed DRL approach is more suitable for multiple UAV-BSs communication system in dynamic environment. Unlike previous works, we characterize the fairness at user-level based on proportional fairness scheduling and formulate a weighted-throughput maximization problem via designing UAV-BSs’ trajectory. Then we model the dynamic deploymentproblem of UAV-BSs as a Markov game and propose a multi-agent deep reinforcement learning-based distributed UAV-BSs control approach named MAUC. MAUC approach adopts the framework of centralized training with distributed execution. Simulation results show that the MAUC can improve fairness of communication service by sacrificing a small amount of throughput. [ABSTRACT FROM AUTHOR]

This article extends the optimal covariance steering (CS) problem for linear stochastic systems subject to chance constraints so as to account for an optimal allocation of the risk. Previous works have assumed a uniform risk allocation in order to cast the optimal control problem as a semidefinite program, which can be solved efficiently using standard SDP solvers. An iterative risk allocation (IRA) formalism is used to solve the optimal risk allocation problem for CS using a two-stage approach. The upper-stage of IRA optimizes the risk, which is a convex problem, while the lower-stage optimizes the controller with the new constraints. The process is applied iteratively until the optimal risk allocation that achieves the lowest total cost is obtained. The proposed framework results in solutions that tend to maximize the terminal covariance, while still satisfying the chance constraints, thus leading to less conservative solutions than previous methodologies. In this article, we consider both polyhedral and cone state chance constraints. Finally, we demonstrate the approach to a spacecraft rendezvous problem and compare the results with other competing approaches. [ABSTRACT FROM AUTHOR]

This article presents a novel recursive smooth trajectory (RST) generation algorithm for application in robotics and in particular for unmanned aerial vehicles (UAVs). RST builds the trajectory recursively as a smooth polynomial path, thus a closed form trajectory satisfying any arbitrary dynamic limitation that translates into kinematic constraints (e.g., position, velocity, acceleration, etc.). Uncertainties and perturbations in the constraints are also discussed, modeled, and finally included in the calculation of the polynomial trajectory coefficients. Moreover, due to its recursive formulation, RST enables an immediate extension toward the solution of a trajectory optimization problem. In particular, it is shown that the minimum-snap piecewise polynomial trajectory can be interpreted as a special case of RST. The effectiveness of the proposed algorithm is demonstrated numerically via two illustrative scenarios. Its application to a UAV structure is also discussed to highlight the advantage of a smooth path over a piecewise one. Finally, the computational complexity and memory requirements are analyzed. [ABSTRACT FROM AUTHOR]

A model predictive control (MPC) strategy based on optimal switching sequence concepts is presented for direct power control of grid-connected three-level neutral-point clamped converters. The proposed control strategy explicitly considers the modulator in its formulation along with the model of the system. Through two well-formulated optimal control problems, the proposed strategy is shown to optimally achieve control of the average trajectory of the active and reactive powers as well as the dc-link capacitor voltages without using weighting factors to tradeoff both control targets. Experimental results demonstrate this strategy produces improved steady-state performance with a well-defined output voltage spectrum and fixed-switching frequency while maintaining the inherent fast dynamic responses of MPC strategies. [ABSTRACT FROM AUTHOR]

In this article, we propose a nonlinear receding horizon game-theoretic planner for autonomous cars in competitive scenarios with other cars. The online planner is specifically formulated for a multiple-car autonomous racing game, in which each car tries to advance along a given track as far as possible with respect to the other cars. The algorithm extends previous work on game-theoretic planning for single-integrator agents to be suitable for autonomous cars in the following ways: 1) by representing the trajectory as a piecewise polynomial; 2) incorporating bicycle kinematics into the trajectory; and 3) enforcing constraints on path curvature and acceleration. The game-theoretic planner iteratively plans a trajectory for the ego vehicle and then the other vehicles in sequence until convergence. Crucially, the trajectory optimization includes a sensitivity term that allows the ego vehicle to reason about how much the other vehicles will yield to the ego vehicle to avoid collisions. The resulting trajectories for the ego vehicle exhibit rich game strategies such as blocking, faking, and opportunistic overtaking. The game-theoretic planner is shown to significantly outperform a baseline planner using model-predictive control, which does not take interaction into account. The performance is validated in high-fidelity numerical simulations with three cars, in experiments with two small-scale autonomous cars, and in experiments with a full-scale autonomous car racing against a simulated vehicle (video is available at https://youtube.com/playlist?list=PLmIcLEh8KMje4rYBqRANDuKvqFvj7LCRp). [ABSTRACT FROM AUTHOR]

In this letter, we investigate an unmanned aerial vehicle (UAV) enabled wireless powered communication network (WPCN), in which the UAV first employs the radio frequency (RF) signal to power ground users, and then the users communicate with the UAV by using the harvested energy. The sum rate maximization problem in WPCN suffers doubly near-far effect caused by the double signal propagation loss in both the energy harvesting and communication stage. It is generally believed that this effect can be alleviated by integrating UAV into WPCN, thanks to its flexible deployment. However, due to the lack of analytical solution in state-of-art research, it is still unclear how to quantify the advantage that the mobility of UAV brings to migrating the doubly near-far effect. To address this issue, by showing that the optimal UAV trajectory has a multi-location hovering structure, we first derive the closed-form optimal solution of resource allocation, as a function of the UAV hovering location for downlink wireless power transfer (WPT). We then prove that the UAV in our case only needs to hover at a single location for WPT. More importantly, it is explicitly shown that the doubly near far effect can be alleviated into near-far effect. Simulation results validate our analysis. [ABSTRACT FROM AUTHOR]

On a grand scale, motion trajectories are usually defined by an origin, a sequence of waypoints, and a destination. A typical example is in air traffic management (ATM), where a flight from an origin passes several waypoints and arrives at a destination. The origin, the waypoints, and the destination contain useful information for trajectory modeling. On the other hand, due to trajectory design criteria and ATM restrictions and requirements, there are long-range dependencies in a flight trajectory. Such dependencies can be modeled by taking the origin, waypoints, and destination into account in trajectory modeling. In this article, we propose a class of conditionally Markov (CM) sequences to model such trajectories with long-range dependencies. First, we define a general CM sequence as a foundation. Then, we discuss its special cases for different scenarios. We derive dynamic models of these CM sequences in the Gaussian case. We show how parameters of the models can be learned from data or designed. We also justify the use of the proposed CM models for trajectory modeling. In addition, we obtain optimal filters and predictors for different models. Simulation demonstrations are given. [ABSTRACT FROM AUTHOR]

An object t equipped with a high-speed striking device moves along a given trajectory . The object is tracked by a spatial observer f, which has to hide behind convex fragments of the environment. A method is proposed for constructing an observer trajectory that makes it possible to track the motion of the object on as long a segment of as possible. Under the assumption that the observer leaves for a shelter along at a constant maximum speed, the object t chooses an optimal mode of speed on its trajectory. [ABSTRACT FROM AUTHOR]

Virtual viewpoints synthesis is an essential process for many immersive applications including Free-viewpoint TV (FTV). A widely used technique for viewpoints synthesis is Depth-Image-Based-Rendering (DIBR) technique. However, such technique may introduce challenging non-uniform spatial-temporal structure-related distortions. Most of the existing state-of-the-art quality metrics fail to handle these distortions, especially the temporal structure inconsistencies observed during the switch of different viewpoints. To tackle this problem, an elastic metric and multi-scale trajectory based video quality metric (EM-VQM) is proposed in this paper. Dense motion trajectory is first used as a proxy for selecting temporal sensitive regions, where local geometric distortions might significantly diminish the perceived quality. Afterwards, the amount of temporal structure inconsistencies and unsmooth viewpoints transitions are quantified by calculating 1) the amount of motion trajectory deformations with elastic metric and, 2) the spatial-temporal structural dissimilarity. According to the comprehensive experimental results on two FTV video datasets, the proposed metric outperforms the state-of-the-art metrics designed for free-viewpoint videos significantly and achieves a gain of 12.86% and 16.75% in terms of median Pearson linear correlation coefficient values on the two datasets compared to the best one, respectively. [ABSTRACT FROM AUTHOR]

In single-port access surgeries, robot size is crucial due to the limited workspace. Thus, a robot may be designed under-actuated. Suturing, in contrast, is a complicated task and requires full actuation. This study aims to overcome this shortcoming by implementing an optimization-based algorithm for autonomous suturing for an under-actuated robot. The proposed algorithm approximates the ideal suturing trajectory by slightly reorienting the needle while deviating as little as possible from the ideal, full degree-of-freedom suturing case. The deviation of the path taken by a custom robot with respect to the ideal trajectory varies depending on the suturing starting location within the workspace as well as the needle size. A quantitative analysis reveals that in 13% of the investigated workspace, the accumulative deviation was less than 10 mm. In the remaining workspace, the accumulative deviation was less than 30 mm. Likewise, the accumulative deviation of a needle with a radius of 10 mm was 2.2 mm as opposed to 8 mm when the radius was 20 mm. The optimization-based algorithm maximized the accuracy of a four-DOF robot to perform a path-constrained trajectory and illustrates the accuracy-workspace correlation. [ABSTRACT FROM AUTHOR]

This letter considers a solar-powered unmanned aerial vehicle (UAV) system, where the UAV collects data from Internet of Things Devices (IoTDs) on the ground while also charging them using laser charging technology. Both the linear and nonlinear laser charging models are considered. We aim to maximize the residual energy of the UAV while satisfying the requirements of IoTDs by jointly optimizing the three-dimensional (3D) trajectory of UAV and scheduling for IoTDs. The optimization problem is formulated as a mixed integer non-convex problem which is difficult to solve in general. We apply the successive convex approximation and block coordinate descent algorithm to address this problem successfully. Simulation results verify the effectiveness of our algorithm compared with two benchmark methods. [ABSTRACT FROM AUTHOR]

The time-optimal trajectory planning problem involves minimizing the time required to follow a path defined in space, subject to kinematic and dynamic constraints. Here, we introduce a novel technique, called the bisection algorithm (BA), which is fully implemented in C++ and extends dynamic programming approaches to the problem. These approaches, which rely on dividing the global problem into a series of simpler subproblems, become increasingly advantageous compared to direct transcription methods as the number of problem constraints increases. In contrast to nearly all other dynamic programming approaches, BA does not rely on finding a maximum-velocity curve or explicitly finding acceleration switching points during the trajectory planning process. Additionally, only one forward and one backward integration are used, during which all constraints are imposed. This approach is made feasible through careful control of the numerical integration process and the use of a bisection algorithm to resolve constraint violations during integration. BA is shown to be significantly simpler, faster, and more robust than recently proposed algorithms: a direct comparison is made for a series of paths to be followed by a serial manipulator, subject to kinematic constraints. The wide applicability of BA is then established by solving the time-optimal problem for a parallel manipulator following a complex path, subject to both kinematic and dynamic constraints. [ABSTRACT FROM AUTHOR]

Recently, unmanned aerial vehicle (UAV) acts as the aerial mobile edge computing (MEC) node to help the battery-limited Internet of Things (IoT) devices relieve burdens from computation and data collection, and prolong the lifetime of operating. However, IoT devices can ONLY ask UAV for either computing or caching help, and collaborative offloading services of UAV are rarely mentioned in the literature. Moreover, IoT device has multiple mutually independent tasks, which make collaborative offloading policy design even more challenging. Therefore, we investigate a UAV-enabled MEC networks with the consideration of multiple tasks either for computing or caching. Taking the quality of experience (QoE) requirement of time-sensitive tasks into consideration, we aim to minimize the total energy consumption of IoT devices by jointly optimizing trajectory, communication and computing resource allocation at UAV, and task offloading decision at IoT devices. Since this problem has highly non-convex objective function and constraints, we first decompose the original problem into three subproblems named as trajectory optimization ( P T ), resource allocation at UAV ( P R ) and offloading decisions at IoT devices ( P O ) and then propose an iterative algorithm based on block coordinate descent method to cope with them in a sequence. Numerical results demonstrate that collaborative offloading can effectively reduce IoT devices' energy consumption while meeting different kinds of offloading services, and satisfy the QoE requirement of time-sensitive tasks at IoT devices. [ABSTRACT FROM AUTHOR]

In principle, the Automatic Identification System (AIS) makes covert rendezvous at sea, such as smuggling and piracy, impossible; in practice, AIS can be spoofed or simply disabled. Previous work showed a means whereby such deviations can be spotted. Here we play the opponent's side, and describe the least-detectable trajectory that the elusive vessel can take. The opponent's route planning problem is formalized as a non-convex optimization problem capitalizing the Kullback-Leibler (KL) divergence between the statistical hypotheses of the nominal and the anomalous trajectories as key performance measure. The velocity of the vessel is modeled with an Ornstein-Uhlenbeck (OU) mean reverting stochastic process, and physical and practical requirements are accounted for by enforcing several constraints at the optimization design stage. To handle the resulting non-convex optimization problem, we propose a globally-optimal and computationally-efficient technique, called the Non-Convex Optimized Stealth Trajectory (N-COST) algorithm. The N-COST algorithm consists amounts to solving multiple convex problems, with the number proportional to the number of segments of the piecewise OU trajectory. The effectiveness of the proposed approach is demonstrated through case studies and a real-world example. [ABSTRACT FROM AUTHOR]

This article proposes a computational trajectory optimization framework for solving the problem of multiobjective automatic parking motion planning. Constrained automatic parking maneuver problem is usually difficult to solve because of some practical limitations and requirements. This problem becomes more challenging when multiple objectives are required to be optimized simultaneously. The designed approach employs a swarm intelligent algorithm to produce the tradeoff front along the objective space. In order to enhance the local search ability of the algorithm, a gradient operation is utilized to update the solution. In addition, since the evolutionary process tends to be sensitive with respect to the flight control parameters, a novel adaptive parameter controller is designed and incorporated in the algorithm framework such that the proposed method can dynamically balance the exploitation and exploration. The performance of using the designed multiobjective strategy is validated and analyzed by performing a number of simulation and experimental studies. The results indicate that the present approach can provide reliable solutions and it can outperform other existing approaches investigated in this article. [ABSTRACT FROM AUTHOR]

Due to the small size, low cost, and autonomous nature, unmanned aerial vehicles (UAVs) have attracted growing attention in improving traditional networks’ performance. This paper considers a multi-UAV enabled large-scale wireless recharge networks, where a group of UAVs is dispatched as mobile wireless power transfer, and information collection systems to serve a set of ground low-power sensor nodes. Specifically, the UAVs employ radio frequency (RF) wireless power transfer (WPT) to supply energy towards the sensor nodes, and the communication services are available via wireless information transfer (WIT) systems. To achieve balanced energy consumption among UAVs, we maximize the energy utilization efficiency of UAVs, and minimize the communication delay by optimizing the trajectory jointly with constraints of the energy capacity, and the area of the target region. The formulated problem is a mixed-integer programming problem that is a variation of multiple traveling salesman problem. Thus we present a heuristic algorithm that combines the evolutionary algorithm, and variable neighborhood search to achieve the optimal visited sequence of the sensor nodes. Finally, extensive numerical results are provided to evaluate the performance of the proposed algorithm. It draws new insights on the estimation of the feasibility of the given UAVs whose energy capacity is limited. [ABSTRACT FROM AUTHOR]

With the exponential growth of data traffic, caching is regarded as a promising solution to combine with unmanned aerial vehicle (UAV)-assisted networks, which can offload cellular traffic and improve the system performance. Moreover, the cache capacity at user side can be leveraged, e.g., through local data storage or device-to-device (D2D) sharing. In this paper, we focus on the performance analysis and trajectory optimization of cache-enabled UAV-assisted networks with underlaid D2D communications. We consider both static and dynamic UAV deployments. For static UAV deployment, we first formulate an optimization problem to design the cache placement in order to maximize the cache hit probability. Then, the successful transfer probability (STP) and sum-rate are analyzed by using stochastic geometry, and their closed-form expressions are derived. For dynamic UAV deployment, the UAV moves over the cell and stops at several path points to serve users. To shorten the time required for the UAV to cover all users, a spiral algorithm is proposed to optimize the UAV trajectory, aiming at minimizing the number of UAV path points. Moreover, since at different locations, the UAV communication will incur different interference on D2D users, we derive the outage probability for the D2D users. Simulation results show the significant performance gain of our proposed probabilistic cache placement over existing strategies. For a given user density, we show that the optimal values for the UAV height which lead to the maximum UAV-STP and sum-rate exist. [ABSTRACT FROM AUTHOR]

An exoatmospheric midcourse guidance law is proposed to intercept a ballistic missile during the free-flight phase. The proposed guidance law generates a thrust direction command for an antiballistic missile to hit the target at the predicted intercept point. For the predicted intercept point, the zero-effort-miss and zero-effort-velocity are determined based on the solutions of the two-body orbital boundary/initial value problems. The intercept point is predicted by using the trajectory shaping parameter that combines the zero effort trajectory and minimum time trajectory. A response surface model for the minimum interception time is constructed as a database, which is the polynomial function of the initial condition. The response surface model provides a predicted minimum time interception position for the midcourse guidance. Case studies are performed to demonstrate the performance of the proposed guidance law considering various uncertainties. [ABSTRACT FROM AUTHOR]