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This paper introduces a comprehensive motion planning–tracking–safety constraint scheme for a 3D ballbot system. A nonlinear control for the 3D ballbot system is designed based on three separate planes by utilizing extended state observer (ESO) to estimate coupling mechanisms. Three virtual control signals are generated from these distinct planes and can be used for formulating actual control signals. To overcome the complexity of nonlinear motion equations, flatness theory is used to construct the time‐optimal trajectory through an optimization problem, facilitating smooth movement of the ballbot, and obstacle avoidance based on RRT* waypoints. Furthermore, our work manipulates the hierarchical sliding mode controller (HSMC) as the nominal controller to ensure that the ballbot tracks to the optimal trajectory, unifying with the exponential control barrier function (ECBF) to address safety constraints in the body's deflection angle. Through extensive simulations and comparative analysis, the system demonstrates its effectiveness and safe operation in various working conditions. [ABSTRACT FROM AUTHOR]

During terminal guidance, the attack platform is provided with a high‐resolution image of the target area through the application of synthetic aperture radar. Additionally, the stealth trajectory with low observability can significantly impact mission success. This paper considers both the performance of missile‐borne synthetic aperture radar imaging and stealth performance as influencing factors for terminal trajectory optimization, which is modelled as a constrained multi‐objective optimization problem. The application of the pseudospectral method in the solution of optimal control problems has led to the proposal of the hybrid genetic algorithm pseudospectral optimization framework. The problem is decomposed into several single‐objective optimal control problems, which can generate a specific initial population for the genetic algorithm to obtain a set of Pareto‐optimal solutions. Finally, the numerical simulations demonstrate the effectiveness of the proposed optimization approach compared with the benchmark scheme. [ABSTRACT FROM AUTHOR]

Video stabilization plays a pivotal role in enhancing video quality by eliminating unwanted jitter in shaky videos. This paper introduces a novel video stabilization algorithm that leverages low‐rank constraint and trajectory optimization to effectively eliminate undesirable motion and generate stabilized videos. In the proposed algorithm, a low‐rank constraint regularization term is incorporated to enhance the smoothness of motion trajectories. Additionally, a predictive path smoothness term is integrated to ensure the consistency of motion across neighbouring frames. To address the problem of excessive cropping resulting from aggressive smoothing, a flexible local window strategy that emphasizes local motion relationships within the trajectories is introduced. The experimental results show that, compared to other excellent video stabilization algorithms, the proposed algorithm improves the stability metric by approximately 2.3%. Furthermore, in the stabilized videos generated by the algorithm, an approximate improvement of 2.18 dB in average image temporal fidelity and a 5.7% increase in average structural similarity between adjacent frames are achieved. The code that implements the proposed method is publicly accessible at https://github.com/CZS0319/VS_Low‐Rank_Constraint_Trajectory_Optimization. [ABSTRACT FROM AUTHOR]

This paper presents a joint synthesis algorithm of trajectory and controlled invariant funnel (CIF) for locally Lipschitz nonlinear systems subject to bounded disturbances. The CIF synthesis refers to a procedure of computing controlled invariance sets and corresponding feedback gains. In contrast to existing CIF synthesis methods that compute the CIF with a predefined nominal trajectory, our work aims to optimize the nominal trajectory and the CIF jointly to satisfy feasibility conditions without the relaxation of constraints and obtain a more cost‐optimal nominal trajectory. The proposed work has a recursive scheme that mainly optimize trajectory update and funnel update. The trajectory update step optimizes the nominal trajectory while ensuring the feasibility of the CIF. Then, the funnel update step computes the funnel around the nominal trajectory so that the CIF guarantees an invariance property. As a result, with the optimized trajectory and CIF, any resulting trajectory propagated from an initial set by the control law with the computed feedback gain remains within the feasible region around the nominal trajectory under the presence of bounded disturbances. We validate the proposed method via two applications from robotics. [ABSTRACT FROM AUTHOR]

Nowadays, the digital development of marine ranching requires a communication system with wide coverage, high transmission rate and stable communication links. It is known that fixed‐wing unmanned aerial vehicles (UAVs) have great advantages in long‐range applications. They have the potential to serve as low‐altitude communication platforms for maritime communication. In this study, with a developmental perspective, considering the intense growth of marine terminals in the future, a new clustering algorithm applied to cluster nonorthogonal multiple access (C‐NOMA) is proposed and its advantages are investigated. In addition, considering the limited energy of marine terminals, combining the wireless power communication (WPC) technology for the UAV to charge terminals, the charging and communication time are optimized with the Lagrange multiplier method and the bisection search method. After completing the above optimization content of charging and communication, combined with the optimization results, it is found the trajectory that maximizes the energy efficiency of the UAV with the convex optimization technique. Experimental results show that the proposed clustering algorithm has good throughput performance, better fairness and lower algorithm complexity, and the proposed trajectory optimization scheme has better energy efficiency. [ABSTRACT FROM AUTHOR]

This article investigates a mobile edge computing (MEC) network assisted by multiple unmanned aerial vehicles (UAVs) to address the computational and offloading requirements for mobile intelligent terminals (MITs) within crowded venues. The objective is to tackle intricate task processing and diminish MITs' waiting times. Considering the randomness of task arrival at the MITs and the imbalance between the amount of data and computation for complex tasks, a dual‐queue model with data cache queue and computation queue is proposed, with minimizing the weighted system total energy consumption and average delay as the optimization objectives. Lyapunov optimization theory is employed to convert the stochastic optimization problem into a deterministic one, and the initial deployment quantity and hovering position of the UAVs are determined by the density‐based spatial clustering of applications with noise (DBSCAN) method with noise. Then PPO algorithm for MIT task, resource allocation, and UAV trajectory optimization. Numerical results display the proposed scheme can efficaciously diminish energy consumption and delay by 10% and 33% respectively, compared with the baseline scheme. This paper proposes a practical and feasible solution for stochastic computing offloading in UAV‐assisted MEC, which fills the gap in existing research on regarding the consideration of complex task imbalances. [ABSTRACT FROM AUTHOR]

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]

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]

Summary: UAVs are capable of providing significant potential to IoT devices through sensors, cameras, GPS systems, and so forth. Therefore, the smart UAV‐IoT collaborative system has become a current hot research topic. However, other concerns require in‐depth investigation and study, such as resource allocation, security, privacy preservation, trajectory optimization, intelligent decision‐making, energy harvesting, and so forth. Here, we suggest a task‐scheduling method that splits IoT devices into distinct clusters based on physical proximity and saves time and energy. Cluster heads can apply an auto regressive moving average (ARMA) model to predict intelligently the timestamp of the arrival of the next task and associated estimated payments. Based on the overall expected payment, a cluster head can smartly advise the UAV about its time of next arrival. According to the findings of the simulation, the proposed ETTS algorithm significantly outperforms Task TSIE and TDMA‐WS in terms of energy use (67%) and delays (36%). [ABSTRACT FROM AUTHOR]

We consider the problem of realigning a space telescope from one observation target to the next in the presence of prohibited directions. More specifically, we want to steer the space telescope – modelled as a gyrostat – from an initial attitude at rest to a final attitude at rest within a fixed time interval. During the motion, the line of sight of the telescope must be kept away from forbidden directions towards bright objects like the sun, moon or earth due to power or thermal requirements. The kinematics of the spacecraft motion are governed by a differential equation on the rotation group SO(3). Treating the angular velocities as control variables, this equation takes the form of a controlled dynamical system. To ensure reorientation maneuvers satisfying these pointing constraints, we introduce a cost functional penalizing proximity of the line of sight of the telescope to any of the forbidden directions. Furthermore, we include penalty terms which provide a smooth motion of the satellite and ensure the execution of a rest‐to‐rest maneuver. The chosen cost functional is minimized over all possible trajectories of the controlled dynamical system between the prescribed initial and target attitudes, which leads to an optimal control problem on SO(3), which is solved by applying a version of Pontryagin's Maximum Principle tailor‐made for optimal control problems on Lie groups. Parametrizing SO(3) in terms of Cardan angles, the solution is formulated as a boundary‐value problem on Euclidean space and hence can be solved numerically by conventional methods. The existence of two first integrals is established and exploited to reduce the computational effort. The applicability of this approach is shown in concrete examples. [ABSTRACT FROM AUTHOR]

With the massive application of unmanned aerial vehicles (UAVs) in disaster relief, fire protection, security and other fields, jamming countermeasures to UAVs in airports and competition venues have become the core link of security in high‐level matches and important places. The existing jamming sources are mainly single point jamming. Due to the shielding of buildings, it is impossible to fully cover the venue, and the existing suppressed jamming will affect the communication broadcasting. Here, a distributed optimal jamming method for massive UAVs is proposed. Through the identification and positioning of massive UAVs, using the location information of distributed jamming sources, the UAV jamming architecture based on satellite navigation is constructed. Combined with tabu search artificial bee colony theory, the distributed optimal jamming of UAVs is realized, which solves the problems of few jamming targets, slow speed and low success rate of the existing optimal jamming methods. The proposed method is compared with the existing methods in three aspects: communication frequency, jamming trajectory deviation and optimization speed. The simulation results show that the proposed method effectively improves the jamming success rate and jamming speed and can meet the application requirements of massive UAV jamming in the region. [ABSTRACT FROM AUTHOR]

Although unmanned aerial vehicle (UAV) relay can provide auxiliary communication due to its flexible mobility, it is vulnerable to jamming attacks. This paper considers the UAV relay anti‐jamming communication issue under the threat of a malicious jammer with beam‐forming jamming capability. To prevent the relay link from deteriorating, UAV trajectory adjustment and transmission mode switching between half‐duplex and full‐duplex are two available schemes, while they will incur the additional flying costs and continuous mode switching, respectively. To balance the trade‐off between trajectory optimization and mode selection, this paper investigates the joint trajectory optimization and mode selection anti‐jamming approach. First, an anti‐jamming utility considering the cost‐efficient and end‐to‐end capacity gains is designed. Second, to model the bounded rationality of both the UAV relay and the jammer due to the adversarial context, a biased Stackelberg game to analyse the competitive system interactions is proposed. Moreover, the existence of Stackelberg equilibrium (SE) in the problem is proved. Finally, a joint mode selection and trajectory optimization (JMSTO) algorithm based on the multi‐armed bandit is proposed to obtain the SE. It is further demonstrated that the JMSTO algorithm has a logarithmic regret. The results show that our proposed JMSTO algorithm is superior to non‐joint optimization methods. [ABSTRACT FROM AUTHOR]

Purpose: This work generates multi‐metastases cranial stereotactic radiosurgery/radiotherapy (SRS/SRT) plans using a novel treatment planning technique in which dynamic couch, collimator, and gantry trajectories are used with periodic binary target collimation. The performance of this planning technique is evaluated against conventional volumetric arc therapy (VMAT) planning in terms of various dose and plan quality metrics. Methods: A 3D cost space (referred to herein as the combined optimization of dynamic axes or CODA cube) was calculated based on an overlap between targets and organs‐at‐risk (OARs) and uncollimated areas between targets (island blocking) for all combinations of couch, gantry, and collimator angles. Gradient descent through the cube was applied to determine dynamic trajectories. At each control point (CP), each target can either be conformally treated or blocked by the multi‐leaf collimator (referred to as intra‐arc binary collimation, iABC). Simulated annealing was used to optimize the collimation patterns throughout the arcs as well as the monitor units (MUs) delivered at each CP. Seven previously treated VMAT plans were selected for comparison against the CODA–iABC planning technique. Two CODA–iABC plans were developed: a single gantry arc plan and a plan with one gantry arc and two couch arcs. Plan quality comparison metrics included maximum and mean dose to OARs (brainstem, chiasm, optic nerves, eyes, and lenses), the volume of normal brain receiving 12 Gy (V12Gy), total MUs, target conformity, and dose‐gradient index. Results: Treatment plans generated with 1‐arc CODA–iABC plans delivered an average of 21% and 30% higher maximum and mean doses to brainstem, respectively, when compared to VMAT plans. Treatment plans generated with 3‐arc CODA–iABC used an average of 24% fewer MUs and resulted in an average reduction of 48% maximum dose and 50% mean dose to the OARs, when compared to VMAT. Target conformity values were worse in both CODA–iABC plans than VMAT by an average of 35% and 15%, respectively. There are no significant differences in V12Gy for all three planning techniques; however, 3‐arc CODA–iABC is more effective at reducing dose to normal brain in the low‐dose region (<12 Gy). Conclusion: CODA–iABC is a novel planning technique that has been developed to automatically generate patient‐specific multi‐axis trajectories for multiple metastases cranial SRS/SRT. This work has demonstrated the feasibility of planning with this novel method. The 1‐arc CODA–iABC planning technique is slightly dosimetric inferior to VMAT. With an increased sampling of a three‐dimensional CODA cube by using a 3‐arc CODA–iABC technique, there was improved total dose sparing to all the OARs and increased MU efficiency, but with a cost in target conformity, when compared to VMAT. [ABSTRACT FROM AUTHOR]

Optimal transition has been widely studied for tail‐sitter unmanned aerial vehicles (UAVs). However, since the derived optimal control can only be applied in an open‐loop form, unmodeled dynamics and external disturbances cannot be restrained. Aiming at this problem, this article presents a method to obtain optimal transition maneuvers in the presence of these uncertainties. The approach includes two steps: nonlinear trajectory optimization and robust trajectory tracking. For the trajectory optimization, the minimum altitude variation front and back transition trajectories are derived. Different from existing optimal transition studies, considerable actuator margins are reserved in this step. Thus the tail‐sitter possesses control efforts to perform closed‐loop corrections for uncertainties. For the trajectory tracking, a robust controller in the form of feedforward plus feedback is proposed. The feedforward term directly employs the derived optimal control to improve the dynamic response of the system. The feedback term adopts linear control and acceleration‐based compensator to place desired poles and restrain all uncertainties. To the authors' knowledge, this article is the first time to study the tail‐sitter robust transition control method considering the transition optimality and actuator margins. It is proved that the tracking errors converge into a specified neighborhood of the origin in a finite time. Simulation studies corroborate the performance of the optimal transition trajectories and the robust trajectory tracking controller. [ABSTRACT FROM AUTHOR]

Purpose: In this work, we explore the potential of region‐of‐interest (ROI) imaging in x‐ray computed tomography (CT). Using two dynamic beam attenuator (DBA) concepts for fluence field modulation (FFM) previously developed, we investigate and evaluate the potential dose savings in comparison with current FFM technology. Methods: ROI imaging is a special application of FFM where the bulk of x‐ray radiation is propagated toward a certain anatomical target (ROI), specified by the imaging task, while the surrounding tissue is spared from radiation. We introduce a criterion suitable to quantitatively describe the balance between image quality inside an ROI and total radiation dose with respect to a given ROI imaging task. It accounts for the mean image variance at the ROI and the effective patient dose calculated from Monte Carlo simulations. The criterion is further used to compile task‐specific DBA trajectories determining the primary x‐ray fluence, and eventually used for comparing different FFM techniques, namely the sheet‐based dynamic beam attenuator (sbDBA), the z‐aligned sbDBA (z‐sbDBA), and an adjustable static operation mode of the z‐sbDBA. Furthermore, two static bowtie filters and the influence of tube current modulation (TCM) are included in the comparison. Results: Our findings demonstrate by simulations that the presented trajectory optimization method determines reasonable DBA trajectories. The influence of TCM is strongly depending on the imaging task. The narrow bowtie filter allows for dose reductions of about 10% compared to the regular bowtie filter in the considered ROI imaging tasks. The DBAs are shown to realize substantially larger dose reductions. In our cardiac imaging scenario, the DBAs can reduce the effective dose by about 30% (z‐sbDBA) or 60% (sbDBA). We can further verify that the noise characteristics are not adversely affected by the DBAs. Conclusion: Our research demonstrates that ROI imaging using the presented DBA concepts is a promising technique toward a more patient‐ and task‐specific CT imaging requiring lower radiation dose. Both the sbDBA and the z‐sbDBA are potential technical solutions for realizing ROI imaging in x‐ray CT. [ABSTRACT FROM AUTHOR]

Symbolic circuit analysis suffers as the symbolic terms increases by many folds with the increase in the size of the circuit. Hence simplification techniques are used for the analysis of the circuits which are larger in size. In this work, multi‐objective evolutionary optimisation algorithms for obtaining simplified symbolic expressions of analog amplifier circuits are presented which are not only very efficient in terms of speed and the amount of circuit reduction but also solve the accuracy problems. Initially, all MOSFETs are replaced with their nullor equivalent model. Then, the formulation of accurate fully‐symbolic noise expressions is carried out by the application of symbolic nodal analysis. The derived exact symbolic expressions are then simplified using an evolutionary approach. This method has been successfully coded in MATLAB. The numerical results obtained before and after simplification are compared with SPICE simulation to demonstrate the efficiency of the proposed methodology. [ABSTRACT FROM AUTHOR]

The loss function of the deep neural network is high dimensional, nonconvex and complex. So far, the geometric properties of the loss surface of the neural network have not been well understood. Different from most theoretical studies on the loss surface, this article makes the experimental exploration on the loss surface of the deep neural network, including trajectories of various adaptive optimization algorithms, the Hessian matrix of the loss function of the deep neural network, the curvature of the loss surface along the trajectories of the various adaptive optimization algorithms. It is found that the gradient direction of the adaptive optimization algorithms is almost perpendicular to the direction of the maximum curvature of the loss surface, while the gradient directions of the stochastic gradient descent (SGD) algorithm do not have such a rule. The Hessian matrix of the loss surface along the trajectory of the optimization algorithm is degraded, which is inconsistent with the hypothetical that nonsingular of the Hessian matrix in many theoretical studies of deep learning. Besides, this article proposes a new ensemble learning method of the neural network based on the scaling invariance of the ReLu neural network and mode connectivity. [ABSTRACT FROM AUTHOR]

We examine the relationship between primal, or force‐based, and dual, or constraint‐based formulations of dynamics. Variational frameworks such as Projective Dynamics have proved popular for deformable simulation, however they have not been adopted for contact‐rich scenarios such as rigid body simulation. We propose a new preconditioned frictional contact solver that is compatible with existing primal optimization methods, and competitive with complementarity‐based approaches. Our relaxed primal model generates improved contact force distributions when compared to dual methods, and has the advantage of being differentiable, making it well‐suited for trajectory optimization. We derive both primal and dual methods from a common variational point of view, and present a comprehensive numerical analysis of both methods with respect to conditioning. We demonstrate our method on scenarios including rigid body contact, deformable simulation, and robotic manipulation. [ABSTRACT FROM AUTHOR]

Purpose: We developed a target‐based cone beam computed tomography (CBCT) imaging framework for optimizing an unconstrained three dimensional (3D) source‐detector trajectory by incorporating prior image information. Our main aim is to enable a CBCT system to provide topical information about the target using a limited angle noncircular scan orbit with a minimal number of projections. Such a customized trajectory should include enough information to sufficiently reconstruct a particular volume of interest (VOI) under kinematic constraints, which may result from the patient size or additional surgical or radiation therapy‐related equipment. Methods: A patient‐specific model from a prior diagnostic computed tomography (CT) volume is used as a digital phantom for CBCT trajectory simulations. Selection of the best projection views is accomplished through maximizing an objective function fed by the imaging quality provided by different x‐ray positions on the digital phantom data. The final optimized trajectory includes a limited angular range and a minimal number of projections which can be applied to a C‐arm device capable of general source‐detector positioning. The performance of the proposed framework is investigated in experiments involving an in‐house‐built box phantom including spherical targets as well as an Alderson‐Rando head phantom. In order to quantify the image quality of the reconstructed image, we use the average full‐width‐half‐maximum (FWHMavg) for the spherical target and feature similarity index (FSIM), universal quality index (UQI), and contrast‐to‐noise ratio (CNR) for an anatomical target. Results: Our experiments based on both the box and head phantom showed that optimized trajectories could achieve a comparable image quality in the VOI with respect to the standard C‐arm circular CBCT while using approximately one quarter of projections. We achieved a relative deviation <7% for FWHMavg between the reconstructed images from the optimized trajectories and the standard C‐arm CBCT for all spherical targets. Furthermore, for the anatomical target, the relative deviation of FSIM, UQI, and CNR between the reconstructed image related to the proposed trajectory and the standard C‐arm circular CBCT was found to be 5.06%, 6.89%, and 8.64%, respectively. We also compared our proposed trajectories to circular trajectories with equivalent angular sampling as the optimized trajectories. Our results show that optimized trajectories can outperform simple partial circular trajectories in the VOI in term of image quality. Typically, an angular range between 116° and 152° was used for the optimized trajectories. Conclusion: We demonstrated that applying limited angle noncircular trajectories with optimized orientations in 3D space can provide a suitable image quality for particular image targets and has a potential for limited angle and low‐dose CBCT‐based interventions under strong spatial constraints. [ABSTRACT FROM AUTHOR]

Purpose: Trajectory‐based treatment planning involves the combination of a gantry‐couch trajectory with volumetric modulated arc therapy (VMAT) treatment plan optimization. This work presents the implementation of an optimization methodology that generates a trajectory simultaneous with treatment plan optimization (simTr‐VMAT). Methods: The optimization algorithm is based on the column generation approach, in which a treatment plan is iteratively constructed through the solution of a subproblem called the "pricing problem." The property of the pricing problem to rank candidate apertures based on their associated price is leveraged to select an optimal aperture while simultaneously determining the trajectory path. A progressively increasing gantry‐couch grid resolution is used to provide an initial coarse sampling of the angular solution space while maintaining fine control point spacing with the final treatment plan. The trajectory optimization was applied and compared to coplanar VMAT treatment plans for a lung patient, a glioblastoma patient, and a prostate patient. Algorithm validation was performed through the generation of 5000 random trajectories and optimization using column generation VMAT for each patient case, representing the solution space for the trajectory optimization problem. The simTr‐VMAT trajectories were compared against these random trajectories based on a quality metric that prefers trajectories with few control points and low objective function value over long, inefficient trajectories. Results: For the lung patient, the simTr‐VMAT plan resulted in a decrease of the mean dose of 1.5 and 1.0 Gy to the heart and ipsilateral lung, respectively. For the glioblastoma patient, the simTr‐VMAT plan resulted in improved planning target volume coverage with a decrease in mean dose to the eyes, lens, nose, and contralateral temporal lobe between 2 and 7 Gy. The prostate patient showed no clinically relevant dosimetric improvement. The simTr‐VMAT treatment plans ranked at the 99.6, 96.3, and 99.4 percentiles compared to the distribution of randomly generated trajectories for the lung, glioblastoma, and prostate patients, respectively. Conclusion: The simTr‐VMAT optimization methodology resulted in treatment plans with equivalent or improved dosimetric outcomes compared to coplanar VMAT treatment plans, with the trajectories resulting from the optimization ranking among the optimal trajectories for each patient case. [ABSTRACT FROM AUTHOR]

Rationale: With the recent introduction of the dynamically harmonized Fourier‐transform ion cyclotron resonance (FT‐ICR) cell, the complexity of tuning has expanded drastically, and fine‐tuning of the direct current voltages is required to optimize the ion cloud movement. As this adjustment must typically be performed manually, more reliable computational methods would be useful. Methods: Here we propose a computational method based on a design of experiments (DoE) strategy to overcome the limits of classical manual tuning. This DoE strategy was exemplarily applied on a 12 T FT‐ICR instrument equipped with a dynamically harmonized ICR cell. The chemometric approach, based on a central composite face (CCF) design, was first applied to a reference material (sodium trifluoroacetate) allowing for the evaluation of the primary cell parameters. Eight factors related to shimming and gating were identified. The summed intensity of the signal corresponding to the even harmonics was defined as one quality criterion. Results: The DoE response allowed for rapid and complete mapping of cell parameters resulting in an optimized parameter set. The new set of cell parameters was applied to the study of an ultra‐complex sample: Tholins, an ultra‐complex mixture that mimics the haze present on Titan, was chosen. We observed a substantial improvement in mass spectrometric performance. The sum of signals related to harmonics was decreased by a factor of three (from 4% for conventional tuning to 1.3%). Furthermore, the dynamic range was also increased, which in turn led to an increase in attributed peaks by 13%. Conclusions: This computational procedure based on an experimental design can be applied to any other mass spectrometric parameter optimization problem. This strategy will lead to a more transparent and data‐driven method development. [ABSTRACT FROM AUTHOR]

We consider the problem of parameter estimation in the case of observation of the trajectory of the diffusion process. We suppose that the drift coefficient has a singularity of cusp type and that the unknown parameter corresponds to the position of the point of the cusp. The asymptotic properties of the maximum likelihood estimator and Bayesian estimators are described in the asymptotic of small noise, that is, as the diffusion coefficient tends to zero. The consistency, limit distributions, and the convergence of moments of these estimators are established. [ABSTRACT FROM AUTHOR]

In this study, we propose a novel optimization algorithm, with application to the refinement of molecular complexes. Particularly, we consider optimization problem as the calculation of quasi‐static trajectories of rigid bodies influenced by the inverse‐inertia‐weighted energy gradient and introduce the concept of advancement region that guarantees displacement of a molecule strictly within a relevant region of conformational space. The advancement region helps to avoid typical energy minimization pitfalls, thus, the algorithm is suitable to work with arbitrary energy functions and arbitrary types of molecular complexes without necessary tuning of its hyper‐parameters. Our method, called controlled‐advancement rigid‐body optimization of nanosystems (Carbon), is particularly useful for the large‐scale molecular refinement, as for example, the putative binding candidates obtained with protein–protein docking pipelines. Implementation of Carbon with user‐friendly interface is available in the SAMSON platform for molecular modeling at https://www.samson-connect.net. © 2019 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Figure skating is one of the most popular ice sports at the Winter Olympic Games. The skaters perform several skating skills to express the beauty of the art on ice. Skating involves moving on ice while wearing skate shoes with thin blades; thus, it requires much practice to skate without losing balance. Moreover, figure skating presents dynamic moves, such as jumping, artistically. Therefore, demonstrating figure skating skills is even more difficult to achieve than basic skating, and professional skaters often fall during Winter Olympic performances. We propose a system to demonstrate figure skating motions with a physically simulated human‐like character. We simulate skating motions with non‐holonomic constraints, which make the skate blade glide on the ice surface. It is difficult to obtain reference motions from figure skaters because figure skating motions are very fast and dynamic. Instead of using motion capture data, we use key poses extracted from videos on YouTube and complete reference motions using trajectory optimization. We demonstrate figure skating skills, such as crossover, three‐turn, and even jump. Finally, we use deep reinforcement learning to generate a robust controller for figure skating skills. [ABSTRACT FROM AUTHOR]

Purpose: Dose calculation is one of the most computationally intensive, yet essential tasks in the treatment planning process. With the recent interest in automatic beam orientation and arc trajectory optimization techniques, there is a great need for more efficient model‐based dose calculation algorithms that can accommodate hundreds to thousands of beam candidates at once. Foundational work has shown the translation of dose calculation algorithms to graphical processing units (GPUs), lending to remarkable gains in processing efficiency. But these methods provide parallelization of dose for only a single beamlet, serializing the calculation of multiple beamlets and under‐utilizing the potential of modern GPUs. In this paper, the authors propose a framework enabling parallel computation of many beamlet doses using a novel beamlet context transformation and further embed this approach in a scalable network of multi‐GPU computational nodes. Methods: The proposed context‐based transformation separates beamlet‐local density and TERMA into distinct beamlet contexts that independently provide sufficient data for beamlet dose calculation. Beamlet contexts are arranged in a composite context array with dosimetric isolation, and the context array is subjected to a GPU collapsed‐cone convolution superposition procedure, producing the set of beamlet‐specific dose distributions in a single pass. Dose from each context is converted to a sparse representation for efficient storage and retrieval during treatment plan optimization. The context radius is a new parameter permitting flexibility between the speed and fidelity of the dose calculation process. A distributed manager‐worker architecture is constructed around the context‐based GPU dose calculation approach supporting an arbitrary number of worker nodes and resident GPUs. Phantom experiments were executed to verify the accuracy of the context‐based approach compared to Monte Carlo and a reference CPU‐CCCS implementation for single beamlets and broad beams composed by addition of beamlets. Dose for representative 4π beam sets was calculated in lung and prostate cases to compare its efficiency with that of an existing beamlet‐sequential GPU‐CCCS implementation. Code profiling was also performed to evaluate the scalability of the framework across many networked GPUs. Results: The dosimetric accuracy of the context‐based method displays <1.35% and 2.35% average error from the existing serialized CPU‐CCCS algorithm and Monte Carlo simulation for beamlet‐specific PDDs in water and slab phantoms, respectively. The context‐based method demonstrates substantial speedup of up to two orders of magnitude over the beamlet‐sequential GPU‐CCCS method in the tested configurations. The context‐based framework demonstrates near linear scaling in the number of distributed compute nodes and GPUs employed, indicating that it is flexible enough to meet the performance requirements of most users by simply increasing the hardware utilization. Conclusions: The context‐based approach demonstrates a new expectation of performance for beamlet‐based dose calculation methods. This approach has been successful in accelerating the dose calculation process for very large‐scale treatment planning problems ‐ such as automatic 4π IMRT beam orientation and VMAT arc trajectory selection, with hundreds of thousands of beamlets ‐ in clinically feasible timeframes. The flexibility of this framework makes it as a strong candidate for use in a variety of other very large‐scale treatment planning tasks and clinical workflows. [ABSTRACT FROM AUTHOR]

Summary In this paper, a unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes is proposed. A feasible reference trajectory taking constraints into consideration is first generated offline by the symplectic pseudospectral optimal control method. Then, a trajectory tracking model predictive controller also based on the symplectic pseudospectral method is developed to track the reference trajectory. At each sampling instant, the trajectory tracking controller works by solving an open‐loop optimal control problem where linearized system dynamics is used instead to improve the computational efficiency. Since the symplectic pseudospectral optimal control method is the core algorithm for both offline trajectory planning and online trajectory tracking, constraints on state variables and control inputs can be easily imposed and hence theoretically guaranteed in solutions. By selecting proper weighted matrices on tracking error and control, the developed controller could achieve control objectives in both accurate trolley positioning and fast suppressing of residual swing angles. Simulations for 3D overhead crane systems in the presence of perturbations in initial conditions, an abrupt variation of system parameter, and various external disturbances demonstrate that the developed controller is robust and of excellent control performance. [ABSTRACT FROM AUTHOR]

Pytim is a versatile python framework for the analysis of interfacial properties in molecular simulations. The code implements several algorithms for the identification of instantaneous interfaces of arbitrary shape, and analysis tools written specifically for the study of interfacial properties, such as intrinsic profiles. The code is written in the python language, and makes use of the numpy and scipy packages to deliver high computational performances. Pytim relies on the MDAnalysis library to analyze the trajectory file formats of popular simulation packages such as gromacs, charmm, namd, lammps or Amber, and can be used to steer OpenMM simulations. Pytim can write information about surfaces and surface atomic layers to vtk, cube, and pdb files for easy visualization. The classes of Pytim can be easily customized and extended to include new interfacial algorithms or analysis tools. The code is available as open source and is free of charge. © 2018 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc Determining the interface between fluid phases described at the molecular level is a complicated problem with no unique solution. The experimental nature of many of the available codes represents a severe limitation to the wider diffusion of such kind of analysis. The authors present a python package that implements several algorithms for the analysis of intrinsic interfaces, allows to analyze the most popular trajectory formats with minimal scripting efforts. [ABSTRACT FROM AUTHOR]

Advances in biomolecular simulation methods and access to large scale computer resources have led to a massive increase in the amount of data generated. The key enablers have been optimization and parallelization of the simulation codes. However, much of the software used to analyze trajectory data from these simulations is still run in serial, or in some cases many threads via shared memory. Here, we describe the addition of multiple levels of parallel trajectory processing to the molecular dynamics simulation analysis software CPPTRAJ. In addition to the existing OpenMP shared‐memory parallelism, CPPTRAJ now has two additional levels of message passing (MPI) parallelism involving both across‐trajectory processing and across‐ensemble processing. All three levels of parallelism can be simultaneously active, leading to significant speed ups in data analysis of large datasets on the NCSA Blue Waters supercomputer by better leveraging the many available nodes and its parallel file system. © 2018 Wiley Periodicals, Inc. Advances in MD simulation speed has enabled the generation of terabytes of data. This article describes how the MD simulation data analysis tool CPPTRAJ has been parallelized to take advantage of modern HPC hardware to accelerate data analysis. [ABSTRACT FROM AUTHOR]

Purpose: Although volumetric modulated arc therapy (VMAT) is a well‐accepted treatment technique in radiotherapy using a coplanar delivery approach, VMAT might be further improved by including dynamic table and collimator rotations leading to dynamic trajectory radiotherapy (DTRT). In this work, an optimization procedure for DTRT was developed and the potential benefit of DTRT was investigated for different treatment sites. Methods: For this purpose, a dedicated optimization framework for DTRT was developed using the Eclipse Scripting Research Application Programming Interface (ESRAPI). The contours of the target and organs at risk (OARs) structures were exported by applying the ESRAPI and were used to determine the fractional volume‐overlap of the OARs with the target from several potential beam directions. Thereby, an additional weighting was applied taking into account the relative position of the OAR with respect to the target and radiation beam, that is, penalizing directions where the OAR is proximal to the target. The resulting two‐dimensional gantry‐table map was used as input for an A* path finding algorithm returning an optimized gantry‐table path. Thereby, the process is also taking into account CT scan length and collision restrictions. The A* algorithm was used again to determine the dynamic collimator angle path by optimizing the area between the MLC leaves and the target contour for each gantry‐table path leading to gantry‐collimator paths. The resulting gantry‐table and gantry‐collimator paths are combined and serve as input for the intensity modulation optimization using a research VMAT optimizer and the ESRAPI resulting in dynamic trajectories. This procedure was evaluated for five clinically motivated cases: two head and neck, one lung, one esophagus, and one prostate. Final dose calculations were performed using the Swiss Monte Carlo Plan (SMCP). Resulting dose distributions for the DTRT treatment plans and for the standard VMAT plans were compared based on dose distributions and dose volume histogram (DVH) parameters. For this comparison, the dose distribution for the VMAT plans were recalculated using the SMCP. In addition, the suitability of the delivery of a DTRT treatment plan was demonstrated by means of gafchromic film measurements on a TrueBeam linear accelerator. Results: DVHs for the target volumes showed similar or improved coverage and dose homogeneity for DTRT compared with VMAT using equal or less number of dynamic trajectories for DTRT than arcs for VMAT for all cases studied. Depending on the case, improvements in mean and maximum dose for the DTRT plans were achieved for almost all OARs compared with the VMAT plans. Improvements in DTRT treatment plans for mean and maximum dose compared to VMAT plans were up to 16% and 38% relative to the prescribed dose, respectively. The measured and calculated dose values resulted in a passing rate of more than 99.5% for the two‐dimensional gamma analysis using 2% and 2 mm criteria and a threshold of 10%. Conclusions: DTRT plans for different treatment sites were generated and compared with VMAT plans. The delivery is suitable and dose comparisons demonstrate a high potential of DTRT to reduce dose to OARs using less dynamic trajectories than arcs, while target coverage is preserved. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study was to develop a treatment technique for dynamic mixed beam radiotherapy (DYMBER) utilizing increased degrees of freedom (DoF) of a conventional treatment unit including different particle types (photons and electrons), intensity and energy modulation and dynamic gantry, table, and collimator rotations. Methods: A treatment planning process has been developed to create DYMBER plans combining photon dynamic trajectories (DTs) and step and shoot electron apertures collimated with the photon multileaf collimator (pMLC). A gantry‐table path is determined for the photon DTs with minimized overlap of the organs at risk (OARs) with the target. In addition, an associated dynamic collimator rotation is established with minimized area between the pMLC leaves and the target contour. pMLC sequences of photon DTs and electron pMLC apertures are then simultaneously optimized using direct aperture optimization (DAO). Subsequently, the final dose distribution of the electron pMLC apertures is calculated using the Swiss Monte Carlo Plan (SMCP). The pMLC sequences of the photon DTs are then re‐optimized with a finer control point resolution and with the final electron dose distribution taken into account. Afterwards, the final photon dose distribution is calculated also using the SMCP and summed together with the one of the electrons. This process is applied for a brain and two head and neck cases. The resulting DYMBER dose distributions are compared to those of dynamic trajectory radiotherapy (DTRT) plans consisting only of photon DTs and clinically applied VMAT plans. Furthermore, the deliverability of the DYMBER plans is verified in terms of dosimetric accuracy, delivery time and collision avoidance. For this purpose, The DYMBER plans are delivered to Gafchromic EBT3 films placed in an anthropomorphic head phantom on a Varian TrueBeam linear accelerator. Results: For each case, the dose homogeneity in the target is similar or better for DYMBER compared to DTRT and VMAT. Averaged over all three cases, the mean dose to the parallel OARs is 16% and 28% lower, D2% to the serial OARs is 17% and 37% lower and V10% to normal tissue is 12% and 4% lower for the DYMBER plans compared to the DTRT and VMAT plans, respectively. The DYMBER plans are delivered without collision and with a 4–5 min longer delivery time than the VMAT plans. The absolute dose measurements are compared to calculation by gamma analysis using 2% (global)/2 mm criteria with passing rates of at least 99%. Conclusions: A treatment technique for DYMBER has been successfully developed and verified for its deliverability. The dosimetric superiority of DYMBER over DTRT and VMAT indicates utilizing increased DoF to be the key to improve brain and head and neck radiation treatments in future. [ABSTRACT FROM AUTHOR]

The paper presents a feedback control design that allows a Dubins vehicle to enter a circular trajectory using only range-based measurements from the vehicle to the center of the trajectory. The controller is derived and analyzed based on a novel state space kinematic model, with the state that is composed of two continuous and one discrete state variables.The evolution of the discrete state variable is not completely defined by the model and the control design has to deal with the ambiguity of this value. Based on the conditions that need to be satisfied for the controller to work, the closed loop dynamics analysis can be performed based on 2D phase portraits, and it can be shown that the controller can work in the case of the bounded turning rate of the vehicle. The conditions define only bounds for the controller parameters and not their specific values. Therefore, the parameters can be selected based on the maximal working range of the controller and linear quadratic regulator design. The proposed control design is illustrated by 2D phase portraits and simulations describing the control implementation, which is based only on range measurements. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Purpose A challenging problem in trajectory optimization for radiotherapy is properly handling the synchronization of the medical accelerators dynamic delivery. The initial coarse sampling of control points implemented in a Progressive Resolution Optimization type approach ( VMAT) routinely results in MLC aperture forming contention issues as the sampling resolution increases. This work presents an approach to optimize continuous, beam-on radiation trajectories through exploration of the anatomical topology present in the patient and formation of a novel dual-metric graph optimization problem. Methods This work presents a new perspective on trajectory optimization in radiotherapy using the concept of sectioning ( TORUS). TORUS avoids degradation of 3D dose optimization quality by mapping the connectedness of target regions from the BEV perspective throughout the space of deliverable coordinates. This connectedness information is then incorporated into a graph optimization problem to define ideal trajectories. The unique usage of two distance functions in this graph optimization permits the TORUS algorithm to generate efficient dynamic trajectories for delivery while maximizing the angular flux through all PTV voxels. 3D dose optimization is performed for trajectories using a commercial TPS progressive resolution optimizer. Results The TORUS algorithm is applied to three example treatments: chest wall, scalp, and the TG-119 C-shape phantom. When static collimator coplanar trajectories are generated for the chest wall and scalp cases, the TORUS trajectories are found to outperform both 7 field IMRT and 2 arc VMAT plans in delivery time, organ at risk sparing, conformality, and homogeneity. For the TG-119 phantom, when static couch and collimator non-coplanar trajectories are optimized, TORUS trajectories have superior sparing of the central core avoidance with shorter delivery times, with similar dose conformality and homogeneity. Conclusions The TORUS algorithm is able to automatically generate trajectories having improved plan quality and delivery time over standard IMRT and VMAT treatments. TORUS offers an exciting and promising avenue forward toward increasing dynamic capabilities in radiation delivery. [ABSTRACT FROM AUTHOR]

This study aimed to organize a body of trajectories in order to identify, search for and classify both common and uncommon behaviors among objects such as aircraft and ships. Existing comparison functions such as the Fréchet distance are computationally expensive and yield counterintuitive results in some cases. We propose an approach using feature vectors whose components represent succinctly the salient information in trajectories. These features incorporate basic information such as the total distance traveled and the distance between start/stop points as well as geometric features related to the properties of the convex hull, trajectory curvature and general distance geometry. Additionally, these features can generally be mapped easily to behaviors of interest to humans who are searching large databases. Most of these geometric features are invariant under rigid transformation. We demonstrate the use of different subsets of these features to identify trajectories similar to an exemplar, cluster a database of several hundred thousand trajectories and identify outliers. [ABSTRACT FROM AUTHOR]

This paper proposes an extension to trajectory optimization using mixed-integer linear programming. The purpose of the extension is to ensure that avoidance constraints are respected at all times between discrete samples, not just at the sampling times themselves. The method is very simple and involves applying the same switched constraints at adjacent time steps. This requires fewer additional constraints than the existing approach and is shown to reduce computation time. A key benefit of efficient inter-sample avoidance is the facility to reduce the number of time steps without having to compensate by enlarging the obstacles. A further extension to the principle is presented to account for curved paths between samples, proving useful in cases where narrow passageways are traversed. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes a novel approach of maximum power control for small wind turbines by using predicted wind speed data. Because of the moment of inertia of the wind turbine, when using conventional control method, the time lag of control will occur due to turbulence in the environment. Our proposed control system uses future information, which is the predicted wind speed, for wind turbine control. The control algorithm creates a reference trajectory of the rotational speed of the wind turbine. The advantage of using the predicted data is that the controller can operate the wind turbine efficiently so that the rotational speed of the wind turbine catches up with the reference speed at the maximum power point. Simulation results show improvement of generation efficiency compared to the conventional control method. Then we discuss the influence of the prediction error of wind speed on control performance. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

Volume 20 (2020), Issue 1 of PAMM "Proceedings in Applied Mathematics and Mechanics" assembles the contributions to the 91st Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (GAMM), organized in 2020 by Universität Kassel, Germany, and held as a virtual conference. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections GAMM related DFG Priority Programmes DFG‐PP 1748 Reliable Simulation Techniques in Solid Mechanics. Development of Non‐Standard Discretization Methods, Mechanical and Mathematical Analysis DFG‐PP 1881 Turbulent Superstructure DFG‐PP 1886 Polymorphic Uncertainty Modelling for the Numerical Design of Structures DFG‐PP 1897 Calm, Smooth and Smart – Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation DFG‐PP 2020 Cyclic Deterioration of High‐Performance Concrete in an Experimental‐Virtual Lab Minisymposia MS 1 Computational Photonics MS 3 Dissipativity, turnpikes and optimal control MS 4 Advanced experimental and computational techniques in polymer mechanics Sections 1–24 S1 Multi‐body dynamics S2 Biomechanics S3 Damage and fracture mechanics S4 Structural mechanics S5 Nonlinear oscillations S6 Material modelling in solid mechanics S7 Coupled problems S8 Multiscales and homogenization S9 Laminar flows and transition S10 Turbulence and reactive flows S11 Interfacial flows S12 Waves and acoustics S13 Flow control S14 Applied analysis S15 Uncertainty quantification S16 Optimization S17 Applied and numerical linear algebra S18 Numerical methods of differential equations S19 Optimization of differential equations S20 Dynamics and control S21 Mathematical signal and image processing S22 Scientific computing S24 History of mechanics Young Researchers' Minisymposia YRM1 Algorithms for coupled multi‐physics problems YRM2 Rank structured matrix and tensor techniques YRM6 Novel discretization methods for phase‐field modeling in fracture mechanics [ABSTRACT FROM AUTHOR]

Flatness‐based trajectory planning for the distributed‐parameter system consisting of a rigid body carried by multiple heavy ropes is discussed. The suspension points (controlled ends) of the ropes are assumed to be freely movable. The other ends of the ropes are parametrized by a flat output of the nonlinear boundary system at the load that describes the motion of the rigid body. This parametrization is then used to express the solution of the linearized partial differential equations for the heavy ropes under small angle approximations around a vertical equilibrium configuration by the means of operational calculus. It is shown that the system trajectories of the ropes depend on distributed delays and advances of the flat output trajectory at the load‐side boundary system. Evaluating the derived parametrization of the heavy ropes at the controllable ends yields the desired open‐loop controller by using a planned trajectory for the flat output. This control can be used to realize a desired transition of the load position and orientation in finite time. The introduced method is illustrated for the example of a linear infinite‐dimensional model of two heavy ropes carrying a rigid rod. [ABSTRACT FROM AUTHOR]

This contribution focuses on the optimal trajectory planning for a Segway model (inverted pendulum on two independently actuated wheels). Basis for this planning is the dynamical model for this under‐actuated, non‐holonomic multibody system. For the stabilization as well as the trajectory control, a partial input/output linearization is performed, where the orientation of the robot w.r.t. the horizontal plane and the inclination angle of the pendulum are used as output. The remaining non‐linear part is linearized about the upright equilibrium position and stabilized with an LQR controller. The trajectory optimization is based on the partially linearized system, where the output (orientation and inclination) is parameterized by B‐Splines. The system is required to move through predefined points in the horizontal plane. For the optimization the control points of the B‐Splines serve as optimization variables and the overall energy of the robot serves as cost functional. Maximum motor velocities, motor torques and the ground reaction forces are the constraints. The latter are crucial when planning trajectories where the robot must pass (swing) under vertical obstacles while not losing ground contact. These maneuvers are characterized by high horizontal accelerations in order to lower the head of the robot and bring it back to upright equilibrium. [ABSTRACT FROM AUTHOR]

Mobile data collection is one of research highlights for sparse threedimensional underwater sensor networks. Therein, optimal or nearoptimal cruise trajectory planning of mobile sink is very crucial. A 3D Dubins curves based continuous path programming algorithm (GA-3DTSP in short) for underwater mobile sink with non-holonomic constraints such as well-known autonomous underwater vehicle is proposed. The objective of GA-3DTSP algorithm is to trace sparsely deployed sensor nodes by mobile sink so as to achieve near-optimal energy conservation efficiency. First, an extended 3D Dubins curve is proposed and the length calculation formulae for 3D Dubins curve are investigated. Furthermore, genetic algorithm is used to tackle this difficult NP-complete problem of planning shortest paths in a heuristic manner. Finally, simulation results verify that the proposed GA- 3DTSP method can conserve cruise energy of mobile sink effectively. [ABSTRACT FROM AUTHOR]

Abstract: Trajectory clustering, which aims at discovering groups of similar trajectories, has long been considered as a corner stone task for revealing movement patterns as well as facilitating higher level applications such as location prediction and activity recognition. Although a plethora of trajectory clustering techniques have been proposed, they often rely on spatio‐temporal similarity measures that are not space and time invariant. As a result, they cannot detect trajectory clusters where the within‐cluster similarity occurs in different regions and time periods. In this paper, we revisit the trajectory clustering problem by learning quality low‐dimensional representations of the trajectories. We first use a sliding window to extract a set of moving behaviour features that capture space‐ and time‐invariant characteristics of the trajectories. With the feature extraction module, we transform each trajectory into a feature sequence to describe object movements and further employ a sequence‐to‐sequence auto‐encoder to learn fixed‐length deep representations. The learnt representations robustly encode the movement characteristics of the objects and thus lead to space‐ and time‐invariant clusters. We evaluate the proposed method on both synthetic and real data and observe significant performance improvements over existing methods. [ABSTRACT FROM AUTHOR]

Enhancing the performance of passive target tracking and trajectory estimation of marine traffic ships is focused using a monocular camera mounted on an unmanned surface vessel. To accurately estimate the trajectory of a target traffic ship, the relative bearing and range information between the observing ship and the target ship is required. Monocular vision provides bearing information with reasonable accuracy but with no explicit range information. The relative range information can be extracted from the bearing changes induced by the relative ship motion in the framework of bearings-only tracking (BOT). BOT can be effective in crossing situations with large bearing angle changes. However, it often fails in head-on or overtaking situations due to small bearing angle changes and the resulting low observability of the tracking filter. To deal with the lack of observability, the vertical pixel distance between the horizon and the target ship in the image is used, which improves the overall target tracking performance. The feasibility and performance of the proposed tracking approach were validated through field experiments at sea. [ABSTRACT FROM AUTHOR]