Efficient Trajectory Research Articles

Ghost: A General Framework for High-Performance Online Similarity Queries over Distributed Trajectory Streams

Trajectory similarity queries, including similarity search and similarity join, offer a foundation for many geo-spatial applications. With the rapid increase of streaming trajectory data volumes, e.g., data from mobile phones, vessel monitoring, or traffic systems, many location-based services benefit from online similarity analytics over trajectory data streams, where moving objects continually emit real-time position data. However, most existing studies focus on offline settings, and thus several major challenges remain unanswered in an online setting. To this end, we describe Ghost, a distributed stream processing framework that enables generic, efficient, and scalable online trajectory similarity search and join. We propose a novel incremental online similarity computation (IOSC) mechanism to accelerate pair-wise streaming trajectory distance calculation, which supports a broad range of trajectory distance metrics. Compared with previous studies, IOSC reduces the complexity from quadratic to linear in terms of trajectory length. Building on this foundation, we propose histogram-based algorithms that exploit histogram indexes and a series of pruning bounds to enable streaming trajectory similarity search and join. Finally, we extend our methods to the distributed platform Flink for scalability, where a CostPartitioner is developed to ensure parallel processing and workload balancing. An experimental study using two real-life and one synthetic datasets shows that Ghost (i) acquires 6-20× efficiency/throughput gains and one order of magnitude memory overhead savings over state-of-the-art baselines, (ii) achieves 3--8× workload balancing gains on Flink, and (iii) exhibits low parameter sensitivity and high robustness.

Efficient and scalable DBSCAN framework for clustering continuous trajectories in road networks

Clustering the trajectories of vehicles moving on road networks is a key data mining technique for understanding human mobility patterns, as well as their interactions with urban environments. The development of efficient and scalable trajectory clustering algorithms, however, still faces challenges because of the computational costs when measuring similarities among a large number of network-constrained trajectories. To address this problem, a novel trajectory clustering framework based on the well-developed Density-Based Spatial Clustering of Applications with Noise (DBSCAN) approach is proposed. This proposed framework accurately quantifies similarities using a trajectory representation of continuous polylines in the space and time dimensions, and does not require trajectory discretization. Further, the proposed framework utilizes the space-time buffering concept to formulate ε -neighborhood queries that directly retrieve the ε -neighbors of trajectories and thus avoids computing a trajectory similarity matrix. State-of-the-art trajectory databases and index structures are incorporated to further improve trajectory clustering performance. A comprehensive case study was carried out using an open dataset of 20,161 trajectories. Results show that the proposed framework efficiently executed trajectory clustering on the large test dataset within 3 min. This was approximately 2,700 times faster than existing DBSCAN algorithms.

Online Stochastic Variational Gaussian Process Mapping for Large-Scale Bathymetric SLAM in Real Time

Rao-Blackwellized particle filter (RBPF) SLAM solutions with Gaussian Process (GP) maps can both maintain multiple hypotheses of a vehicle pose estimate and perform implicit data association for loop closure detection in continuous terrain representations. Both qualities are of particular interest for SLAM with autonomous underwater vehicles (AUVs) in the open sea, where distinguishable features are scarce. However, the applicability of GP regression to parallel, real-time mapping in an RBPF framework remains limited by the size of the area to survey and the computational cost of the GP training. To overcome these constraints, in this letter we propose the adaption of Stochastic Variational GP (SVGP) regression to online mapping in combination with a novel, efficient particle trajectory storing in the RBPF. We show how the resulting RBPF-SVGP framework can achieve real-time performance in an embedded platform on two AUV surveys containing millions of points. We further test the framework on a live mission on an AUV and we make the implementation publicly available.

Direct multiple shooting for computationally efficient train trajectory optimization

Energy efficient train control has been an active field of research for several decades, with Pontryagin’s maximum principle and dynamic programming being the two most common approaches for the computation of optimal trajectories. In this paper, we detail how direct multiple shooting can be used in the same context and highlight its two main advantages: the flexibility in the problem formulation and the availability of computationally efficient open-source software. Using the proposed framework, which is made publicly available, we are able to solve particularly challenging train trajectory optimization problems within only a few seconds.

Optimal trajectory planning of the industrial robot using hybrid S-curve-PSO approach

PurposeThe paper aims to develop an efficient and compact hybrid S-curve-PSO (particle swarm optimization) controller for the optimal trajectory planning of industrial robots in the presence of obstacles, especially those used in pick-and-place operations.Design/methodology/approachThe proposed methodology comprises a monotonic trajectory through bounded entropy of speed, velocity, acceleration and jerk. Thus, the robot’s trajectory planning corresponds with S-curve-PSO duality. This is achieved by dual navigation with minimal computational complexity. The matrix algebra-based computational complexity transforms the trajectory from random to compact. The linear programming problem represents the proposed robot in Euclidean space, and its optimal solution sets the corresponding optimal trajectory.FindingsThe proposed work ensures the efficient trajectory planning of the industrial robot in the presence of obstacles with optimized path length and time. The real-time and simulation analysis of the robot is presented for performance measurement, and their outcomes demonstrate a good correlation. Compared with the existing controller, it gives a noteworthy improvement in performance.Originality/valueThe novel S-curve-PSO hybrid approach is presented here, along with the LIDAR sensors, which generate the environment map and detect obstacles for autonomous trajectory planning. Based on the sensory information, the proposed approach generates the optimal trajectory by avoiding obstacles and minimizing the travel time, jerk, velocity and acceleration. The hybrid S-curve-PSO approach for optimal trajectory planning of the industrial robot in the presence of obstacles has not been presented by any researchers. This method considers the robot’s kinematics as well as its dynamics. The implementation of the PSO makes it computationally superior and faster. The selection of best-fit parameters by PSO assures the optimized trajectory in the presence of obstacles and uncertainty.

Managing Sets of Flying Base Stations Using Energy Efficient 3D Trajectory Planning in Cellular Networks

Unmanned aerial vehicles (UAVs) in cellular networks have garnered considerable interest. One of their applications is as flying base stations (FBSs), which can increase coverage and quality of service (QoS). Because FBSs are battery-powered, regulating their energy usage is a vital aspect of their use; and therefore the appropriate placement and trajectories of FBSs throughout their operation are critical to overcoming this challenge. In this paper, we propose a method of solving a multi-FBS 3D trajectory problem that considers FBS energy consumption, operation time, flight distance limits, and inter-cell interference constraints. Our method is divided into two phases: FBS placement and FBS trajectory. In taking this approach, we break the problem into several snapshots. First, we find the minimum number of FBSs required and their proper 3D positions in each snapshot. Then, between every two snapshots, the trajectory phase is executed. The optimal path between the origin and destination of each FBS is determined during the trajectory phase by utilizing a proposed binary linear problem (BLP) model that considers FBS energy consumption and flight distance constraints. Then, the shortest path for each FBS is determined while taking obstacles and collision avoidance into consideration. The number of FBSs needed may vary between snapshots, so we present an FBS set management (FSM) technique to manage the set of FBSs and their power. The results demonstrate that the proposed approach is applicable to real-world situations and that the outcomes are consistent with expectations.

Clothoid-Based Path Planning for a Formation of Fixed-Wing UAVs

Unmanned aerial vehicles (UAVs) are playing an increasingly crucial role in many applications such as search and rescue, delivery services, and military operations. However, one of the significant challenges in this area is to plan efficient and safe trajectories for UAV formations. This paper presents an optimization procedure for trajectory planning for fixed-wing UAV formations using graph theory and clothoid curves. The proposed planning strategy consists of two main steps. Firstly, the geometric optimization of paths is carried out using graphs for each UAV, providing piece-wise linear paths whose smooth connections are made with clothoids. Secondly, the geometric paths are transformed into time-dependent trajectories, optimizing the assigned aircraft speeds to avoid collisions by solving a mixed-integer optimal control problem for each UAV of the flight formation. The proposed method is effective in achieving suboptimal paths while ensuring collision avoidance between aircraft. A sensitivity analysis of the main parameters of the algorithm was conducted in ideal conditions, highlighting the possibility of decreasing the length of the optimal path by about 4.19%, increasing the number of points used in the discretization and showing a maximum path length reduction of about 10% compared with the average solution obtained with a similar algorithm using a graph based on random directions. Furthermore, the use of clothoids, whose parameters depend on the UAV performance constraints, provides smoother connections, giving a significant improvement over traditional straight-line or circular trajectories in terms of flight dynamics compliance and trajectory tracking capabilities. The method can be applied to various UAV formation scenarios, making it a versatile and practical tool for mission planning.

Optimizing trajectories for highway driving with offline reinforcement learning

Achieving feasible, smooth and efficient trajectories for autonomous vehicles which appropriately take into account the long-term future while planning, has been a long-standing challenge. Several approaches have been considered, roughly falling under two categories: rule-based and learning-based approaches. The rule-based approaches, while guaranteeing safety and feasibility, fall short when it comes to long-term planning and generalization. The learning-based approaches are able to account for long-term planning and generalization to unseen situations, but may fail to achieve smoothness, safety and the feasibility which rule-based approaches ensure. Hence, combining the two approaches is an evident step towards yielding the best compromise out of both. We propose a Reinforcement Learning-based approach, which learns target trajectory parameters for fully autonomous driving on highways. The trained agent outputs continuous trajectory parameters based on which a feasible polynomial-based trajectory is generated and executed. We compare the performance of our agent against four other highway driving agents. The experiments are conducted in the Sumo simulator, taking into consideration various realistic, dynamically changing highway scenarios, including surrounding vehicles with different driver behaviors. We demonstrate that our offline trained agent, with randomly collected data, learns to drive smoothly, achieving velocities as close as possible to the desired velocity, while outperforming the other agents.

Digital disruption of optimal co-innovation configurations

We evaluate the co-innovation trajectory of firms adopting different collaborative innovation networks (i.e., vertical, horizontal, and institutional). The results of the empirical applications are obtained from a multilevel regression, and a Nash bargaining model estimated via data envelopment analysis on a sample of 734 enterprises from seven OECD countries form Europe and Latin America. Findings point to important national and firm-level distinctions across the optimal co-innovation configurations: whereas vertical co-innovation strategies are characteristic of firms with the highest innovation efficiency, institutions are frequently found to be optimal for co-innovation success in less developed innovation systems that may be faced with structural deficiencies. However, digital competency is found to disrupt co-innovation configurations for successful innovation, facilitating the development of efficient vertical and horizontal co-innovation trajectories.

Combination of different trajectory description approaches improves the trajectory synthesis performance: Validation by a coarse-to-fine method

In the past decade, trajectory synthesis methods seem to reach a bottleneck. These methods occasionally fail when some complex trajectories and linkage configurations are encountered. One important reason is that each trajectory description approach has its limitations. Is it possible to combine these description approaches to obtain better synthesis precision and versatility of different configurations? In this study, a coarse-to-fine optimal method for trajectory synthesis is proposed to verify the above conjecture. This method incorporates a well-designed multi-objective optimization model based on Fourier series (FS) and a single-objective optimization model based on discrete points (DP). FS and DP are selected because they are able to describe the overall shape and local details of the trajectory well, respectibely. In a synthesis problem of a leg mechanism, the method achieves better synthesis accuracy than others and demonstrates the applicability to both complex trajectories and multiple configurations. This work proves that the combination of different trajectory description methods leads to a better synthesis performance, which we believe provides new ideas for developing more efficient trajectory synthesis methods.

A Distributed Deep Reinforcement Learning Technique for Application Placement in Edge and Fog Computing Environments

Fog/Edge computing is a novel computing paradigm supporting resource-constrained Internet of Things (IoT) devices by placement of their tasks on edge and/or cloud servers. Recently, several Deep Reinforcement Learning (DRL)-based placement techniques have been proposed in fog/edge computing environments, which are only suitable for centralized setups. The training of well-performed DRL agents requires manifold training data while obtaining training data is costly. Hence, these centralized DRL-based techniques lack generalizability and quick adaptability, thus failing to efficiently tackle application placement problems. Moreover, many IoT applications are modeled as Directed Acyclic Graphs (DAGs) with diverse topologies. Satisfying dependencies of DAG-based IoT applications incur additional constraints and increase the complexity of placement problem. To overcome these challenges, we propose an actor-critic-based distributed application placement technique, working based on the IMPortance weighted Actor-Learner Architectures (IMPALA). IMPALA is known for efficient distributed experience trajectory generation that significantly reduces exploration costs of agents. Besides, it uses an adaptive off-policy correction method for faster convergence to optimal solutions. Our technique uses recurrent layers to capture temporal behaviors of input data and a replay buffer to improve the sample efficiency. The performance results, obtained from simulation and testbed experiments, demonstrate that our technique significantly improves execution cost of IoT applications up to 30\% compared to its counterparts.

Multi-Stage RF Emitter Search and Geolocation With UAV: A Cognitive Learning-Based Method

This paper investigates the issue of searching and geolocating a radio frequency (RF) emitter with an unmanned aerial vehicle (UAV) in a rich scattering environment. The absence of knowledge of the characteristics of the target RF signals, the ground-to-air channels, and the potential geographical distribution of the RF emitter makes efficient trajectory planning (TP) and geolocating intractable. Since the average signal-to-noise ratio (SNR) of the signal captured by the UAV changes across the search area, state-of-the-art TP is inapplicable due to the assumption of a single problem domain, according to the No Free Lunch (NFL) theorem. In contrast, we develop a cognitive multi-stage search and geolocation (CMSG) framework, which adjusts the adopted TP algorithms in various search stages. In the stage with extremely-low SNRs, a random-walk-based TP is proposed to avoid meaningless detours. For stages with higher SNRs, the TP follows policies optimized by a novel search method based on direction of arrival (DOA) estimation and reinforcement learning. To alleviate the impairment of unreliable DOA estimations, empirical emitter position estimations are exploited to find the best flight directions. Simulation results confirm the advantages of the proposed CMSG over various baselines in lowering both failure rate and time consumption.

Energy efficient robots based on structures with tensegrity features and cable-driven mechanisms

The paper presents concept of energy efficient motion control of robots and other machines based on structures with tensegrity features and/or cable-driven mechanisms. The essence of concept is generalization of so called eigenmotion idea for these multi-DOF complex mechanisms. The term eigenmotion here refers to a motion of a mechanism in which the constant sum of kinetic and potential energy is maximally preserved. The operation of the drives is ideally used only to eliminate passive resistances and to minimize deviations of motion from the required trajectory. The main advantage of mechanisms with tensegrity features and cable-driven ones is a relatively high number of elements such as springs, active cables or variable bodies, whose energy absorbing properties can be suitably adjusted during design and some also continuously during operation. The variability of attainable eigenmotion trajectories of these types of mechanisms can be further extended thanks to number of drives higher than number of end-effector degrees of freedom. The concept is demonstrated on two planar systems, one structure with tensegrity features and one serial–parallel cable-driven robot. The examples show the optimization of the parameters to achieve the eigenmotion properties on the given trajectories, as well as the change of the eigenmotion trajectory by changing the adjustable parameters. The final control of mechanical models along energy efficient trajectories is realized by computed torque control method.

Multi-IRS and Multi-UAV-Assisted MEC System for 5G/6G Networks: Efficient Joint Trajectory Optimization and Passive Beamforming Framework

This article presents a multi-intelligent reflecting surface (IRS)- and multi-unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) system for 5G/6G networks. In the studied system, multiple UAVs are integrated for providing services to large-scale user equipment (UEs) with the help of multiple IRSs. This article aims to minimize the overall cost including energy consumption, completion time, and maintenance cost of UAVs by jointly optimizing the trajectories of UAVs and phase shifts of IRSs. When solving this problem, one has to count in mind the deployment of stop points (SPs) of UAVs, and consider the association among UEs, and UAVs (i.e., which UE will send data to which UAV at which SP), the order of SPs, and the phase shifts of IRSs. Therefore, traditional optimization techniques may not solve the above-mentioned problem in an efficient way. To tackle the above-mentioned problem, this article proposes an algorithm called TPaPBA that consists of four phases. The first phase optimizes the SPs’ deployment via using a differential evolution algorithm having variable population size. As a result, all the SPs of UAVs can be obtained. Then, the second phase optimizes the association among UEs, SPs, and UAVs. Specifically, TPaPBA first adopts a clustering algorithm to optimize the SPs-UAVs association, and then a close criterion is introduced to optimize UEs-SPs association. Subsequently, third phase adopts a low-complexity greedy algorithm to optimize the order of SPs for UAVs. Finally, the phase shifts of IRSs are optimized to enhance the data rate between UEs and UAVs. The simulation results of TPaPBA on ten instances having UEs ranging from 100 to 1000, reveals that TPaPBA has significantly improved the system performance contribution and outperforms other approaches in terms of reducing the overall cost of UAVs.

AI-Empowered Trajectory Anomaly Detection and Classification in 6G-V2X

The immense growth of Autonomous Vehicles (AVs) and networking technologies have paved the way for advanced Intelligent Transportation Systems (ITS). AVs increase data demands from in-vehicle users, which pose a significant risk to the vehicular trajectory data and are extremely vulnerable to security threats. It is challenging to describe and detect the trajectory anomalies in urban motion behavior due to the enormous coverage and complexity of ITS in the V2X environment. Most existing systems rely on a restricted number of single detection strategies, such as determining frequent patterns and have limited accuracy in detecting anomalous trajectories. However, they focus only on outlier detection, failing to consider different patterns of anomalous trajectories. This paper proposes Efficient Trajectory Anomaly Detection and Classification (ETADC) framework in a 6G-V2X environment. The proposed ETADC framework employs the Deep Deterministic Policy Gradient algorithm (DDPG) to improve accuracy and efficiency by analyzing multiple strategies, namely driving speed, driving distance, driving direction, and driving time. The result analysis shows that the proposed ETADC technique outperforms the existing systems by 97% accuracy.

Maneuver Conditioned Vehicle Trajectory Prediction Using Self-Attention

Forecasting the motion of surrounding vehicles is necessary for a self-driving vehicle to plan a safe and efficient trajectory for the future. Like experienced human drivers, the self-driving vehicle needs to perceive the interaction of surrounding vehicles and decide the best trajectory from many choices. However, previous methods either lack modeling of interactions or ignore the multi-modal nature of this problem. In this paper, we focus on two important cues of trajectory prediction: interaction and maneuver, and propose Maneuver conditioned Attentional Network named MAN. MAN learns the interactions of all vehicles in a scenario in parallel by self-attention social pooling and the attentional decoder generates the future trajectory conditioned on the predicted maneuver among 3 classes: Lane Changing Left (LCL), Lane Changing Right (LCR) and Lane Keeping (LK). Experiments demonstrate the improvement of our model in prediction on the publicly available NGSIM and HighD datasets. We also present quantitative analysis to study the relationship between maneuver prediction accuracy and trajectory error.

Trajectory Synthesis for a UAV Swarm Based on Resilient Data Collection Objectives

The use of Unmanned Aerial Vehicles (UAVs) for collecting data from remotely located sensor systems is emerging. The data can be time-sensitive and require to be transmitted to a data processing center. However, planning the trajectory for a swarm of UAVs depends on multi-fold constraints, such as data collection requirements, UAV maneuvering capacities, and budget limitations. Since a UAV may fail or be compromised, it is important to provide necessary resilience to such contingencies, thus ensuring data security. It is important to provide the UAVs with efficient spatio-temporal trajectories so that they can efficiently cover necessary data sources. In this work, we present Synth4UAV, a formal approach for automated synthesis of efficient trajectories for a UAV swarm by logically modeling the aerial space and data point topology, UAV moves, and associated constraints in terms of the turning and climbing angle, fuel usage, data collection point coverage, data freshness, and resiliency properties. We use efficient, logical formulas to encode and solve the complex model. The solution to the model provides the routing and maneuvering plan for each UAV, including the time to visit the points on the paths and corresponding fuel usage such that the necessary data points are visited while satisfying the resiliency requirements. We evaluate the proposed trajectory synthesizer, and the results show that the relationship among different parameters follows the requirements while the tool scales well with the problem size.

AI-Based Mobility-Aware Energy Efficient Resource Allocation and Trajectory Design for NFV Enabled Aerial Networks

In this paper, we propose a novel joint intelligent trajectory design and resource allocation algorithm based on users’ mobility and their requested services for unmanned aerial vehicles (UAVs) assisted networks, where UAVs act as nodes of a network function virtualization (NFV) enabled network. Our objective is to maximize energy efficiency and minimize the average delay on all services by allocating the limited radio and NFV resources. In addition, due to the traffic conditions and mobility of users, we let some virtual network functions (VNFs) migrate from their current locations to other locations to satisfy the Quality of Service requirements. We formulate our problem to find near-optimal locations of UAVs, transmit power, subcarrier assignment, VNF placement, and VNF scheduling over the UAVs and perform suitable VNF migration. Then we propose a novel hierarchical hybrid continuous and discrete action (HHCDA) deep reinforcement learning method to solve the proposed problem. Finally, the convergence and computational complexity of the proposed algorithm and its performance is analyzed for different parameters. Simulation results show that our proposed HHCDA method decreases the average end-to-end delay by 31.5% and increases the energy efficiency by 40% compared to the state-of-the-art Deep Deterministic Policy Gradient method.

Optimal Trajectory Planning for Connected and Automated Vehicles in Lane-Free Traffic With Vehicle Nudging

The paper presents a movement strategy for Connected and Automated Vehicles (CAVs) in a lane-free traffic environment with vehicle nudging by use of an optimal control approach. State-dependent constraints on control inputs are considered to ensure that the vehicle moves within the road boundaries and to prevent collisions. An objective function, comprising various weighted sub-objectives, is designed, whose minimization leads to vehicle advancement at the desired speed, when possible, while avoiding obstacles. A nonlinear optimal control problem (OCP) is formulated for the minimization of the objective function subject to constraints for each vehicle. A computationally efficient Feasible Direction Algorithm (FDA) is called, on event-triggered basis, to compute in real-time the numerical solution for finite time-horizons within a Model Predictive Control (MPC) framework. The approach is applied to each vehicle on the road, while running simulations on a lane-free ring-road, for a wide range of vehicle densities and different types of vehicles. From the simulations, which create myriads of driving episodes for each involved vehicle, it is observed that the proposed approach is highly efficient in delivering safe, comfortable and efficient vehicle trajectories, as well as high traffic flow outcomes. The approach is under investigation for further use in various lane-free road infrastructures for CAV traffic.

A Hybrid Trajectory Planning Strategy for Intelligent Vehicles in On-Road Dynamic Scenarios

Efficient trajectory planning for intelligent vehicles in dynamic environments is a non-trivial task due to the diversity and complexity of driving scenarios. It requires the planner to be capable of responding to the changes in driving scenarios in real-time. This paper proposes a hybrid trajectory planning framework by combining the sampling- and numerical optimization-based approaches to cope with the complex driving scenarios. First, a risk field model is introduced to assess the risks with the static and moving obstacles. Then, the sampling-based approach is used to generate collision-free trajectory candidates via the Path Velocity Decomposition method. Thus, the optimal behavior trajectory can be obtained by considering curve smoothness, collision risk, and travel time. The optimization-based method is adopted to optimize the behavior trajectory to guarantee safety, vehicle dynamics stability, and driving comfort using the Sequential Quadratic Programming within the spatio-temporal boundaries. Finally, the proposed framework is examined in typical dynamic driving scenarios through simulation, and the results verify its competency in generating high-quality trajectories in real-time.