The explosion in the availability of GPS-enabled devices has resulted in an abundance of trajectory data. In reality, however, majority of these trajectories are collected at a low sampling rate and only provide partial observations on their actually traversed routes. Consequently, they are mired with uncertainty. In this paper, we develop a technique called Infer Tra to infer uncertain trajectories from network-constrained partial observations. Rather than predicting the most likely route, the inferred uncertain trajectory takes the form of an edge-weighted graph and summarizes all probable routes in a holistic manner. For trajectory inference, Infer Tra employs Gibbs sampling by learning a Network Mobility Model (NMM) from a database of historical trajectories. Extensive experiments on real trajectory databases show that the graph-based approach of Infer Tra is up to 50 more accurate, 20 times faster, and immensely more versatile than state-of-the-art techniques.
More recently, a technique @cite_6 was designed to study the trajectory inference problem in a setting where trajectories are not constrained by a network. Due to the focus on network-free trajectories, @cite_6 is not applicable to our problem.
@cite_6
2141596757
In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps. GPS-equipped taxis can be viewed as pervasive sensors and the large-scale digital traces produced allow us to reveal many hidden "facts" about the city dynamics and human behaviors. In this paper, we aim to discover anomalous driving patterns from taxi's GPS traces, targeting applications like automatically detecting taxi driving frauds or road network change in modern cites. To achieve the objective, firstly we group all the taxi trajectories crossing the same source destination cell-pair and represent each taxi trajectory as a sequence of symbols. Secondly, we propose an Isolation-Based Anomalous Trajectory (iBAT) detection method and verify with large scale taxi data that iBAT achieves remarkable performance (AUC>0.99, over 90 detection rate at false alarm rate of less than 2 ). Finally, we demonstrate the potential of iBAT in enabling innovative applications by using it for taxi driving fraud detection and road network change detection. This work deals with trajectory optimization for a robotic sensor network sampling a spatio-temporal random field. We examine the optimal sampling problem of minimizing the maximum predictive variance of the estimator over the space of network trajectories. This is a high-dimensional, multi-modal, nonsmooth optimization problem, known to be NP-hard even for static fields and discrete design spaces. Under an asymptotic regime of near-independence between distinct sample locations, we show that the solutions to a novel generalized disk-covering problem are solutions to the optimal sampling problem. This result effectively transforms the search for the optimal trajectories into a geometric optimization problem. Constrained versions of the latter are also of interest as they can accommodate trajectories that satisfy a maximum velocity restriction on the robots. We characterize the solution for the unconstrained and constrained versions of the geometric optimization problem as generalized multicircumcenter trajectories, and provide algorithms which enable the network to find them in a distributed fashion. Several simulations illustrate our results. Focus on movement data has increased as a consequence of the larger availability of such data due to current GPS, GSM, RFID, and sensors techniques. In parallel, interest in movement has shifted from raw movement data analysis to more application-oriented ways of analyzing segments of movement suitable for the specific purposes of the application. This trend has promoted semantically rich trajectories, rather than raw movement, as the core object of interest in mobility studies. This survey provides the definitions of the basic concepts about mobility data, an analysis of the issues in mobility data management, and a survey of the approaches and techniques for: (i) constructing trajectories from movement tracks, (ii) enriching trajectories with semantic information to enable the desired interpretations of movements, and (iii) using data mining to analyze semantic trajectories and extract knowledge about their characteristics, in particular the behavioral patterns of the moving objects. Last but not least, the article surveys the new privacy issues that arise due to the semantic aspects of trajectories. 0. Background Notes.- 1. Continuous Partitions of Unity.- 2. Absolutely Continuous Functions.- 3. Some Compactness Theorems.- 4. Weak Convergence and Asymptotic Center of Bounded Sequences.- 5. Closed Convex Hulls and the Mean-Value Theorem.- 6. Lower Semicontinuous Convex Functions and Projections of Best Approximation.- 7. A Concise Introduction to Convex Analysis.- 1. Set-Valued Maps.- 1. Set-Valued Maps and Continuity Concepts.- 2. Examples of Set-Valued Maps.- 3. Continuity Properties of Maps with Closed Convex Graph.- 4. Upper Hemicontinuous Maps and the Convergence Theorem.- 5. Hausdorff Topology.- 6. The Selection Problem.- 7. The Minimal Selection.- 8. Chebishev Selection.- 9. The Barycentric Selection.- 10. Selection Theorems for Locally Selectionable Maps.- 11. Michael's Selection Theorem.- 12. The Approximate Selection Theorem and Kakutani's Fixed Point Theorem.- 13. (7-Selectionable Maps.- 14. Measurable Selections.- 2. Existence of Solutions to Differential Inclusions.- 1. Convex Valued Differential Inclusions.- 2. Qualitative Properties of the Set of Trajectories of Convex-Valued Differential Inclusions.- 3. Nonconvex-Valued Differential Inclusions.- 4. Differential Inclusions with Lipschitzean Maps and the Relaxation Theorem.- 5. The Fixed-Point Approach.- 6. The Lower Semicontinuous Case.- 3. Differential Inclusions with Maximal Monotone Maps.- 1. Maximal Monotone Maps.- 2. Existence and Uniqueness of Solutions to Differential Inclusions with Maximal Monotone Maps.- 3. Asymptotic Behavior of Trajectories and the Ergodic Theorem.- 4. Gradient Inclusions.- 5. Application: Gradient Methods for Constrained Minimization Problems.- 4. Viability Theory: The Nonconvex Case.- 1. Bouligand's Contingent Cone.- 2. Viable and Monotone Trajectories.- 3. Contingent Derivative of a Set-Valued Map.- 4. The Time Dependent Case.- 5. A Continuous Version of Newton's Method.- 6. A Viability Theorem for Continuous Maps with Nonconvex Images..- 7. Differential Inclusions with Memory.- 5. Viability Theory and Regulation of Controled Systems: The Convex Case.- 1. Tangent Cones and Normal Cones to Convex Sets.- 2. Viability Implies the Existence of an Equilibrium.- 3. Viability Implies the Existence of Periodic Trajectories.- 4. Regulation of Controled Systems Through Viability.- 5. Walras Equilibria and Dynamical Price Decentralization.- 6. Differential Variational Inequalities.- 7. Rate Equations and Inclusions.- 6. Liapunov Functions.- 1. Upper Contingent Derivative of a Real-Valued Function.- 2. Liapunov Functions and Existence of Equilibria.- 3. Monotone Trajectories of a Differential Inclusion.- 4. Construction of Liapunov Functions.- 5. Stability and Asymptotic Behavior of Trajectories.- Comments. Controlling the robot with a permanently-updated optimal trajectory, also known as model predictive control, is the Holy Grail of whole-body motion generation. Before obtaining it, several challenges should be faced: computation cost, non-linear local minima, algorithm stability, etc. In this paper, we address the problem of applying the updated optimal control in real-time on the physical robot. In particular, we focus on the problems raised by the delays due to computation and by the differences between the real robot and the simulated model. Based on the optimal-control solver MuJoCo, we implemented a complete model-predictive controller and we applied it in real-time on the physical HRP-2 robot. It is the first time that such a whole-body model predictive controller is applied in real-time on a complex dynamic robot. Aside from the technical contributions cited above, the main contribution of this paper is to report the experimental results of this premiere implementation. In traffic research, management, and planning a number of path-based analyses are heavily used, e.g., for computing turn-times, evaluating green waves, or studying traffic flow. These analyses require retrieving the trajectories that follow the full path being analyzed. Existing path queries cannot sufficiently support such path-based analyses because they retrieve all trajectories that touch any edge in the path. In this paper, we define and formalize the strict path query. This is a novel query type tailored to support path-based analysis, where trajectories must follow all edges in the path. To efficiently support strict path queries, we present a novel NET work-constrained TRAjectory index (NETTRA). This index enables very efficient retrieval of trajectories that follow a specific path, i.e., strict path queries. NETTRA uses a new path encoding scheme that can determine if a trajectory follows a specific path by only retrieving data from the first and last edge in the path. To correctly answer strict path queries existing network-constrained trajectory indexes must retrieve data from all edges in the path. An extensive performance study of NETTRA using a very large real-world trajectory data set, consisting of 1.7 million trajectories (941 million GPS records) and a road network with 1.3 million edges, shows a speed-up of two orders of magnitude compared to state-of-the-art trajectory indexes. With the advent of ubiquitous computing, we can easily acquire the locations of moving objects. This paper studies clustering problems for trajectory data that is constrained by the road network. While many trajectory clustering algorithms have been proposed, they do not consider the spatial proximity of objects across the road network. For this kind of data, we propose a new distance measure that reflects the spatial proximity of vehicle trajectories on the road network, and an efficient clustering method that reduces the number of distance computations during the clustering process. Experimental results demonstrate that our proposed method correctly identifies clusters using real-life trajectory data yet reduces the distance computations by up to 80 against the baseline algorithm. The matching of similar pairs of objects, called similarity join, is fundamental functionality in data management. We consider the case of trajectory similarity join (TS-Join), where the objects are trajectories of vehicles moving in road networks. Thus, given two sets of trajectories and a threshold θ, the TS-Join returns all pairs of trajectories from the two sets with similarity above θ. This join targets applications such as trajectory near-duplicate detection, data cleaning, ridesharing recommendation, and traffic congestion prediction. With these applications in mind, we provide a purposeful definition of similarity. To enable efficient TS-Join processing on large sets of trajectories, we develop search space pruning techniques and take into account the parallel processing capabilities of modern processors. Specifically, we present a two-phase divide-and-conquer algorithm. For each trajectory, the algorithm first finds similar trajectories. Then it merges the results to achieve a final result. The algorithm exploits an upper bound on the spatiotemporal similarity and a heuristic scheduling strategy for search space pruning. The algorithm's per-trajectory searches are independent of each other and can be performed in parallel, and the merging has constant cost. An empirical study with real data offers insight in the performance of the algorithm and demonstrates that is capable of outperforming a well-designed baseline algorithm by an order of magnitude. Spatial trajectories have been bringing the unprecedented wealth to a variety of research communities. A spatial trajectory records the paths of a variety of moving objects, such as people who log their travel routes with GPS trajectories. The field of moving objects related research has become extremely active within the last few years, especially with all major database and data mining conferences and journals. Computing with Spatial Trajectories introduces the algorithms, technologies, and systems used to process, manage and understand existing spatial trajectories for different applications. This book also presents an overview on both fundamentals and the state-of-the-art research inspired by spatial trajectory data, as well as a special focus on trajectory pattern mining, spatio-temporal data mining and location-based social networks. Each chapter provides readers with a tutorial-style introduction to one important aspect of location trajectory computing, case studies and many valuable references to other relevant research work. Computing with Spatial Trajectories is designed as a reference or secondary text book for advanced-level students and researchers mainly focused on computer science and geography. Professionals working on spatial trajectory computing will also find this book very useful. We present a novel optimization-based motion planning algorithm for high degree-of-freedom (DOF) robots in dynamic environments. Our approach decomposes the high-dimensional motion planning problem into a sequence of low-dimensional sub-problems. We compute collision-free and smooth paths using optimization-based planning and trajectory perturbation for each sub-problem. The overall algorithm does not require a priori knowledge about global motion or trajectories of dynamic obstacles. Rather, we compute a conservative local bound on the position or trajectory of each obstacle over a short time and use the bound to incrementally compute a collision-free trajectory for the robot. The high-DOF robot is treated as a tightly coupled system, and we incrementally use constrained coordination to plan its motion. We highlight the performance of our planner in simulated environments on robots with tens of DOFs. It is difficult to extract meaningful patterns from massive trajectory data. One of the main challenges is to characterise, compare and generalise trajectories to find overall patterns and trends. The major limitation of existing methods is that they do not consider topological relations among trajectories. This research proposes a graph-based approach that converts trajectory data to a graph-based representation and treats them as a complex network. Within the context of vehicle movements, the research develops a sequence of steps to extract representative points to reduce data redundancy, interpolate trajectories to accurately establish topological relationships among trajectories and locations, construct a graph (or matrix) representation of trajectories, apply a spatially constrained graph partitioning method to discover natural regions defined by trajectories and use the discovered regions to search and visualise trajectory clusters. Applications with a real data set shows that our new approach can effectively facilitate the understanding of spatial and spatiotemporal patterns in trajectories and discover novel patterns that existing methods cannot find. Tracking and managing the locations of moving objects are essential in modern intelligent transportation systems (ITSs). However, a number of limitations in existing methods make them unsuitable for real-world ITS applications. In particular, Euclidean-based methods are not accurate enough in representing locations and in analyzing traffic, unless the locations are frequently updated. Network-based methods require either digital maps to be installed in moving objects or transmission of prediction policies, which inevitably increase the cost. To solve these problems, we propose a network-matched trajectory-based moving-object database (NMTMOD) mechanism and a traffic flow analysis method using the NMTMOD. In the NMTMOD, the locations of moving objects are tracked through a dense sampling and batch uploading strategy, and a novel edge-centric network-matching method, which is running at the server side, is adopted to efficiently match the densely sampled GPS points to the network. In addition, a deviation-based trajectory optimization method is provided to minimize the trajectory size. Empirical studies with large real trajectory data set offer insight into the design properties of the proposed NMTMOD and suggest that the NMTMOD significantly outperforms other mobile-map free-moving-object database models in terms of precision of both location tracking and network-based traffic flow analysis. The advances in location-acquisition technologies have led to a myriad of spatial trajectories. These trajectories are usually generated at a low or an irregular frequency due to applications' characteristics or energy saving, leaving the routes between two consecutive points of a single trajectory uncertain (called an uncertain trajectory). In this paper, we present a Route Inference framework based on Collective Knowledge (abbreviated as RICK) to construct the popular routes from uncertain trajectories. Explicitly, given a location sequence and a time span, the RICK is able to construct the top-k routes which sequentially pass through the locations within the specified time span, by aggregating such uncertain trajectories in a mutual reinforcement way (i.e., uncertain + uncertain → certain). Our work can benefit trip planning, traffic management, and animal movement studies. The RICK comprises two components: routable graph construction and route inference. First, we explore the spatial and temporal characteristics of uncertain trajectories and construct a routable graph by collaborative learning among the uncertain trajectories. Second, in light of the routable graph, we propose a routing algorithm to construct the top-k routes according to a user-specified query. We have conducted extensive experiments on two real datasets, consisting of Foursquare check-in datasets and taxi trajectories. The results show that RICK is both effective and efficient. In the study of task coordination for multiagent systems, formation control has received considerable attention due to its potential applications in civil and or military prac-tices. Fundamentally, formation control problem for multiagent systems can be formulated as making a group of agents follow the desired trajectory while maintaining certain prescribed geometric distances among agents. In this paper, we consider the formation control problem for mobile robots with nonlinear dynamics and moving in a 2D environment. To address the inherent challenges due to nonlinear system dynamics and agents' limited sensing communication capabilities, we instill an idea of integrating the recently developed distributed consensus theory into the standard feedback control, and propose a new time-varying cooperative control strategy to solve the formation control problem for multiagent systems. In particular, the proposed design only requires the local and intermittent information exchange among agents to achieve the formation control objective. More importantly, we remove the restriction on the need of the desired trajectory for every agent, and instead design a distributed observer for obtaining the desired trajectory in order to establish the formation in the design. The overall distributed formation control system stability is rigorously proved by using a contraction mapping method under the condition that the sensing communication network among robots is sequentially complete. Simulation is provided to validate the effectiveness of the proposed design. Emerging vehicular trajectory data have opened up opportunities to benefit many real-world applications, e.g., frequent trajectory based navigation systems, road planning, car pooling, etc. The similarity join is a key operation to enable such applications, which finds similar trajectory pairs from two large collections of trajectories. Existing similarity metrics on trajectories rely on aligning sampling points of two trajectories. However, due to different sampling rates or different vehicular speeds, the sample points in similar trajectories may not be aligned. To address this problem, we propose a new bi-directional mapping similarity ( @math ), which allows a sample point of a trajectory to align to the closest location (which may not be a sample point) on the other trajectory, and vice versa. Since it is expensive to enumerate every two trajectories and compute their similarity, we propose Strain-Join , a signature-based trajectory similarity join framework. Strain-Join first generates signatures for each trajectory such that if two trajectories do not share common signatures, they cannot be similar. In order to utilize this property to prune dissimilar pairs, we devise several techniques to generate high-quality signatures and propose an efficient filtering algorithm to prune dissimilar pairs. For the pairs not pruned by the filtering algorithm, we propose effective verification algorithms to verify whether they are similar. Experimental results on real datasets show that our algorithm outperforms state-of-the-art techniques in terms of both effectiveness and efficiency. This paper addresses the task of trajectory cost prediction, a new learning task for trajectories. The goal of this task is to predict the cost for an arbitrary (possibly unknown) trajectory, based on a set of previous trajectory-cost pairs. A typical example of this task is travel-time prediction on road networks. The main technical challenge here is to infer the costs of trajectories including links with no or little passage history. To tackle this, we introduce a weight propagation mechanism over the links, and show that the problem can be reduced to a simple form of kernel ridge regression. We also show that this new formulation leads us to a unifying view, where a natural choice of the kernel is suggested to an existing kernel-based alternative. Motion planning is a fundamental tool in robotics, used to generate collision-free, smooth, trajectories, while satisfying task-dependent constraints. In this paper, we present a novel approach to motion planning using Gaussian processes. In contrast to most existing trajectory optimization algorithms, which rely on a discrete state parameterization in practice, we represent the continuous-time trajectory as a sample from a Gaussian process (GP) generated by a linear time-varying stochastic differential equation. We then provide a gradient-based optimization technique that optimizes continuous-time trajectories with respect to a cost functional. By exploiting GP interpolation, we develop the Gaussian Process Motion Planner (GPMP), that finds optimal trajectories parameterized by a small number of states. We benchmark our algorithm against recent trajectory optimization algorithms by solving 7-DOF robotic arm planning problems in simulation and validate our approach on a real 7-DOF WAM arm. We present a new approach to the design of smooth trajectories for quadrotor unmanned aerial vehicles (UAVs), which are free of collisions with obstacles along their entire length. To avoid the non-convex constraints normally required for obstacle-avoidance, we perform a mixed-integer optimization in which polynomial trajectories are assigned to convex regions which are known to be obstacle-free. Prior approaches have used the faces of the obstacles themselves to define these convex regions. We instead use IRIS, a recently developed technique for greedy convex segmentation [1], to pre-compute convex regions of safe space. This results in a substantially reduced number of integer variables, which improves the speed with which the optimization can be solved to its global optimum, even for tens or hundreds of obstacle faces. In addition, prior approaches have typically enforced obstacle avoidance at a finite set of sample or knot points. We introduce a technique based on sums-of-squares (SOS) programming that allows us to ensure that the entire piecewise polynomial trajectory is free of collisions using convex constraints. We demonstrate this technique in 2D and in 3D using a dynamical model in the Drake toolbox for Matlab [2]. Destination prediction is an essential task for many emerging location-based applications such as recommending sightseeing places and targeted advertising according to destinations. A common approach to destination prediction is to derive the probability of a location being the destination based on historical trajectories. However, almost all the existing techniques use various kinds of extra information such as road network, proprietary travel planner, statistics requested from government, and personal driving habits. Such extra information, in most circumstances, is unavailable or very costly to obtain. Thereby we approach the task of destination prediction by using only historical trajectory dataset. However, this approach encounters the "data sparsity problem", i.e., the available historical trajectories are far from enough to cover all possible query trajectories, which considerably limits the number of query trajectories that can obtain predicted destinations. We propose a novel method named Sub-Trajectory Synthesis (SubSyn) to address the data sparsity problem. SubSyn first decomposes historical trajectories into sub-trajectories comprising two adjacent locations, and then connects the sub-trajectories into "synthesised" trajectories. This process effectively expands the historical trajectory dataset to contain much more trajectories. Experiments based on real datasets show that SubSyn can predict destinations for up to ten times more query trajectories than a baseline prediction algorithm. Furthermore, the running time of the SubSyn-training algorithm is almost negligible for a large set of 1.9 million trajectories, and the SubSyn-prediction algorithm runs over two orders of magnitude faster than the baseline prediction algorithm constantly.