In this paper we solve the problem of finding a trajectory that shows that a given hybrid dynamical system with deterministic evolution leaves a given set of states considered to be safe. The algorithm combines local with global search for achieving both efficiency and global convergence. In local search, it exploits derivatives for efficient computation. Unlike other methods for falsification of hybrid systems with deterministic evolution, we do not restrict our search to trajectories of a certain bounded length but search for error trajectories of arbitrary length.
Zuthsi and co-authors @cite_27 present a method for falsification of hybrid systems that also uses multiple shooting based local search. However, the method assumes a given upper bound on the length of the error trajectory the method searches for. Moreover, their local search method always follows a given sequence of modes and transitions. They propose to search for such a sequence using tools that compute abstractions of hybrid systems, or by random search. The form of the used trajectory segments is more restricted than in our method since trajectory segments always stay in one mode, and end in the guard leading to another mode.
@cite_27
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This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory. We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations. In this paper, we address the problem of local search for the falsification of hybrid automata with affine dynamics. Namely, if we are given a sequence of locations and a maximum simulation time, we return the trajectory that comes the closest to the unsafe set. In order to solve this problem, we formulate it as a differentiable optimization problem which we solve using Sequential Quadratic Programming. The purpose of developing such a local search method is to combine it with high level stochastic optimization algorithms in order to falsify hybrid systems with complex discrete dynamics and high dimensional continuous spaces. Experimental results indicate that indeed the local search procedure improves upon the results of pure stochastic optimization algorithms. Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform. We present an algorithm for falsifying safety properties of hybrid systems, i.e., for finding a trajectory to an unsafe state. The approach is to approximate how close a point is to being an initial point of an error trajectory using a real-valued quality function, and then to use numerical optimisation to search for an optimum of this function. The function is computed by running simulations, where information coming from abstractions computed by a verification algorithm is exploited to determine whether a simulation looks promising and should be continued or cancelled. This information becomes more reliable as the abstraction becomes more refined. We thus interleave falsification and verification attempts. Moving Object Databases (MOD), although ubiquitous, still call for methods that will be able to understand, search, analyze, and browse their spatiotemporal content. In this paper, we propose a method for trajectory segmentation and sampling based on the representativeness of the (sub)trajectories in the MOD. In order to find the most representative subtrajectories, the following methodology is proposed. First, a novel global voting algorithm is performed, based on local density and trajectory similarity information. This method is applied for each segment of the trajectory, forming a local trajectory descriptor that represents line segment representativeness. The sequence of this descriptor over a trajectory gives the voting signal of the trajectory, where high values correspond to the most representative parts. Then, a novel segmentation algorithm is applied on this signal that automatically estimates the number of partitions and the partition borders, identifying homogenous partitions concerning their representativeness. Finally, a sampling method over the resulting segments yields the most representative subtrajectories in the MOD. Our experimental results in synthetic and real MOD verify the effectiveness of the proposed scheme, also in comparison with other sampling techniques. Given a specific object as query, object instance search aims to not only retrieve the images or frames that contain the query, but also locate all its occurrences. In this work, we explore the use of spatio-temporal cues to improve the quality of object instance search from videos. To this end, we formulate this problem as the spatio-temporal trajectory search problem, where a trajectory is a sequence of bounding boxes that locate the object instance in each frame. The goal is to find the top- @math trajectories that are likely to contain the target object. Despite the large number of trajectory candidates, we build on a recent spatio- temporal search algorithm for event detection to efficiently find the optimal spatio- temporal trajectories in large video volumes , with complexity linear to the video volume size. We solve the key bottleneck in applying this approach to object instance search by leveraging a randomized approach to enable fast scoring of any bounding boxes in the video volume. In addition , we present a new dataset for video object instance search. Experimental results on a 73-hour video dataset demonstrate that our approach improves the performance of video object instance search and localization over the state-of-the-art search and tracking methods. This paper describes a probabilistic multiple-hypothesis framework for tracking highly articulated objects. In this framework, the probability density of the tracker state is represented as a set of modes with piecewise Gaussians characterizing the neighborhood around these modes. The temporal evolution of the probability density is achieved through sampling from the prior distribution, followed by local optimization of the sample positions to obtain updated modes. This method of generating hypotheses from state-space search does not require the use of discrete features unlike classical multiple-hypothesis tracking. The parametric form of the model is suited for high dimensional state-spaces which cannot be efficiently modeled using non-parametric approaches. Results are shown for tracking Fred Astaire in a movie dance sequence. This paper proposes a method for automatic generation of time-optimal robot motion trajectories for the task of collecting and moving a finite number of objects to particular spots in space, while maintaining predefined temporal logic constraints. The continuous robot dynamics change upon an object pick-up or drop-off. The temporal constraints are expressed as syntactically co-safe Linear Temporal Logic (scLTL) formulas over the set of object and drop-off sites. We propose an approach based on constructing a discrete abstraction of the hybrid system modeling the robot in the form of a finite weighted transition system. Then, by employing tools from automata-based model checking, we obtain an automaton containing only paths that satisfy the specification. The shortest path in this automaton is found by graph search and corresponds directly to the time-optimal hybrid trajectory. The method is applied to a case study with a mobile ground robot and a case study involving a quadrotor moving in an environment with obstacles, thus reflecting its computational advantage over a direct optimization approach. Modern automated systems evolve both continuously and discretely, and hence require estimation techniques that go well beyond the capability of a typical Kalman filter. Multiple model (MM) estimation schemes track these system evolutions by applying a bank of filters, one for each discrete system mode. Modern systems, however, are often composed of many interconnected components that exhibit rich behaviors, due to complex, system-wide interactions. Modeling these systems leads to complex stochastic hybrid models that capture the large number of operational and failure modes. This large number of modes makes a typical MM estimation approach infeasible for online estimation. This paper analyzes the shortcomings of MM estimation, and then introduces an alternative hybrid estimation scheme that can efficiently estimate complex systems with large number of modes. It utilizes search techniques from the toolkit of model-based reasoning in order to focus the estimation on the set of most likely modes, without missing symptoms that might be hidden amongst the system noise. In addition, we present a novel approach to hybrid estimation in the presence of unknown behavioral modes. This leads to an overall hybrid estimation scheme for complex systems that robustly copes with unforeseen situations in a degraded, but fail-safe manner. We present a Monte-Carlo optimization technique for finding inputs to a system that falsify a given Metric Temporal Logic (MTL) property. Our approach performs a random walk over the space of inputs guided by a robustness metric defined by the MTL property. Robustness can be used to guide our search for a falsifying trajectory by exploring trajectories with smaller robustness values. We show that the notion of robustness can be generalized to consider hybrid system trajectories. The resulting testing framework can be applied to non-linear hybrid systems with external inputs. We show through numerous experiments on complex systems that using our framework can help automatically falsify properties with more consistency as compared to other means such as uniform sampling. Trajectory Prediction of dynamic objects is a widely studied topic in the field of artificial intelligence. Thanks to a large number of applications like predicting abnormal events, navigation system for the blind, etc. there have been many approaches to attempt learning patterns of motion directly from data using a wide variety of techniques ranging from hand-crafted features to sophisticated deep learning models for unsupervised feature learning. All these approaches have been limited by problems like inefficient features in the case of hand crafted features, large error propagation across the predicted trajectory and no information of static artefacts around the dynamic moving objects. We propose an end to end deep learning model to learn the motion patterns of humans using different navigational modes directly from data using the much popular sequence to sequence model coupled with a soft attention mechanism. We also propose a novel approach to model the static artefacts in a scene and using these to predict the dynamic trajectories. The proposed method, tested on trajectories of pedestrians, consistently outperforms previously proposed state of the art approaches on a variety of large scale data sets. We also show how our architecture can be naturally extended to handle multiple modes of movement (say pedestrians, skaters, bikers and buses) simultaneously. User mobility has given rise to a variety of Web applications, in which the global positioning system (GPS) plays many important roles in bridging between these applications and end users. As a kind of human behavior, transportation modes, such as walking and driving, can provide pervasive computing systems with more contextual information and enrich a user's mobility with informative knowledge. In this article, we report on an approach based on supervised learning to automatically infer users' transportation modes, including driving, walking, taking a bus and riding a bike, from raw GPS logs. Our approach consists of three parts: a change point-based segmentation method, an inference model and a graph-based post-processing algorithm. First, we propose a change point-based segmentation method to partition each GPS trajectory into separate segments of different transportation modes. Second, from each segment, we identify a set of sophisticated features, which are not affected by differing traffic conditions (e.g., a person's direction when in a car is constrained more by the road than any change in traffic conditions). Later, these features are fed to a generative inference model to classify the segments of different modes. Third, we conduct graph-based postprocessing to further improve the inference performance. This postprocessing algorithm considers both the commonsense constraints of the real world and typical user behaviors based on locations in a probabilistic manner. The advantages of our method over the related works include three aspects. (1) Our approach can effectively segment trajectories containing multiple transportation modes. (2) Our work mined the location constraints from user-generated GPS logs, while being independent of additional sensor data and map information like road networks and bus stops. (3) The model learned from the dataset of some users can be applied to infer GPS data from others. Using the GPS logs collected by 65 people over a period of 10 months, we evaluated our approach via a set of experiments. As a result, based on the change-point-based segmentation method and Decision Tree-based inference model, we achieved prediction accuracy greater than 71 percent. Further, using the graph-based post-processing algorithm, the performance attained a 4-percent enhancement. Motivation: Since 1990, the basic local alignment search tool (BLAST) has become one of the most popular and fundamental bioinformatics tools for sequence similarity searching, receiving extensive attention from the research community. The two pioneering papers on BLAST have received over 96 000 citations. Given the huge population of BLAST users and the increasing size of sequence databases, an urgent topic of study is how to improve the speed. Recently, graphics processing units (GPUs) have been widely used as low-cost, highperformance computing platforms. The existing GPU-BLAST is a promising software tool that uses a GPU to accelerate protein sequence alignment. Unfortunately, there is still no GPU-accelerated software tool for BLAST-based nucleotide sequence alignment. Results: We developed G-BLASTN, a GPU-accelerated nucleotide alignment tool based on the widely used NCBI-BLAST. G-BLASTN can produce exactly the same results as NCBI-BLAST, and it has very similar user commands. Compared with the sequential NCBIBLAST, G-BLASTN can achieve an overall speedup of 14.80X under ‘megablast’ mode. More impressively, it achieves an overall speedup of 7.15X over the multithreaded NCBI-BLAST running on 4 CPU cores. When running under ‘blastn’ mode, the overall speedups are 4.32X (against 1-core) and 1.56X (against 4-core). G-BLASTN also supports a pipeline mode that further improves the overall performance by up to 44 when handling a batch of queries as a whole. Currently G-BLASTN is best optimized for databases with long sequences. We plan to optimize its performance on short database sequences Abstract We investigate solution techniques for numerical constraint-satisfaction problems and validated numerical set integration methods for computing reachable sets of nonlinear hybrid dynamical systems in the presence of uncertainty. To use interval simulation tools with higher-dimensional hybrid systems, while assuming large domains for either initial continuous state or model parameter vectors, we need to solve the problem of flow sets intersection in an effective and reliable way. The main idea developed in this paper is first to derive an analytical expression for the boundaries of continuous flows, using interval Taylor methods and techniques for controlling the wrapping effect. Then, the event detection and localization problems underlying flow sets intersection are expressed as numerical constraint-satisfaction problems, which are solved using global search methods based on branch-and-prune algorithms, interval analysis and consistency techniques. The method is illustrated with hybrid systems with uncertain nonlinear continuous dynamics and nonlinear invariants and guards. Innovative methods have been developed for diagnosis, activity monitoring, and state estimation that achieve high accuracy through the use of stochastic models involving hybrid discrete and continuous behaviors. A key bottleneck is the automated acquisition of these hybrid models, and recent methods have focused predominantly on Jump Markov processes and piecewise autoregressive models. In this paper, we present a novel algorithm capable of performing unsupervised learning of guarded Probabilistic Hybrid Automata (PHA) models, which extends prior work by allowing stochastic discrete mode transitions in a hybrid system to have a functional dependence on its continuous state. Our experiments indicate that guarded PHA models can yield significant performance improvements when used by hybrid state estimators, particularly when diagnosing the true discrete mode of the system, without any noticeable impact on their real-time performance. We present a policy search method that uses iteratively refitted local linear models to optimize trajectory distributions for large, continuous problems. These trajectory distributions can be used within the framework of guided policy search to learn policies with an arbitrary parameterization. Our method fits time-varying linear dynamics models to speed up learning, but does not rely on learning a global model, which can be difficult when the dynamics are complex and discontinuous. We show that this hybrid approach requires many fewer samples than model-free methods, and can handle complex, nonsmooth dynamics that can pose a challenge for model-based techniques. We present experiments showing that our method can be used to learn complex neural network policies that successfully execute simulated robotic manipulation tasks in partially observed environments with numerous contact discontinuities and underactuation. This paper concerns computational methods for verifying properties of polyhedral invariant hybrid automata (PIHA), which are hybrid automata with discrete transitions governed by polyhedral guards. To verify properties of the state trajectories for PIHA, the planar switching surfaces are partitioned to define a finite set of discrete states in an approximate quotient transition system (AQTS). State transitions in the AQTS are determined by the reachable states, or flow pipes, emitting from the switching surfaces according to the continuous dynamics. This paper presents a method for computing polyhedral approximations to flow pipes. It is shown that the flow-pipe approximation error can be made arbitrarily small for general nonlinear dynamics and that the computations can be made more efficient for affine systems. The paper also describes CheckMate, a MATLAB-based tool for modeling, simulating and verifying properties of hybrid systems based on the computational methods previously described. In this paper, a new method is presented for motion planning in dynamic environments, that is, finding a trajectory for a robot in a scene consisting of both static and dynamic, moving obstacles. We propose a practical algorithm based on a roadmap that is created for the static part of the scene. On this roadmap, an approximately time-optimal trajectory from a start to a goal configuration is computed, such that the robot does not collide with any moving obstacle. The trajectory is found by performing a two-level search for a shortest path. On the local level, trajectories on single edges of the roadmap are found using a depth-first search on an implicit grid in state-time space. On the global level, these local trajectories are coordinated using an A sup * -search to find a global trajectory to the goal configuration. The approach is applicable to any robot type in configuration spaces with any dimension, and the motions of the dynamic obstacles are unconstrained, as long as they are known beforehand. The approach has been implemented for both free-flying and articulated robots in three-dimensional workspaces, and it has been applied to multirobot motion planning, as well. Experiments show that the method achieves interactive performance in complex environments. In this paper, we propose a deep learning-based vehicle trajectory prediction technique which can generate the future trajectory sequence of the surrounding vehicles in real time. We employ the encoder-decoder architecture which analyzes the pattern underlying in the past trajectory using the long short term memory (LSTM)-based encoder and generates the future trajectory sequence using the LSTM-based decoder. This structure produces the @math most likely trajectory candidates over occupancy grid map by employing the beam search technique which keeps the @math locally best candidates from the decoder output. The experiments conducted on highway traffic scenarios show that the prediction accuracy of the proposed method is significantly higher than the conventional trajectory prediction techniques. Abstract : Human motion sequences that are generated by computer algorithms may contain abrupt transitions: places where consecutive body positions would require physically impossible or stylistically illegal moves. We use graph--theoretic methods to learn the "grammar" of joint movements in a given corpus and then apply memory-bounded A* search to the resulting transition graphs--using an in order to reduce the search space--to find appropriate interpolation sequences. The application that motivated the development of these methods is an algorithm that uses the mathematical properties of chaos to generate variations on dance and martial arts sequences.