MAPF is the problem of finding paths for multiple agents such that every agent reaches its goal and the agents do not collide. Most prior work on MAPF were on grid, assumed all actions cost the same, agents do not have a volume, and considered discrete time steps. In this work we propose a MAPF algorithm that do not assume any of these assumptions, is complete, and provides provably optimal solutions. This algorithm is based on a novel combination of SIPP, a continuous time single agent planning algorithms, and CBS, a state of the art multi-agent pathfinding algorithm. We analyze this algorithm, discuss its pros and cons, and evaluate it experimentally on several standard benchmarks.
dRRT* is a MAPF algorithm designed for continuous spaces @cite_25 . It is a sample-based technique that is asymptotically complete and optimal. is optimal and complete, and is designed to run over a discrete graph. ORCA @cite_19 @cite_27 and ALAN @cite_18 are also MAPF algorithms designed for continuous space. They are fast and distributed, but do not provide optimality or completeness guarantees.
@cite_19 @cite_27 @cite_18 @cite_25
2136323427 2729017031 2091449379 1864112212 2141664020 108082272 2887556118 2016930536 2163973643 2737130609 2088303535 2166771065 2590877996 2142224528 2044688447 2101866605 2114493937 2294808847 2056579540 2010676632
We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated RRT algorithm for the discrete case of a graph, and it enables a rapid exploration of the high-dimensional configuration space by carefully walking through an implicit representation of a tensor product of roadmaps for the individual robots. We demonstrate our approach experimentally on scenarios of up to 60 degrees of freedom where our algorithm is faster by a factor of at least ten when compared to existing algorithms that we are aware of. Finding asymptotically-optimal paths in multi-robot motion planning problems could be achieved, in principle, using sampling-based planners in the composite configuration space of all of the robots in the space. The dimensionality of this space increases with the number of robots, rendering this approach impractical. This work focuses on a scalable sampling-based planner for coupled multi-robot problems that provides asymptotic optimality. It extends the dRRT approach, which proposed building roadmaps for each robot and searching an implicit roadmap in the composite configuration space. This work presents a new method, dRRT* , and develops theory for scalable convergence to optimal paths in multi-robot problems. Simulated experiments indicate dRRT* converges to high-quality paths while scaling to higher numbers of robots where the naive approach fails. Furthermore, dRRT* is applicable to high-dimensional problems, such as planning for robot manipulators In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependant relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between FaLRTC and HaLRTC the former is more efficient to obtain a low accuracy solution and the latter is preferred if a high-accuracy solution is desired. In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm FMT*. The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a 'lazy' dynamic programming recursion on a predetermined number of probabilistically drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As such, this algorithm combines features of both single-query algorithms chiefly RRT and multiple-query algorithms chiefly PRM, and is reminiscent of the Fast Marching Method for the solution of Eikonal equations. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds-the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order On −1 d+? , where n is the number of sampled points, d is the dimension of the configuration space, and ? is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our theoretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive. A simple and efficient randomized algorithm is presented for solving single-query path planning problems in high-dimensional configuration spaces. The method works by incrementally building two rapidly-exploring random trees (RRTs) rooted at the start and the goal configurations. The trees each explore space around them and also advance towards each other through, the use of a simple greedy heuristic. Although originally designed to plan motions for a human arm (modeled as a 7-DOF kinematic chain) for the automatic graphic animation of collision-free grasping and manipulation tasks, the algorithm has been successfully applied to a variety of path planning problems. Computed examples include generating collision-free motions for rigid objects in 2D and 3D, and collision-free manipulation motions for a 6-DOF PUMA arm in a 3D workspace. Some basic theoretical analysis is also presented. RTDP is a recent heuristic-search DP algorithm for solving non-deterministic planning problems with full observability. In relation to other dynamic programming methods, RTDP has two benefits: first, it does not have to evaluate the entire state space in order to deliver an optimal policy, and second, it can often deliver good policies pretty fast. On the other hand, RTDP final convergence is slow. In this paper we introduce a labeling scheme into RTDP that speeds up its convergence while retaining its good anytime behavior. The idea is to label a state s as solved when the heuristic values, and thus, the greedy policy defined by them, have converged over s and the states that can be reached from s with the greedy policy. While due to the presence of cycles, these labels cannot be computed in a recursive, bottom-up fashion in general, we show nonetheless that they can be computed quite fast, and that the overhead is compensated by the recomputations avoided. In addition, when the labeling procedure cannot label a state as solved, it improves the heuristic value of a relevant state. This results in the number of Labeled RTDP trials needed for convergence, unlike the number of RTDP trials, to be bounded. From a practical point of view, Labeled RTDP (LRTDP) converges orders of magnitude faster than RTDP, and faster also than another recent heuristic-search DP algorithm, LAO*. Moreover, LRTDP often converges faster than value iteration, even with the heuristic h = 0, thus suggesting that LRTDP has a quite general scope. Abstract Visual tracking algorithms based on structured output support vector machine (SOSVM) have demonstrated excellent performance. However, sampling methods and optimization strategies of SOSVM undesirably increase the computational overloads, which hinder real-time application of these algorithms. Moreover, due to the lack of high-dimensional features and dense training samples, SOSVM-based algorithms are unstable to deal with various challenging scenarios, such as occlusions and scale variations. Recently, visual tracking algorithms based on discriminative correlation filters (DCF), especially the combination of DCF and features from deep convolutional neural networks (CNN), have been successfully applied to visual tracking, and attains surprisingly good performance on recent benchmarks. The success is mainly attributed to two aspects: the circular correlation properties of DCF and the powerful representation capabilities of CNN features. Nevertheless, compared with SOSVM, DCF-based algorithms are restricted to simple ridge regression which has a weaker discriminative ability. In this paper, a novel circular and structural operator tracker (CSOT) is proposed for high performance visual tracking, it not only possesses the powerful discriminative capability of SOSVM but also efficiently inherits the superior computational efficiency of DCF. Based on the proposed circular and structural operators, a set of primal confidence score maps can be obtained by circular correlating feature maps with their corresponding structural correlation filters. Furthermore, an implicit interpolation is applied to convert the multi-resolution feature maps to the continuous domain and make all primal confidence score maps have the same spatial resolution. Then, we exploit an efficient ensemble post-processor based on relative entropy, which can coalesce primal confidence score maps and create an optimal confidence score map for more accurate localization. The target is localized on the peak of the optimal confidence score map. Besides, we introduce a collaborative optimization strategy to update circular and structural operators by iteratively training structural correlation filters, which significantly reduces computational complexity and improves robustness. Experimental results demonstrate that our approach achieves state-of-the-art performance in mean AUC scores of 71.5 and 69.4 on the OTB2013 and OTB2015 benchmarks respectively, and obtains a third-best expected average overlap (EAO) score of 29.8 on the VOT2017 benchmark. A new framework which adopts a rapidly-exploring random tree (RRT) path planner with a Gaussian process (GP) occupancy map is developed for the navigation and exploration of an unknown but cluttered environment. The GP map outputs the probability of occupancy given any selected query point in the continuous space and thus makes it possible to explore the full space when used in conjunction with a continuous path planner. Furthermore, the GP map-generated path is embedded with the probability of collision along the path which lends itself to obstacle avoidance. Finally, the GP map-building algorithm is extended to include an exploration mission considering the differential constraints of a rotary unmanned aerial vehicle and the limitation arising from the environment. Using mutual information as an information-theoretic measure, an informative path which reduces the uncertainty of the environment is generated. Simulation results show that GP map combined with RRT planner can achieve the 3D navigation and e... Recent compressive sensing results show that it is possible to accurately reconstruct certain compressible signals from relatively few linear measurements via solving nonsmooth convex optimization problems. In this paper, we propose the use of the alternating direction method - a classic approach for optimization problems with separable variables (D. Gabay and B. Mercier, ?A dual algorithm for the solution of nonlinear variational problems via finite-element approximations,? Computer and Mathematics with Applications, vol. 2, pp. 17-40, 1976; R. Glowinski and A. Marrocco, ?Sur lapproximation par elements finis dordre un, et la resolution par penalisation-dualite dune classe de problemes de Dirichlet nonlineaires,? Rev. Francaise dAut. Inf. Rech. Oper., vol. R-2, pp. 41-76, 1975) - for signal reconstruction from partial Fourier (i.e., incomplete frequency) measurements. Signals are reconstructed as minimizers of the sum of three terms corresponding to total variation, ?1-norm of a certain transform, and least squares data fitting. Our algorithm, called RecPF and published online, runs very fast (typically in a few seconds on a laptop) because it requires a small number of iterations, each involving simple shrinkages and two fast Fourier transforms (or alternatively discrete cosine transforms when measurements are in the corresponding domain). RecPF was compared with two state-of-the-art algorithms on recovering magnetic resonance images, and the results show that it is highly efficient, stable, and robust. Maximizing information gathered within a budget is a relevant problem for information gathering tasks for robots with cost or operating time constraints. This problem is also known as the informative path planning (IPP) problem or correlated orienteering. It can be formalized as that of finding budgeted routes in a graph such that the reward collected by the route is maximized, where the reward at nodes can be dependent. Unfortunately, the problem is NP-Hard and the state of the art methods are too slow to even present an approximate solution online. Here we present Randomized Anytime Orienteering (RAOr) algorithm that provides near optimal solutions while demonstrably converging to an efficient solution in runtimes that allows the solver to be run online. The key idea of our approach is to pose orienteering as a combination of a Constraint Satisfaction Problem and a Traveling Salesman Problem. This formulation allows us to restrict the search space to routes that incur minimum distance to visit a set of selected nodes, and rapidly search this space using random sampling. The paper provides the analysis of asymptotic near-optimality, convergence rates for RAOr algorithms, and present strategies to improve anytime performance of the algorithm. Our experimental results suggest an improvement by an order of magnitude over the state of the art methods in relevant simulation and in real world scenarios. In this paper, an estimation of distribution algorithm (EDA)-based memetic algorithm (MA) is proposed for solving the distributed assembly permutation flow-shop scheduling problem (DAPFSP) with the objective to minimize the maximum completion time. A novel bi-vector-based method is proposed to represent a solution for the DAPFSP. In the searching phase of the EDA-based MA (EDAMA), the EDA-based exploration and the local-search-based exploitation are incorporated within the MA framework. For the EDA-based exploration phase, a probability model is built to describe the probability distribution of superior solutions. Besides, a novel selective-enhancing sampling mechanism is proposed for generating new solutions by sampling the probability model. For the local-search-based exploitation phase, the critical path of the DAPFSP is analyzed to avoid invalid searching operators. Based on the analysis, a critical-path-based local search strategy is proposed to further improve the potential solutions obtained in the EDA-based searching phase. Moreover, the effect of parameter setting is investigated based on the Taguchi method of design-of-experiment. Suitable parameter values are suggested for instances with different scales. Finally, numerical simulations based on 1710 benchmark instances are carried out. The experimental results and comparisons with existing algorithms show the effectiveness of the EDAMA in solving the DAPFSP. In addition, the best-known solutions of 181 instances are updated by the EDAMA. Map-matching is the process of aligning a sequence of observed user positions with the road network on a digital map. It is a fundamental pre-processing step for many applications, such as moving object management, traffic flow analysis, and driving directions. In practice there exists huge amount of low-sampling-rate (e.g., one point every 2--5 minutes) GPS trajectories. Unfortunately, most current map-matching approaches only deal with high-sampling-rate (typically one point every 10--30s) GPS data, and become less effective for low-sampling-rate points as the uncertainty in data increases. In this paper, we propose a novel global map-matching algorithm called ST-Matching for low-sampling-rate GPS trajectories. ST-Matching considers (1) the spatial geometric and topological structures of the road network and (2) the temporal speed constraints of the trajectories. Based on spatio-temporal analysis, a candidate graph is constructed from which the best matching path sequence is identified. We compare ST-Matching with the incremental algorithm and Average-Frechet-Distance (AFD) based global map-matching algorithm. The experiments are performed both on synthetic and real dataset. The results show that our ST-matching algorithm significantly outperform incremental algorithm in terms of matching accuracy for low-sampling trajectories. Meanwhile, when compared with AFD-based global algorithm, ST-Matching also improves accuracy as well as running time. Abstract Most traditional algorithms for compressive sensing image reconstruction suffer from the intensive computation. Recently, deep learning-based reconstruction algorithms have been reported, which dramatically reduce the time complexity than iterative reconstruction algorithms. In this paper, we propose a novel Deep Residual Reconstruction Network (DR2-Net) to reconstruct the image from its Compressively Sensed (CS) measurement. The DR2-Net is proposed based on two observations: (1) linear mapping could reconstruct a high-quality preliminary image, and (2) residual learning could further improve the reconstruction quality. Accordingly, DR2-Net consists of two components, i.e., linear mapping network and residual network, respectively. Specifically, the fully-connected layer in neural network implements the linear mapping network. We then expand the linear mapping network to DR2-Net by adding several residual learning blocks to enhance the preliminary image. Extensive experiments demonstrate that the DR2-Net outperforms traditional iterative methods and recent deep learning-based methods by large margins at measurement rates 0.01, 0.04, 0.1, and 0.25, respectively. The code of DR2-Net has been released on: https: github.com coldrainyht caffe_dr2 . We present a new optimization-based approach for robotic motion planning among obstacles. Like CHOMP (Covariant Hamiltonian Optimization for Motion Planning), our algorithm can be used to find collision-free trajectories from naA¯ve, straight-line initializations that might be in collision. At the core of our approach are (a) a sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary, and (b) an efficient formulation of the no-collisions constraint that directly considers continuous-time safety Our algorithm is implemented in a software package called TrajOpt. We report results from a series of experiments comparing TrajOpt with CHOMP and randomized planners from OMPL, with regard to planning time and path quality. We consider motion planning for 7 DOF robot arms, 18 DOF full-body robots, statically stable walking motion for the 34 DOF Atlas humanoid robot, and physical experiments with the 18 DOF PR2. We also apply TrajOpt to plan curvature-constrained steerable needle trajectories in the SE(3) configuration space and multiple non-intersecting curved channels within 3D-printed implants for intracavitary brachytherapy. Details, videos, and source code are freely available at: http: rll.berkeley.edu trajopt ijrr. The data placement strategy greatly affects the efficiency of MapReduce. The current strategy only takes the map phase into account to optimize the map time. But the ignored shuffle phase may increase the total running time significantly in many jobs. We propose a new data placement strategy, named OPTAS, which optimizes both the map and shuffle phases to reduce their total time. However, the huge search space makes it difficult to find out an optimal data placement instance (DPI) rapidly. To address this problem, an algorithm is proposed which can prune most of the search space and find out an optimal result quickly. The search space firstly is segmented in ascending order according to the potential map time. Within each segment, we propose an efficient method to construct a local optimal DPI with the minimal total time of both the map and shuffle phases. To find the global optimal DPI, we scan the local optimal DPIs in order. We have proven that the global optimal DPI can be found as the first local optimal DPI whose total time stops decreasing, thus further pruning the search space. In practice, we find that at most fourteen local optimal DPIs are scanned in tens of thousands of segments with the pruning strategy. Extensive experiments with real trace data verify not only the theoretic analysis of our pruning strategy and construction method but also the optimality of OPTAS. The best improvements obtained in our experiments can be over 40 compared with the existing strategy used by MapReduce. We present a novel discriminative regression based approach for the Constrained Local Models (CLMs) framework, referred to as the Discriminative Response Map Fitting (DRMF) method, which shows impressive performance in the generic face fitting scenario. The motivation behind this approach is that, unlike the holistic texture based features used in the discriminative AAM approaches, the response map can be represented by a small set of parameters and these parameters can be very efficiently used for reconstructing unseen response maps. Furthermore, we show that by adopting very simple off-the-shelf regression techniques, it is possible to learn robust functions from response maps to the shape parameters updates. The experiments, conducted on Multi-PIE, XM2VTS and LFPW database, show that the proposed DRMF method outperforms state-of-the-art algorithms for the task of generic face fitting. Moreover, the DRMF method is computationally very efficient and is real-time capable. The current MATLAB implementation takes 1 second per image. To facilitate future comparisons, we release the MATLAB code and the pre-trained models for research purposes. This paper provides a novel technique for the analysis of randomized algorithms for optimization problems on metric spaces, by relating the randomized performance ratio for any, metric space to the randomized performance ratio for a set of "simple" metric spaces. We define a notion of a set of metric spaces that probabilistically-approximates another metric space. We prove that any metric space can be probabilistically-approximated by hierarchically well-separated trees (HST) with a polylogarithmic distortion. These metric spaces are "simple" as being: (1) tree metrics; (2) natural for applying a divide-and-conquer algorithmic approach. The technique presented is of particular interest in the context of on-line computation. A large number of on-line algorithmic problems, including metrical task systems, server problems, distributed paging, and dynamic storage rearrangement are defined in terms of some metric space. Typically for these problems, there are linear lower bounds on the competitive ratio of deterministic algorithms. Although randomization against an oblivious adversary has the potential of overcoming these high ratios, very little progress has been made in the analysis. We demonstrate the use of our technique by obtaining substantially improved results for two different on-line problems. We present ( RRT^ X ), the first asymptotically optimal sampling-based motion planning algorithm for real-time navigation in dynamic environments (containing obstacles that unpredictably appear, disappear, and move). Whenever obstacle changes are observed, e.g., by onboard sensors, a graph rewiring cascade quickly updates the search-graph and repairs its shortest-path -to-goal subtree. Both graph and tree are built directly in the robot’s state space, respect the kinematics of the robot, and continue to improve during navigation. ( RRT^ X ) is also competitive in static environments—where it has the same amortized per iteration runtime as RRT and RRT* ( ( n ) ) and is faster than RRT# ( ( ^2 n ) ). In order to achieve (O ( n ) ) iteration time, each node maintains a set of (O ( n ) ) expected neighbors, and the search graph maintains ( )-consistency for a predefined ( ). Several motion planning methods using networks of randomly generated nodes in the free space have been shown to perform well in a number of cases, however their performance degrades when paths are required to pass through narrow passages in the free space. In previous work we proposed MAPRM, a method of sampling the configuration space in which randomly generated configurations, free or not, are retracted onto the medial axis of the free space without having to first compute the medial axis; this was shown to increase sampling in narrow passages. In this paper we give details of the MAPRM algorithm for the case of a rigid body moving in three dimensions, and show that the retraction may be carried out without explicitly computing the C-obstacles or the medial axis. We give theoretical and experimental results to show this improves performance on problems involving narrow corridors and compare the performance to uniform random sampling from the free space. We propose an algorithm which combines the discriminative information from depth images as well as from 3D joint positions to achieve high action recognition accuracy. To avoid the suppression of subtle discriminative information and also to handle local occlusions, we compute a vector of many independent local features. Each feature encodes spatiotemporal variations of depth and depth gradients at a specific space-time location in the action volume. Moreover, we encode the dominant skeleton movements by computing a local 3D joint position difference histogram. For each joint, we compute a 3D space-time motion volume which we use as an importance indicator and incorporate in the feature vector for improved action discrimination. To retain only the discriminant features, we train a random decision forest (RDF). The proposed algorithm is evaluated on three standard datasets and compared with nine state-of-the-art algorithms. Experimental results show that, on the average, the proposed algorithm outperform all other algorithms in accuracy and have a processing speed of over 112 frames second.