We present a novel, reusable and task-agnostic primitive for assessing the outcome of a force-interaction robotic skill, useful e.g. for applications such as quality control in industrial manufacturing. The proposed method is easily programmed by kinesthetic teaching, and the desired adaptability and reusability are achieved by machine learning models. The primitive records sensory data during both demonstrations and reproductions of a movement. Recordings include the end-effector's Cartesian pose and exerted wrench at each time step. The collected data are then used to train Gaussian Processes which create models of the wrench as a function of the robot's pose. The similarity between the wrench models of the demonstration and the movement's reproduction is derived by measuring their Hellinger distance. This comparison creates features that are fed as inputs to a Naive Bayes classifier which estimates the movement's probability of success. The evaluation is performed on two diverse robotic assembly tasks -- snap-fitting and screwing -- with a total of 5 use cases, 11 demonstrations, and more than 200 movement executions. The performance metrics prove the proposed method's capability of generalization to different demonstrations and movements.
An alternative solution to assess the task outcome is statistically setting a threshold regarding the wrench signature and the pose trajectories. Costa al @cite_7 verify the success of a process by setting a threshold for eccentricity and typicality, distance metrics for time series. Haidu al @cite_10 define lower and upper bounds of the trajectory profile based on successful trails. Thus, trajectory profiles that exceed the threshold indicates a failure. Nevertheless, the movement reproduction varies for different task parameters (e.g. start and goal state) and demonstrations. In those cases, the bounds have to be changed accordingly which requires reprogramming.
@cite_10 @cite_7
2219364599 1654125355
We address the problem of performing efficient similarity join for large sets of moving objects trajectories. Unlike previous approaches which use a dedicated index in a transformed space, our premise is that in many applications of location-based services, the trajectories are already indexed in their native space, in order to facilitate the processing of common spatio-temporal queries, e.g., range, nearest neighbor etc. We introduce a novel distance measure adapted from the classic Frechet distance, which can be naturally extended to support lower upper bounding using the underlying indices of moving object databases in the native space. This, in turn, enables efficient implementation of various trajectory similarity joins. We report on extensive experiments demonstrating that our methodology provides performance speed-up of trajectory similarity join by more than 50 on average, while maintaining effectiveness comparable to the well-known approaches for identifying trajectory similarity based on time-series analysis. 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. Gestures are characterized by intermediary or final landmarks (real or virtual) in task space or joint space that can change during the course of the motion, and that are described by varying accuracy and correlation constraints. Generalizing these trajectories in robot learning by imitation is challenging, because of the small number of demonstrations provided by the user. We present an approach to statistically encode movements in a task-parameterized mixture model, and derive an expectation-maximization (EM) algorithm to train it. The model automatically extracts the relevance of candidate coordinate systems during the task, and exploits this information during reproduction to adapt the movement in real-time to changing position and orientation of landmarks or objects. The approach is tested with a robotic arm learning to roll out a pizza dough. It is compared to three categories of task-parameterized models: 1) Gaussian process regression (GPR) with a trajectory models database; 2) Multi-streams approach with models trained in several frames of reference; and 3) Parametric Gaussian mixture model (PGMM) modulating the Gaussian centers with the task parameters. We show that the extrapolation capability of the proposed approach outperforms existing methods, by extracting the local structures of the task instead of relying on interpolation principles. The best current estimates of the thresholds for the existence of solutions in random constraint satisfaction problems ('CSPs') mostly derive from the first and the second moment method. Yet apart from a very few exceptional cases these methods do not quite yield matching upper and lower bounds. According to deep but non-rigorous arguments from statistical mechanics, this discrepancy is due to a change in the geometry of the set of solutions called condensation that occurs shortly before the actual threshold for the existence of solutions (Krzakala, Montanari, Ricci-Tersenghi, Semerjian, Zdeborova: PNAS 2007). To cope with condensation, physicists have developed a sophisticated but non-rigorous formalism called Survey Propagation (Me-zard, Parisi, Zecchina: Science 2002). This formalism yields precise conjectures on the threshold values of many random CSPs. Here we develop a new Survey Propagation inspired second moment method for the random k-NAESAT problem, which is one of the standard benchmark problems in the theory of random CSPs. This new technique allows us to overcome the barrier posed by condensation rigorously. We prove that the threshold for the existence of solutions in random k-NAESAT is 2k-1ln2-(ln 2 2+1 4)+ek, where |ek| ≤ 2-(1-ok(1))k, thereby verifying the statistical mechanics conjecture for this problem. The paper concerns the synthesis of supervisory controllers for a class of continuous-time hybrid systems with discrete-valued input signals that select differential inclusions for continuous-valued state trajectories and event-valued output signals generated by threshold crossings in the continuous state space, the supervisor is allowed to switch the input signal value when threshold events are observed. The objective is to synthesize a nonblocking supervisor such that the set of possible sequences of control and threshold event pairs for the closed-loop system lies between given upper and lower bounds in the sense of set containment. We show how this problem can be converted into a supervisor synthesis problem for a standard controlled discrete-event system (DES). A finite representation may not exist for the exact DES model of the hybrid system, however. To circumvent this difficulty, we present an algorithm for constructing finite-state Muller automata that accept outer approximations to the exact controlled threshold-event language, and we demonstrate that supervisors that solve the synthesis problem for the approximating automata achieve the control specifications when applied to the original hybrid system. In this paper, we address the problem of simultaneously achieving low trajectory tracking errors and compliant control without using explicit mathematical models of task dynamics. To achieve this goal, we propose a new movement representation called compliant movement primitives (CMPs), which encodes position trajectory and associated torque profiles and can be learned from a single user demonstration. With the proposed control framework, the robot can remain compliant and consequently safe for humans sharing its workspace, even if high trajectory tracking accuracy is required. We developed a statistical learning approach that can use a database of existing CMPs and compute new ones, adapted for novel task variations. The proposed approach was evaluated on a Kuka LWR-4 robot performing 1) a discrete pick-and-place task with objects of varying weight and 2) a periodic handle turning operation. The evaluation of the discrete task showed a 15-fold decrease of the tracking error while exhibiting compliant behavior compared to the standard feedback control approach. It also indicated no significant rise in the tracking error while using generalized primitives computed by the statistical learning method. With respect to unforeseen collisions, the proposed approach resulted in a 75 drop of contact forces compared to standard feedback control. The periodic task demonstrated on-line use of the proposed approach to accomplish a task of handle turning. This paper studies an unmanned aerial vehicle (UAV)-enabled multicasting system, where a UAV is dispatched to disseminate a common file to a number of geographically distributed ground terminals (GTs). Our objective is to design the UAV trajectory to minimize its mission completion time, while ensuring that each GT is able to successfully recover the file with a high probability required. We consider the use of practical random linear network coding (RLNC) for UAV multicasting, so that each GT is able to recover the file as long as it receives a sufficiently large number of coded packets. However, the formulated UAV trajectory optimization problem is non-convex and difficult to be directly solved. To tackle this issue, we first derive an analytical lower bound for the success probability of each GT's file recovery. Based on this result, we then reformulate the problem into a more tractable form, where the UAV trajectory only needs to be designed to meet a set of constraints each on the minimum connection time with a GT, during which their distance is below a designed threshold. We show that the optimal UAV trajectory only needs to constitute connected line segments, thus it can be obtained by determining first the optimal set of waypoints and then UAV speed along the lines connecting the waypoints. We propose practical schemes for the waypoints design based on a novel concept of virtual base station (VBS) placement and by applying convex optimization techniques. Furthermore, for given set of waypoints, we obtain the optimal UAV speed over the resulting path efficiently by solving a linear programming (LP) problem. Numerical results show that the proposed UAV-enabled multicasting with optimized trajectory design achieves significant performance gains as compared to benchmark schemes. We prove new upper and lower bounds on the sample complexity of (a#x03B5;, a#x03B4;) differentially private algorithms for releasing approximate answers to threshold functions. A threshold function cx over a totally ordered domain X evaluates to cx(y) = 1 if y a#x2264; x, and evaluates to 0 otherwise. We give the first nontrivial lower bound for releasing thresholds with (a#x03B5;, a#x03B4;) differential privacy, showing that the task is impossible over an infinite domain X, and moreover requires sample complexity n a#x2265; (log* |X|), which grows with the size of the domain. Inspired by the techniques used to prove this lower bound, we give an algorithm for releasing thresholds with n a#x2264; 2(1+o(1)) log* |X| samples. This improves the previous best upper bound of 8(1+o(1)) log* |X| (, RANDOM'13). Our sample complexity upper and lower bounds also apply to the tasks of learning distributions with respect to Kolmogorov distance and of properly PAC learning thresholds with differential privacy. The lower bound gives the first separation between the sample complexity of properly learning a concept class with (a#x03B5;, a#x03B4;) differential privacy and learning without privacy. For properly learning thresholds in 'dimensions, this lower bound extends to n a#x2265; (l a#x2219; log* |X|). To obtain our results, we give reductions in both directions from releasing and properly learning thresholds and the simpler interior point problem. Given a database D of elements from X, the interior point problem asks for an element between the smallest and largest elements in D. We introduce new recursive constructions for bounding the sample complexity of the interior point problem, as well as further reductions and techniques for proving impossibility results for other basic problems in differential privacy. The main objective of this paper is to develop an efficient method for learning and reproduction of complex trajectories for robot programming by demonstration. Encoding of the demonstrated trajectories is performed with hidden Markov model, and generation of a generalized trajectory is achieved by using the concept of key points. Identification of the key points is based on significant changes in position and velocity in the demonstrated trajectories. The resulting sequences of trajectory key points are temporally aligned using the multidimensional dynamic time warping algorithm, and a generalized trajectory is obtained by smoothing spline interpolation of the clustered key points. The principal advantage of our proposed approach is utilization of the trajectory key points from all demonstrations for generation of a generalized trajectory. In addition, variability of the key points' clusters across the demonstrated set is employed for assigning weighting coefficients, resulting in a generalization procedure which accounts for the relevance of reproduction of different parts of the trajectories. The approach is verified experimentally for trajectories with two different levels of complexity. We address the fundamental problem of goal-directed path planning in an uncertain environment represented as a probability (of occupancy) map. Most methods generally use a threshold to reduce the grayscale map to a binary map before applying off-the-shelf techniques to find the best path. This raises the somewhat ill-posed question, what is the right (optimal) value to threshold the map? We instead suggest a persistent homology approach to the problem-a topological approach in which we seek the homology class of trajectories that is most persistent for the given probability map. In other words, we want the class of trajectories that is free of obstacles over the largest range of threshold values. In order to make this problem tractable, we use homology in ℤ 2 coefficients (instead of the standard ℤ coefficients), and describe how graph search-based algorithms can be used to find trajectories in different homology classes. Our simulation results demonstrate the efficiency and practical applicability of the algorithm proposed in this paper.paper. Describes a synergistic integration of a grasping simulator and a real-time visual tracking system, that work in concert to (1) find an object's pose, (2) plan grasps and movement trajectories, and (3) visually monitor task execution. Starting with a CAD model of an object to be grasped, the system can find the object's pose through vision which then synchronizes the state of the robot workcell with an online, model-based grasp planning and visualization system we have developed called GraspIt. GraspIt can then plan a stable grasp for the object, and direct the robotic hand system to perform the grasp. It can also generate trajectories for the movement of the grasped object, which are used by the visual control system to monitor the task and compare the actual grasp and trajectory with the planned ones. We present experimental results using typical grasping tasks. Experiments on solvingr-SAT random formulae have provided evidence of a satisfiability threshold phenomenon with respect to the ratio of the number of clauses to the number of variables of formulae. Presently, only the threshold of 2-SAT formulae has been proved to exist and has been computed to be equal to 1. For 3-SAT formulae and more generally forr-SAT formulae, lower and upper bounds of the threshold have been established. The best established bounds concern 3-SAT. For an observed threshold of about 4.25, the best lower bound is 3.003 and the best upper bound 4.76. In this paper we establish a general upper bound of the threshold forr-SAT formulae giving a value for 3-SAT of 4.64, significantly improving the previous best upper bound. For this we have defined a more restrictive structure than a satisfying truth assignment for characterizing the satisfiability of a SAT formula which we have called negatively prime solution (NPS). By merely applying the first moment method to negatively prime solutions of a randomr-SAT formula we obtain our bound. This paper formulates the vehicle navigation task as a constrained optimal control problem with constraints bounding a traversable region of the environment. A model predictive controller iteratively plans an optimal vehicle trajectory through the constrained corridor and uses this trajectory to establish the minimum threat posed to the vehicle given its current state and driver inputs. Based on this threat assessment, the level of controller intervention required to prevent departure from the traversable corridor is calculated and driver controller inputs are scaled accordingly. Simulated and experimental results are presented to demonstrate multiple threat metrics and configurable intervention laws. The adoption of everyday decisions in public affairs, fashion, movie-going, and consumer behavior is now thoroughly believed to migrate in a population through an influential network. The same diffusion process when being imitated by intention is called viral marketing. This process can be modeled by a (directed) graph G=(V,E) with a threshold t(v) for every vertex v?V, where v becomes active once at least t(v) of its (in-)neighbors are already active. A Perfect Target Set is a set of vertices whose activation will eventually activate the entire graph, and the Perfect Target Set Selection Problem (PTSS) asks for the minimum such initial set. It is known (Chen (2008) 6) that PTSS is hard to approximate, even for some special cases such as bounded-degree graphs, or majority thresholds.We propose a combinatorial model for this dynamic activation process, and use it to represent PTSS and its variants by linear integer programs. This allows one to use standard integer programming solvers for solving small-size PTSS instances. We also show combinatorial lower and upper bounds on the size of the minimum Perfect Target Set. Our upper bound implies that there are always Perfect Target Sets of size at most |V| 2 and 2|V| 3 under majority and strict majority thresholds, respectively, both in directed and undirected graphs. This improves the bounds of 0.727|V| and 0.7732|V| found recently by Chang and Lyuu (2010) 5 for majority and strict majority thresholds in directed graphs, and matches their bound under majority thresholds in undirected graphs. Furthermore, our proof is much simpler, and we observe that some of these bounds are tight. One interesting and perhaps surprising implication of our lower bound for undirected graphs, is that it is easy to get a constant factor approximation for PTSS for “relatively balanced” graphs (e.g., bounded-degree graphs, nearly regular graphs) with a “more than majority” threshold (that is, t(v)=??deg(v), for every v?V and some constant ?>1 2), whereas no polylogarithmic approximation exists for “more than majority” graphs. This paper discusses experimental robot identification based on a statistical framework. It presents a new approach toward the design of optimal robot excitation trajectories, and formulates the maximum-likelihood estimation of dynamic robot model parameters. The differences between the new design approach and the existing approaches lie in the parameterization of the excitation trajectory and in the optimization criterion. The excitation trajectory for each joint is a finite Fourier series. This approach guarantees periodic excitation which is advantageous because it allows: 1) time-domain data averaging; 2) estimation of the characteristics of the measurement noise, which is valuable in the case of maximum-likelihood parameter estimation. In addition, the use of finite Fourier series allows calculation of the joint velocities and acceleration in an analytic way from the measured position response, and allows specification of the bandwidth of the excitation trajectories. The optimization criterion is the uncertainty on the estimated parameters or a lower bound for it, instead of the often used condition of the parameter estimation problem. Simulations show that this criterion yields parameter estimates with smaller uncertainty bounds than trajectories optimized according to the classical criterion. Experiments on an industrial robot show that the presented trajectory design and maximum-likelihood parameter estimation approaches complement each other to make a practicable robot identification technique which yields accurate robot models. Most animal and human locomotion behaviors for solving complex tasks involve dynamic motions and rich contact interaction. In fact, complex maneuvers need to consider dynamic movement and contact events at the same time. We present a hierarchical trajectory optimization approach for planning dynamic movements with unscheduled contact sequences. We compute whole-body motions that achieve goals that cannot be reached in a kinematic fashion. First, we find a feasible CoM motion according to the centroidal dynamics of the robot. Then, we refine the solution by applying the robot's full-dynamics model, where the feasible CoM trajectory is used as a warm-start point. To accomplish the unscheduled contact behavior, we use complementarity constraints to describe the contact model, i.e. environment geometry and non-sliding active contacts. Both optimization phases are posed as Mathematical Program with Complementarity Constraints (MPCC). Experimental trials demonstrate the performance of our planning approach in a set of challenging tasks. This paper addresses the problem of understanding the shape of the locomotor trajectories for a human being walking in an empty space to reach a goal defined both in position and in direction. Among all the possible trajectories reaching a given goal what are the fundamental reasons to chose one trajectory instead of another (see Fig. (1))? The underlying idea to attack this question has been to relate this problem to an optimal control problem: the trajectory is chosen according to some optimization principle. This is our basic starting assumption. The subject being viewed as a controlled system, the question becomes what criteria is optimized? Is it the time to perform the trajectory? the length of the path? the minimum jerk along the path?... In this study we show that the human locomotor trajectories are well approximated by the geodesics of a differential system minimizing the L2 norm of the control. Such geodesics are made of arcs of clothoids. The clothoid or Cornu spiral is a curve, whose curvature grows with the distance from the origin. The study is based on an experimental protocol involving 7 subjects. They had to walk within a motion capture room from a fixed starting point, and to cross over distant porches from which both position in the room and orientation were changing over trials. We propose a segmentation and feature extraction method for trajectories of moving objects. The methodology consists of three stages: trajectory data preparation; global descriptors computation; and local feature extraction. The key element is an algorithm that decomposes the profiles generated for different movement parameters (velocity, acceleration, etc.) using variations in sinuosity and deviation from the median line. Hence, the methodology enables the extraction of local movement features in addition to global ones that are essential for modeling and analyzing moving objects in applications such as trajectory classification, simulation and extraction of movement patterns. As a case study, we show how the method can be employed in classifying trajectory data generated by unknown moving objects and assigning them to known types of moving objects, whose movement characteristics have been previously learned. We have conducted a series of experiments that provide evidence about the similarities and differences that exist among different types of moving objects. The experiments show that the methodology can be successfully applied in automatic transport mode detection. It is also shown that eye-movement data cannot be successfully used as a proxy of full-body movement of humans, or vehicles. The paper investigates the possibilities of using clustering techniques in visual exploration and analysis of large numbers of trajectories, that is, sequences of time-stamped locations of some moving entities. Trajectories are complex spatio-temporal constructs characterized by diverse non-trivial properties. To assess the degree of (dis)similarity between traiectories, specific methods (distance functions) are required. A single distance function accounting for all properties of trajectories, (1) is difficult to build, (2) would require much time to compute, and (3) might be difficult to understand and to use. We suggest the procedure of progressive clustering where a simple distance function with a clear meaning is applied on each step, which leads to easily interpretable outcomes. Successive application of several different functions enables sophisticated analyses through gradual refinement of earlier obtained results. Besides the advantages from the sense-making perspective, progressive clustering enables a rational work organization where time-consuming computations are applied to relatively small potentially interesting subsets obtained by means of 'cheap' distance functions producing quick results. We introduce the concept of progressive clustering by an example of analyzing a large real data set. We also review the existing clustering methods, describe the method OPTICS suitable for progressive clustering of trajectories, and briefly present several distance functions for trajectories. We formalize the problem of adapting a demonstrated trajectory to a new start and goal configuration as an optimization problem over a Hilbert space of trajectories: minimize the distance between the demonstration and the new trajectory subject to the new end point constraints. We show that the commonly used version of Dynamic Movement Primitives (DMPs) implement this minimization in the way they adapt demonstrations, for a particular choice of the Hilbert space norm. The generalization to arbitrary norms enables the robot to select a more appropriate norm for the task, as well as learn how to adapt the demonstration from the user. Our experiments show that this can significantly improve the robot's ability to accurately generalize the demonstration.