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
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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 presents the application of a Bayesian nonparametric time-series model to process monitoring and fault classification for industrial robotic tasks. By means of an alignment task performed with a real robot, we show how the proposed approach allows to learn a set of sensor signature models encoding the spatial and temporal correlations among wrench measurements recorded during a number of successful task executions. Using these models, it is possible to detect continuously and on-line deviations from the expected sensor readings. Separate models are learned for a set of possible error scenarios involving a human modifying the workspace configuration. These non-nominal task executions are correctly detected and classified with an on-line algorithm, which opens the possibility for the development of error-specific recovery strategies. Our work is complementary to previous approaches in robotics, where process monitors based on probabilistic models, but limited to contact events, were developed for control purposes. Instead, in this paper we focus on capturing dynamic models of sensor signatures throughout the whole task, therefore allowing continuous monitoring and extending the system ability to interpret and react to errors. Consider a setting where robots must visit sites represented as nodes in a graph, but each robot may fail when traversing an edge. The goal is to find a set of paths for a team of robots which maximizes the expected number of nodes collectively visited, while guaranteeing that the paths satisfy a notion of “independence” formalized by a matroid (e.g. limits on team size, number of visits to regions), and that the probabilities that each robot survives to its destination are above a given threshold. We call this problem the Matroid Team Surviving Orienteers (MTSO) problem, which has broad applications such as environmental monitoring in risky regions and search and rescue in dangerous conditions. We present the MTSO formally and detail numerous examples of matroids in a path planning context. We then propose an approximate greedy algorithm for selecting a feasible set of paths and prove that the value of the output is within a factor p s p s + λ of the optimum, where p s is the per-robot survival probability threshold and 1 λ ≤ 1 is the approximation factor of an oracle routine for the well known orienteering problem. We demonstrate the efficiency of our approach by applying it to a scenario where a team of robots must gather information while avoiding pirates in the Coral Triangle. In order to track moving objects in long range against occlusion, interruption, and background clutter, this paper proposes a unified approach for global trajectory analysis. Instead of the traditional frame-by-frame tracking, our method recovers target trajectories based on a short sequence of video frames, e.g., 15 frames. We initially calculate a foreground map at each frame obtained from a state-of-the-art background model. An attribute graph is then extracted from the foreground map, where the graph vertices are image primitives represented by the composite features. With this graph representation, we pose trajectory analysis as a joint task of spatial graph partitioning and temporal graph matching. The task can be formulated by maximizing a posteriori under the Bayesian framework, in which we integrate the spatio-temporal contexts and the appearance models. The probabilistic inference is achieved by a data-driven Markov chain Monte Carlo algorithm. Given a period of observed frames, the algorithm simulates an ergodic and aperiodic Markov chain, and it visits a sequence of solution states in the joint space of spatial graph partitioning and temporal graph matching. In the experiments, our method is tested on several challenging videos from the public datasets of visual surveillance, and it outperforms the state-of-the-art methods. We present a task-parameterized probabilistic model encoding movements in the form of virtual spring-damper systems acting in multiple frames of reference. Each candidate coordinate system observes a set of demonstrations from its own perspective, by extracting an attractor path whose variations depend on the relevance of the frame at each step of the task. This information is exploited to generate new attractor paths in new situations (new position and orientation of the frames), with the predicted covariances used to estimate the varying stiffness and damping of the spring-damper systems, resulting in a minimal intervention control strategy. The approach is tested with a 7-DOFs Barrett WAM manipulator whose movement and impedance behavior need to be modulated in regard to the position and orientation of two external objects varying during demonstration and reproduction. For robotic systems to realise lifelong autonomy they must be able to navigate accurately in changing environments. In this thesis we describe, implement and validate a new approach to the problem of long-term navigation. To begin, we present our stereo visual odometry system which provides highly accurate pose estimation. Our approach combines several techniques found in existing implementations and a recently published image descriptor that simplifies the solution architecture. The performance and versatility of our system is demonstrated through testing on multiple datasets. Equipped with our visual odometry system, we describe a new approach to the problem of lifelong navigation. We learn a model whose complexity varies naturally in accordance with the variation of scene appearance. As the robot repeatedly traverses its workspace, it accumulates distinct visual experiences that, in concert, implicitly represent the scene variation - each experience captures a visual mode. When operating in a previously visited area, we continually try to localise in these previous experiences while simultaneously running the visual odometry. Failure to localise in a sufficient number of prior experiences indicates an insufficient model of the workspace and instigates the laying down of the live image sequence as a new distinct experience. In this way, over time we can capture the typical temporally varying appearance of an environment and the number of experiences required tends to a constant. Although we focus on vision as a primary sensor, the ideas we present here are equally applicable to other sensor modalities. We demonstrate our approach working on a road vehicle operating over a three month period at different times of day, in different weather and lighting conditions. 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. Structure from Motion (SfM) algorithms take as input multi-view stereo images (along with internal calibration information) and yield a 3D point cloud and camera orientations poses in a common 3D coordinate system. In the case of an incremental SfM pipeline, the process requires repeated model estimations based on detected feature points: homography, fundamental and essential matrices, as well as camera poses. These estimations have a crucial impact on the quality of 3D reconstruction. We propose to improve these estimations using the a contrario methodology. While SfM pipelines usually have globally-fixed thresholds for model estimation, the a contrario principle adapts thresholds to the input data and for each model estimation. Our experiments show that adaptive thresholds reach a significantly better precision. Additionally, the user is free from having to guess thresholds or to optimistically rely on default values. There are also cases where a globally-fixed threshold policy, whatever the threshold value is, cannot provide the best accuracy, contrary to an adaptive threshold policy. We explore fundamental performance limits of tracking a target in a two-dimensional field of binary proximity sensors, and design algorithms that attain those limits. In particular, using geometric and probabilistic analysis of an idealized model, we prove that the achievable spatial resolution Δ in localizing a target's trajectory is of the order of 1overρ R, where R is the sensing radius and ρ is the sensor density per unit area. Using an Occam's razor approach, we then design a geometric algorithm for computing an economical (in descriptive complexity) piecewise linear path that approximates the trajectory within this fundamental limit of accuracy. We employ analogies between binary sensing and sampling theory to contend that only a "lowpass" approximation of the trajectory is attainable, and explore the implications of this obervation for estimating the target's velocity.We show through simulation the effectiveness of the geometric algorithm in tracking both the trajectory and the velocity of the target for idealized models. For non-ideal sensors exhibiting sensing errors, the geometric algorithm can yield poor performance. We show that non-idealities can be handled well using a particle filter based approach, and that geometric post-processing of the output of the Particle Filter algorithm yields an economical path description as in the idealized setting. Finally, we report on our lab-scale experiments using motes with acoustic sensors to validate our theoretical and simulation results. The approach of inferring user's intended task and optimizing low-level robot motions has promise for making robot teleoperation interfaces more intuitive and responsive. But most existing methods assume a finite set of candidate tasks, which limits a robot's functionality. This paper proposes the notion of freeform tasks that encode an infinite number of possible goals (e.g., desired target positions) within a finite set of types (e.g., reach, orient, pick up). It also presents two technical contributions to help make freeform UIs possible. First, an intent predictor estimates the user's desired task, and accepts freeform tasks that include both discrete types and continuous parameters. Second, a cooperative motion planner continuously updates the robot's trajectories to achieve the inferred tasks by repeatedly solving optimal control problems. The planner is designed to respond interactively to changes in the indicated task, avoid collisions in cluttered environments, handle time-varying objective functions, and achieve high-quality motions using a hybrid of numerical and sampling-based techniques. The system is applied to the problem of controlling a 6D robot manipulator using 2D mouse input in the context of two tasks: static target reaching and dynamic trajectory tracking. Simulations suggest that it enables the robot to reach intended targets faster and to track intended trajectories more closely than comparable techniques. The problem of consistently estimating the sparsity pattern of a vector β* ∈ RP based on observations contaminated by noise arises in various contexts, including signal denoising, sparse approximation, compressed sensing, and model selection. We analyze the behavior of l1-constrained quadratic programming (QP), also referred to as the Lasso, for recovering the sparsity pattern. Our main result is to establish precise conditions on the problern dimension p, the number k of nonzero elements in β*, and the number of observations n that are necessary and sufficient for sparsity pattern recovery using the Lasso. We first analyze the case of observations made using deterministic design matrices and sub-Gaussian additive noise, and provide sufficient conditions for support recovery and l∞-error bounds, as well as results showing the necessity of incoherence and bounds on the minimum value. We then turn to the case of random designs, in which each row of the design is drawn from a N(0, Σ) ensemble. For a broad class of Gaussian ensembles satisfying mutual incoherence conditions, we compute explicit values of thresholds 0 0, if n > 2(θu + δ)k log(p - k), then the Lasso succeeds in recovering the sparsity pattern with probability converging to one for large problems, whereas for n < 2(θl - δ)k log(p - k), then the probability of successful recovery converges to zero. For the special case of the uniform Gaussian ensemble (Σ = I p×p), we show that θl = θu = 1, so that the precise threshold n = 2k log (p - k) is exactly determined. A probabilistic method for tracking 3D articulated human figures in monocular image sequences is presented. Within a Bayesian framework, we define a generative model of image appearance, a robust likelihood function based on image graylevel differences, and a prior probability distribution over pose and joint angles that models how humans move. The posterior probability distribution over model parameters is represented using a discrete set of samples and is propagated over time using particle filtering. The approach extends previous work on parameterized optical flow estimation to exploit a complex 3D articulated motion model. It also extends previous work on human motion tracking by including a perspective camera model, by modeling limb self occlusion, and by recovering 3D motion from a monocular sequence. The explicit posterior probability distribution represents ambiguities due to image matching, model singularities, and perspective projection. The method relies only on a frame-to-frame assumption of brightness constancy and hence is able to track people under changing viewpoints, in grayscale image sequences, and with complex unknown backgrounds. The state of the art in articulated hand tracking has been greatly advanced by hybrid methods that fit a generative hand model to depth data, leveraging both temporally and discriminatively predicted starting poses. In this paradigm, the generative model is used to define an energy function and a local iterative optimization is performed from these starting poses in order to find a "good local minimum" (i.e. a local minimum close to the true pose). Performing this optimization quickly is key to exploring more starting poses, performing more iterations and, crucially, exploiting high frame rates that ensure that temporally predicted starting poses are in the basin of convergence of a good local minimum. At the same time, a detailed and accurate generative model tends to deepen the good local minima and widen their basins of convergence. Recent work, however, has largely had to trade-off such a detailed hand model with one that facilitates such rapid optimization. We present a new implicit model of hand geometry that mostly avoids this compromise and leverage it to build an ultra-fast hybrid hand tracking system. Specifically, we construct an articulated signed distance function that, for any pose, yields a closed form calculation of both the distance to the detailed surface geometry and the necessary derivatives to perform gradient based optimization. There is no need to introduce or update any explicit "correspondences" yielding a simple algorithm that maps well to parallel hardware such as GPUs. As a result, our system can run at extremely high frame rates (e.g. up to 1000fps). Furthermore, we demonstrate how to detect, segment and optimize for two strongly interacting hands, recovering complex interactions at extremely high framerates. In the absence of publicly available datasets of sufficiently high frame rate, we leverage a multiview capture system to create a new 180fps dataset of one and two hands interacting together or with objects. We conceived a novel notion of a signature to characterize evolvability.We conducted an extensive comparison of approaches to evolve robot gaits.A better evolvability signature corresponds to faster adaption time in new scenarios.Our evolvability measure is an analysis tool, beyond standard performance benchmarks. Evolutionary robotics is a promising approach to autonomously synthesize machines with abilities that resemble those of animals, but the field suffers from a lack of strong foundations. In particular, evolutionary systems are currently assessed solely by the fitness score their evolved artifacts can achieve for a specific task, whereas such fitness-based comparisons provide limited insights about how the same system would evaluate on different tasks, and its adaptive capabilities to respond to changes in fitness (e.g., from damages to the machine, or in new situations). To counter these limitations, we introduce the concept of "evolvability signatures", which picture the post-mutation statistical distribution of both behavior diversity (how different are the robot behaviors after a mutation?) and fitness values (how different is the fitness after a mutation?). We tested the relevance of this concept by evolving controllers for hexapod robot locomotion using five different genotype-to-phenotype mappings (direct encoding, generative encoding of open-loop and closed-loop central pattern generators, generative encoding of neural networks, and single-unit pattern generators (SUPG)). We observed a predictive relationship between the evolvability signature of each encoding and the number of generations required by hexapods to adapt from incurred damages. Our study also reveals that, across the five investigated encodings, the SUPG scheme achieved the best evolvability signature, and was always foremost in recovering an effective gait following robot damages. Overall, our evolvability signatures neatly complement existing task-performance benchmarks, and pave the way for stronger foundations for research in evolutionary robotics. In this paper, we present a convex optimization problem to generate Center of Mass (CoM) and momentum trajectories of a walking robot, such that the motion robustly satisfies the friction cone constraints on uneven terrain. We adopt the Contact Wrench Cone (CWC) criterion to measure a robot's dynamical stability, which generalizes the venerable Zero Moment Point (ZMP) criterion. Unlike the ZMP criterion, which is ideal for walking on flat ground with unbounded tangential friction forces, the CWC criterion incorporates non-coplanar contacts with friction cone constraints. We measure the robustness of the motion using the margin in the Contact Wrench Cone at each time instance, which quantifies the capability of the robot to instantaneously resist external force torque disturbance, without causing the foot to tip over or slide. For pre-specified footstep location and time, we formulate a convex optimization problem to search for robot linear and angular momenta that satisfy the CWC criterion. We aim to maximize the CWC margin to improve the robustness of the motion, and minimize the centroidal angular momentum (angular momentum about CoM) to make the motion natural. Instead of directly minimizing the non-convex centroidal angular momentum, we resort to minimizing a convex upper bound. We show that our CWC planner can generate motion similar to the result of the ZMP planner on flat ground with sufficient friction. Moreover, on an uneven terrain course with friction cone constraints, our CWC planner can still find feasible motion, while the outcome of the ZMP planner violates the friction limit. This paper presents a method for optimal trajectory generation for discrete-time nonlinear systems with linear temporal logic (LTL) task specifications. Our approach is based on recent advances in stochastic optimization algorithms for optimal trajectory generation. These methods rely on estimation of the rare event of sampling optimal trajectories, which is achieved by incrementally improving a sampling distribution so as to minimize the cross-entropy. A key component of these stochastic optimization algorithms is determining whether or not a trajectory is collision-free. We generalize this collision checking to efficiently verify whether or not a trajectory satisfies a LTL formula. Interestingly, this verification can be done in time polynomial in the length of the LTL formula and the trajectory. We also propose a method for efficiently re-using parts of trajectories that only partially satisfy the specification, instead of simply discarding the entire sample. Our approach is demonstrated through numerical experiments involving Dubins car and a generic point-mass model subject to complex temporal logic task specifications. We propose a method to forecast a vehicle’s ego-motion as a distribution over spatiotemporal paths, conditioned on features (e.g., from LIDAR and images) embedded in an overhead map. The method learns a policy inducing a distribution over simulated trajectories that is both “diverse” (produces most of the likely paths) and “precise” (mostly produces likely paths). This balance is achieved through minimization of a symmetrized cross-entropy between the distribution and demonstration data. By viewing the simulated-outcome distribution as the pushforward of a simple distribution under a simulation operator, we obtain expressions for the cross-entropy metrics that can be efficiently evaluated and differentiated, enabling stochastic-gradient optimization. We propose concrete policy architectures for this model, discuss our evaluation metrics relative to previously-used degenerate metrics, and demonstrate the superiority of our method relative to state-of-the-art methods in both the Kitti dataset and a similar but novel and larger real-world dataset explicitly designed for the vehicle forecasting domain. We propose a novel schedulability analysis for verifying the feasibility of large periodic task sets under the rate monotonic algorithm when the exact test cannot be applied on line due to prohibitively long execution times. The proposed test has the same complexity as the original Liu and Layland (1973) bound, but it is less pessimistic, thus allowing it to accept task sets that would be rejected using the original approach. The performance of the proposed approach is evaluated with respect to the classical Liu and Layland method and theoretical bounds are derived as a function of n (the number of tasks) and for the limit case of n tending to infinity. The analysis is also extended to include aperiodic servers and blocking times due to concurrency control protocols. Extensive simulations on synthetic tasks sets are presented to compare the effectiveness of the proposed test with respect to the Liu and Layland method and the exact response time analysis. Evaluation of tracking algorithms in the absence of ground truth is a challenging problem. There exist a variety of approaches for this problem, ranging from formal model validation techniques to heuristics that look for mismatches between track properties and the observed data. However, few of these methods scale up to the task of visual tracking, where the models are usually nonlinear and complex and typically lie in a high-dimensional space. Further, scenarios that cause track failures and or poor tracking performance are also quite diverse for the visual tracking problem. In this paper, we propose an online performance evaluation strategy for tracking systems based on particle filters using a time-reversed Markov chain. The key intuition of our proposed methodology relies on the time-reversible nature of physical motion exhibited by most objects, which in turn should be possessed by a good tracker. In the presence of tracking failures due to occlusion, low SNR, or modeling errors, this reversible nature of the tracker is violated. We use this property for detection of track failures. To evaluate the performance of the tracker at time instant t, we use the posterior of the tracking algorithm to initialize a time-reversed Markov chain. We compute the posterior density of track parameters at the starting time t = 0 by filtering back in time to the initial time instant. The distance between the posterior density of the time-reversed chain (at t = 0) and the prior density used to initialize the tracking algorithm forms the decision statistic for evaluation. It is observed that when the data are generated by the underlying models, the decision statistic takes a low value. We provide a thorough experimental analysis of the evaluation methodology. Specifically, we demonstrate the effectiveness of our approach for tackling common challenges such as occlusion, pose, and illumination changes and provide the Receiver Operating Characteristic (ROC) curves. Finally, we also show the applicability of the core ideas of the paper to other tracking algorithms such as the Kanade-Lucas-Tomasi (KLT) feature tracker and the mean-shift tracker. 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.