Kalman Filtering is a computational tool with widespread applications in robotics, financial and weather forecasting, environmental engineering and defense. Given observation and state transition models, the Kalman Filter (KF) recursively estimates the state variables of a dynamic system. However, the KF requires a cubic time matrix inversion operation at every timestep which prevents its application in domains with large numbers of state variables. We propose Relational Gaussian Models to represent and model dynamic systems with large numbers of variables efficiently. Furthermore, we devise an exact lifted Kalman Filtering algorithm which takes only linear time in the number of random variables at every timestep. We prove that our algorithm takes linear time in the number of state variables even when individual observations apply to each variable. To our knowledge, this is the first lifted (linear time) algorithm for filtering with continuous dynamic relational models.

Activity recognition aims to discover one or more users’ actions and goals based on sensor readings. In the real world, a single user’s data are often insufficient for training an activity recognition model due to the data sparsity problem. This is especially true when we are interested in obtaining a personalized model. In this paper, we study how to collaboratively use different users’ sensor data to train a model that can provide personalized activity recognition for each user. We propose a user-dependent aspect model for this collaborative activity recognition task. Our model introduces user aspect variables to capture the user grouping information, so that a target user can also benefit from her similar users in the same group to train the recognition model. In this way, we can greatly reduce the need for much valuable and expensive labeled data required in training the recognition model for each user. Our model is also capable of incorporating time information and handling new user in activity recognition. We evaluate our model on a real-world WiFi data set obtained from an indoor environment, and show that the proposed model can outperform several state-of-art baseline algorithms.

We focus on recovering the 2D Euclidean structure in one view from the projections of N parallel conics in this paper. This work denotes that the conic dual to the absolute points is the general form of the conic dual to the circular points, but it does not encode the Euclidean structure. Therefore, we have to recover the circular point-envelope to find out some useful information about the Euclidean structure, which relies on the fact that the line at infinity and the symmetric axis can be recovered. We provide a solution to recover the two lines and deduce the constraints for recovering the conic dual to the circular points, then apply them on the camera calibration. Our work relaxes the problem conditions and gives a more general framework than the past. Experiments with simulated and real data are carried out to show the validity of the proposed algorithm. Especially, our method is applied in the endoscope operation to calibrate the camera for tracking the surgical tools, that is the main interest-point we pay attention to.

Object detection is a basic skill for a robot to perform tasks in human environments. In order to build a good object classifier, a large training set of labeled images is required; this is typically collected and labeled (often painstakingly) by a human. This method is not scalable and therefore limits the robot's detection performance. We propose an algorithm for a robot to collect more data in the environment during its training phase so that in the future it could detect objects more reliably. The first step is to plan a path for collecting additional training images, which is hard because a previously visited location affects the decision for the future locations. One key component of our work is path planning by building a sparse graph that captures these dependencies. The other key component is our learning algorithm that weighs the errors made in robot's data collection process while updating the classifier. In our experiments, we show that our algorithms enable the robot to improve its object classifiers significantly.

The variability of human behavior during plan execution poses a difficult challenge for human-robot teams. In this paper, we use the concepts of theory of mind to enable robots to account for two sources of human variability during team operation. When faced with an unexpected action by a human teammate, a robot uses a simulation analysis of different hypothetical cognitive models of the human to identify the most likely cause for the human's behavior. This allows the cognitive robot to account for variances due to both different knowledge and beliefs about the world, as well as different possible paths the human could take with a given set of knowledge and beliefs. An experiment showed that cognitive robots equipped with this functionality are viewed as both more natural and intelligent teammates, compared to both robots who either say nothing when presented with human variability, and robots who simply point out any discrepancies between the human's expected, and actual, behavior. Overall, this analysis leads to an effective, general approach for determining what thought process is leading to a human's actions.

Robots depend on captured images for perceiving the environment. A robot can replace a human in capturing quality photographs for publishing. In this paper, we employ an iterative photo capture by robots (by repositioning itself) to capture good quality photographs. Our image quality assessment approach is based on few high level features of the image combined with some of the aesthetic guidelines of professional photography. Our system can also be used in web image search applications to rank images. We test our quality assessment approach on a large and diversified dataset and our system is able to achieve a classification accuracy of 79%. We assess the aesthetic error in the captured image and estimate the change required in orientation of the robot to retake an aesthetically better photograph. Our experiments are conducted on NAO robot with no stereo vision. The results demonstrate that our system can be used to capture professional photographs which are in accord with the human professional photography.

We study a pursuit-evasion game in which one or more cops try to capture a robber by moving onto the robber's current location. All players have equal maximum velocities. They can observe each other at all times. We show that three cops can capture the robber in any polygonal environment (which can contain any finite number of holes).

In contrast to the studied in single-period optimization [Miller and Wagner, standard approach that studies the expected performance, 1965; Prékopa, 1970]. However, little has been done in we consider the policy that maximizes the context of sequential decision problem including MDPs. the probability of achieving a predetermined target The standard approaches in risk-averse MDPs include maximization performance, a criterion we term probabilistic of expected utility function [Bertsekas, 1995], goal Markov decision processes. We show that and optimization of a coherent risk measure [Riedel, 2004; this problem is NPhard, but can be solved using a Le Tallec, 2007]. Both approaches lead to formulations that pseudo-polynomial algorithm. We further consider can not be solved in polynomial time, except for special a variant dubbed "chance-constraint Markov decision cases including exponential utility function [Chung and Sobel, problems," that treats the probability of achieving 1987], piecewise linear utility function with a single target performance as a constraint instead of the break down point [Liu and Koenig, 2005], and risk measures maximizing objective. This variant is NPhard, but that can be reduced to robust MDPs satisfying the socalled can be solved in pseudo-polynomial time.

We propose a novel approach for solving unary SAS+ planning problems. This approach extends an SAS+ instance with new state variables representing intentions about how each original state variable will be used or changed next, and splits the original actions into several stages of intention followed by eventual execution. The result is a new SAS+ instance with the same basic solutions as the original. While the transformed problem is larger, it has additional structure that can be exploited to reduce the branching factor, leading to reachable state spaces that are many orders of magnitude smaller (and hence much faster planning) in several test domains with acyclic causal graphs.

This paper investigates the effectiveness of two state representations, CNF and DNF, in contingent planning. To this end, we developed a new contingent planner, called CNFct, using the AND/OR forward search algorithm PrAO [To et al., 2011] and an extension of the CNF representation of [To et al., 2010] for conformant planning to handle nondeterministic and sensing actions for contingent planning. The study uses CNFct and DNFct [To et al., 2011] and proposes a new heuristic function for both planners. The experiments demonstrate that both CNFct and DNFct offer very competitive performance in a large range of benchmarks but neither of the two representations is a clear winner over the other. The paper identifies properties of the representation schemes that can affect their performance on different problems.