Temporal Landscapes: A Graphical Temporal Logic for Reasoning

We present an elementary introduction to a new logic for reasoning about behaviors that occur over time. This logic is based on temporal type theory. The syntax of the logic is similar to the usual first-order logic; what differs is the notion of truth value. Instead of reasoning about whether formulas are true or false, our logic reasons about temporal landscapes. A temporal landscape may be thought of as representing the set of durations over which a statement is true. To help understand the practical implications of this approach, we give a wide variety of examples where this logic is used to reason about autonomous systems.Comment: 20 pages, lots of figure

Hearing the clusters in a graph: A distributed algorithm

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies

ECO: Egocentric Cognitive Mapping

We present a new method to localize a camera within a previously unseen environment perceived from an egocentric point of view. Although this is, in general, an ill-posed problem, humans can effortlessly and efficiently determine their relative location and orientation and navigate into a previously unseen environments, e.g., finding a specific item in a new grocery store. To enable such a capability, we design a new egocentric representation, which we call ECO (Egocentric COgnitive map). ECO is biologically inspired, by the cognitive map that allows human navigation, and it encodes the surrounding visual semantics with respect to both distance and orientation. ECO possesses three main properties: (1) reconfigurability: complex semantics and geometry is captured via the synthesis of atomic visual representations (e.g., image patch); (2) robustness: the visual semantics are registered in a geometrically consistent way (e.g., aligning with respect to the gravity vector, frontalizing, and rescaling to canonical depth), thus enabling us to learn meaningful atomic representations; (3) adaptability: a domain adaptation framework is designed to generalize the learned representation without manual calibration. As a proof-of-concept, we use ECO to localize a camera within real-world scenes---various grocery stores---and demonstrate performance improvements when compared to existing semantic localization approaches

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

A verified hierarchical control architecture for co-ordinated multi-vehicle operations

A layered control architecture for executing multi-vehicle team co-ordination algorithms is presented along with the specifications for team behaviour. The control architecture consists of three layers: team control, vehicle supervision and maneuver control. It is shown that the controller implementation is consistent with the system specification on the desired team behaviour. Computer simulations with accurate models of autonomous underwater vehicles illustrate the overall approach in the co-ordinated search for the minimum of a scalar field. The co-ordinated search is based on the simplex optimization algorithm