Observability of Lattice Graphs

We consider a graph observability problem: how many edge colors are needed for an unlabeled graph so that an agent, walking from node to node, can uniquely determine its location from just the observed color sequence of the walk? Specifically, let G(n,d) be an edge-colored subgraph of d-dimensional (directed or undirected) lattice of size n^d = n * n * ... * n. We say that G(n,d) is t-observable if an agent can uniquely determine its current position in the graph from the color sequence of any t-dimensional walk, where the dimension is the number of different directions spanned by the edges of the walk. A walk in an undirected lattice G(n,d) has dimension between 1 and d, but a directed walk can have dimension between 1 and 2d because of two different orientations for each axis. We derive bounds on the number of colors needed for t-observability. Our main result is that Theta(n^(d/t)) colors are both necessary and sufficient for t-observability of G(n,d), where d is considered a constant. This shows an interesting dependence of graph observability on the ratio between the dimension of the lattice and that of the walk. In particular, the number of colors for full-dimensional walks is Theta(n^(1/2)) in the directed case, and Theta(n) in the undirected case, independent of the lattice dimension. All of our results extend easily to non-square lattices: given a lattice graph of size N = n_1 * n_2 * ... * n_d, the number of colors for t-observability is Theta (N^(1/t))

Oblivious Sensor Fusion via Secure Multi-Party Combinatorial Filter Evaluation

This thesis examines the problem of fusing data from several sensors, potentially distributed throughout an environment, in order to consolidate readings into a single coherent view. We consider the setting when sensor units do not wish others to know their specific sensor streams. Standard methods for handling this fusion make no guarantees about what a curious observer may learn. Motivated by applications where data sources may only choose to participate if given privacy guarantees, we introduce a fusion approach that limits what can be inferred. Our approach is to form an aggregate stream, oblivious to the underlying sensor data, and to evaluate a combinatorial filter on that stream. This is achieved via secure multi-party computational techniques built on cryptographic primitives, which we extend and apply to the problem of fusing discrete sensor signals. We prove that the extensions preserve security under the semi- honest adversary model. Though the approach enables several applications of potential interest, we specifically consider a target tracking case study as a running example. Finally, we also report on a basic, proof-of-concept implementation, demonstrating that it can operate in practice; which we report and analyze the (empirical) running times for components in the architecture, suggesting directions for future improvement

Golf ball picker robot: path generation in unstructured environments towards multiple targets

Tese de doutoramento Engineering Design and Advanced Manufacturing Leaders for Technical IndustriesThe new TWIN-RRT* algorithm solves a motion planning problem in which an agent has multiple possible targets where none of them is compulsory, and retrieves feasible, ―low cost‖, asymptotically optimal and probabilistically complete paths. The TWIN-RRT* algorithm solves path planning problems for both holonomic and non-holonomic robots with or without kinodynamic constraints in a 2D environment, but it was designed to work as well with higher DOF agents and different applications. The new algorithm provides a practical implementation of feasible and fast planning especially where a closed loop is required. Initial and final configurations are allowed to be exactly the same. The TWIN-RRT* algorithm computes an efficient path for one sole agent towards multiple targets where none of them is mandatory. It inherits the low computational cost, probabilistic completeness and asymptotical optimality from RRT*. It uses efficiency as cost function, which can be adapted depending on the application. The TWIN-RRT* complies both with kinodynamic constraints and different cost functions. It was developed to solve a real problem where a robot has to collect golf balls in a driving range, where thousands of balls accumulate every day. This thesis is part of a bigger project, Golfminho, to develop an autonomous robot capable of efficiently collecting balls in a golf practice field.O novo algoritmo TWIN-RRT* resolve problemas de planeamento de trajetórias em que um agente tem múltiplos alvos, onde nenhum deles é obrigatório, e produz um plano exequível, de "baixo custo" computacional, assintoticamente ótimo e probabilisticamente completo. O TWINRRT* resolve problemas de planeamento de trajetórias tanto para robôs holonómicos como não holonómicos com ou sem restrições cinemáticas e/ou dinâmicas num ambiente 2D, mas foi projetado para funcionar também com agentes com maiores graus de liberdade e em diferentes aplicações. O novo algoritmo fornece uma implementação prática de um planeamento viável e rápido, especialmente quando é necessário produzir uma trajetória fechada. As configurações iniciais e finais podem ser exatamente iguais. O algoritmo TWIN-RRT* calcula um caminho eficiente para um agente único em direção a múltiplos alvos, onde nenhum deles é obrigatório. Herda o baixo custo computacional, integralidade probabilística e otimização assintótica do RRT*. Usa a eficiência como função de custo, que pode ser adaptada em função das diferentes aplicações. Para além de diferentes funções de custo, o TWIN-RRT* também mostra conformidade com restrições cinemáticas. Foi desenvolvido para resolver um problema real em que um robô tem que recolher bolas de golfe num Driving Range, onde se acumulam milhares de bolas de golfe por dia. Esta tese é parte integrante do projeto Golfminho, para o desenvolvimento de um robô autónomo capaz de recolher eficientemente bolas num campo de práticas de golfe.Fundação para a Ciência e Tecnologia (FCT) for the PhD grant nº. SFRH/BD/43008/2008

Automata-Theoretic Approaches to Planning in Robotics: Combinatorial Filter Minimization, Planning to Chronicle, Temporal Logic Planning With Soft Specifications, and Sensor Selection for Detecting Deviations From a Planned Itinerary

In this dissertation, we present a collection of new planning algorithms that enable robots to achieve complex goals, beyond simple point-to-point path planning, using automata-theoretic methods, and we consider the filter minimization (FM) problem and a variant of it, filter partitioning minimization (FPM) problem, which aims to minimize combinatorial filters, used for filtering and automata-theoretic planning in systems with discrete sensor data. We introduce a new variant of bisimulation, compatibility, and using this notion we identify several classes of filters for which FM or FPM is solvable in polynomial time, and propose several integer linear programming (ILP) formulations of FM and FPM. Then, we consider a problem, planning to chronicle, in which a robot is tasked with observing an uncertain time-extended process to produce a ‘chronicle’ of occurrent events that meets a given specification. This problem is useful in applications where we deploy robots to autonomously make structured videos or documentaries from events occurring in an unpredictable environment. Next, we study two variants of temporal logic planning in which the objective is to synthesize a trajectory that satisfies an optimal selection of soft constraints while nevertheless satisfying a hard constraint expressed in linear temporal logic (LTL). We also extend planning to chronicle with the idea of this problem. Then, we consider the problem of planning where to observe the behavior of an agent to ensure that the agent’s execution within the environment fits a pre-disclosed itinerary. This problem arises in a range of contexts including in validating safety claims about robot behavior, applications in security and surveillance, and for both the conception and the (physical) design and logistics of scientific experiments