Fault-Tolerant, but Paradoxical Path-Finding in Physical and Conceptual Systems

We report our initial investigations into reliability and path-finding based models and propose future areas of interest. Inspired by broken sidewalks during on-campus construction projects, we develop two models for navigating this "unreliable network." These are based on a concept of "accumulating risk" backward from the destination, and both operate on directed acyclic graphs with a probability of failure associated with each edge. The first serves to introduce and has faults addressed by the second, more conservative model. Next, we show a paradox when these models are used to construct polynomials on conceptual networks, such as design processes and software development life cycles. When the risk of a network increases uniformly, the most reliable path changes from wider and longer to shorter and narrower. If we let professional inexperience--such as with entry level cooks and software developers--represent probability of edge failure, does this change in path imply that the novice should follow instructions with fewer "back-up" plans, yet those with alternative routes should be followed by the expert?Comment: 8 page

Efficient query processing over uncertain road networks

One of the fundamental problems on spatial road networks has been the shortest traveling time query, with applications such as location-based services (LBS) and trip planning. Algorithms have been made for the shortest time queries in deterministic road networks, in which vertices and edges are known with certainty. Emerging technologies are available and make it easier to acquire information about the traffic. In this paper, we consider uncertain road networks, in which speeds of vehicles are imprecise and probabilistic. We will focus on one important query type, continuous probabilistic shortest traveling time query (CPSTTQ), which retrieves sets of objects that have the smallest traveling time to a moving query point q from point s to point e on road networks with high confidences. We propose effective pruning methods to prune the search space of our CPSTTQ query, and design an efficient query procedure to answer CPSTTQ via an index structure

Approximate Equivalence of the Hybrid Automata with Taylor Theory

Hybrid automaton is a formal model for precisely describing a hybrid system in which the computational processes interact with the physical ones. The reachability analysis of the polynomial hybrid automaton is decidable, which makes the Taylor approximation of a hybrid automaton applicable and valuable. In this paper, we studied the simulation relation among the hybrid automaton and its Taylor approximation, as well as the approximate equivalence relation. We also proved that the Taylor approximation simulates its original hybrid automaton, and similar hybrid automata could be compared quantitatively, for example, the approximate equivalence we proposed in the paper

Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms

Similarly to funnel equations of Panasyuk, the so-called mutational equations of Aubin provide a generalization of ordinary differential equations to locally compact metric spaces. Here we present their extension to a nonempty set with a possibly nonsymmetric distance. A distribution-like approach leads to so-called right-hand forward solutions. This concept is applied to a type of geometric evolution having motivated the definitions : compact subsets of the Euclidean space evolve according to nonlocal properties of both the set and their limiting normal cones at the boundary. The existence of a solution is based on Euler method using reachable sets of differential inclusions as "elementary deformations" (called forward transitions). Thus, the regularity of these reachable sets at the topological boundaries is studied extensively in the appendix

Vehicle control from temporal logic specifications with probabilistic satisfaction guarantees

Thesis (Ph.D.)--Boston UniversityTemporal logics, such as Linear Temporal Logic (LTL) and Computation Tree Logic (CTL), have become increasingly popular for specifying complex mission specifications in motion planning and control synthesis problems. This dissertation proposes and evaluates methods and algorithms for synthesizing control strategies for different vehicle models from temporal logic specifications. Complex vehicle models that involve systems of differential equations evolving over continuous domains are considered. The goal is to synthesize control strategies that maximize the probability that the behavior of the system, in the presence of sensing and actuation noise, satisfies a given temporal logic specification. The first part of this dissertation proposes an approach for designing a vehicle control strategy that maximizes the probability of accomplishing a motion specification given as a Probabilistic CTL (PCTL) formula. Two scenarios are examined. First, a threat-rich environment is considered when the motion of a vehicle in the environment is given as a finite transition system. Second, a noisy Dubins vehicle is considered. For both scenarios, the motion of the vehicle in the environment is modeled as a Markov Decision Process (MDP) and an approach for generating an optimal MDP control policy that maximizes the probability of satisfying the PCTL formula is introduced. The second part of this dissertation introduces a human-supervised control synthesis method for a noisy Dubins vehicle such that the expected time to satisfy a PCTL formula is minimized, while maintaining the satisfaction probability above a given probability threshold. A method for abstracting the motion of the vehicle in the environment in the form of an MDP is presented. An algorithm for synthesizing an optimal MDP control policy is proposed. If the probability threshold cannot be satisfied with the initial specification, the presented framework revises the specifica- tion until the supervisor is satisfied with the revised specification and the satisfaction probability is above the threshold. The third part of this dissertation focuses on the problem of stochastic control of a noisy differential drive mobile robot such that the probability of satisfying a time constrained specification, given as a Bounded LTL (BLTL) formula, is maximized. A method for mapping noisy sensor measurements to an MDP is introduced. Due to the size of the MDP, finding the exact solution is computationally too expensive. Correctness is traded for scalability, and an MDP control synthesis method based on Statistical Model Checking is introduced

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