Counting Moving Bodies Using Sparse Sensor Beams

Abstract This paper examines the problem of determining the distribution of a number of indistinguishable moving bodies located in regions separated by sensor beams that can detect whether a body moves across them. We characterize the conditions under which an exact distribution of bodies can be determined, and compute bounds on the expected number of sensor observations required to determine this exact distribution for a certain movement model of the bodies.

Supplemental Data for Counting Moving Bodies Using Sparse Sensor Beams

This document contains supplemental simulation data for "Counting Moving Bodies Using Sparse Sensor Beams" by Lawrence H. Erickson, Jingjin Yu, Yaonan Huang, and Steven M. LaValle.unpublishednot peer reviewe

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