Evasion Paths in Mobile Sensor Networks

Suppose that ball-shaped sensors wander in a bounded domain. A sensor doesn't know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists in this sensor network if a moving intruder can avoid detection. In "Coordinate-free coverage in sensor networks with controlled boundaries via homology", Vin deSilva and Robert Ghrist give a necessary condition, depending only on the time-varying connectivity data of the sensors, for an evasion path to exist. Using zigzag persistent homology, we provide an equivalent condition that moreover can be computed in a streaming fashion. However, no method with time-varying connectivity data as input can give necessary and sufficient conditions for the existence of an evasion path. Indeed, we show that the existence of an evasion path depends not only on the fibrewise homotopy type of the region covered by sensors but also on its embedding in spacetime. For planar sensors that also measure weak rotation and distance information, we provide necessary and sufficient conditions for the existence of an evasion path

Multi-robot behaviors with bearing-only sensors and scale-free coordinates

This thesis presents a low-cost multi-robot system for large populations of robots, a new coordinate system for the robot based on angles between robots and a series of experiments validating robot performance. The new robot platform, the r-one will serve as an educational, outreach and research platform for robotics. I consider the robot's bearing-only sensor model, where each robot is capable of measuring the bearing, but not the distance, to each of its neighbors. This work also includes behaviors demonstrating the efficiency of this approach with this bearing-only sensor model. The new local coordinate systems based on angular information is introduced as scale-free coordinate system . Each robot produces its own local scale-free coordinates to determine the relative positions of its neighbors up to an unknown scaling factor. The computation of scale-free coordinates is analyzed with hardware and simulation validation. For hardware, the scale-free algorithm is tailored to low-cost systems with limited communication bandwidth and sensor resolution. The algorithm also uses a noise sensitivity model to reduce the impact of noise on the computed scale-free coordinates. I validate the algorithm with static and dynamic motion experiments

Surrounding nodes in coordinate-free networks

Summary. Consider a network of nodes in the plane whose locations are unknown but which establish communication links based on proximity. We solve the following problems: given a node in the network, (1) determine if a given cycle surrounds the node; and (2) find some cycle that surrounds the node. The only localization capabilities assumed are unique IDs with binary proximity measure, and, in some cases, cyclic orientation of neighbors. We give complete algorithms for finding and verifying surrounding cycles when cyclic orientation data is available. We also provide an efficient but non-complete algorithm in the case where angular data is not available.