Swarm Interpolation with Mobile Sensor

Sensors can be used in a variety of monitoring applications, such as measuring the state of large-scale, spatially complex phenomena like fires or oil spills. In applications like these, the primary goal is to collect information about the region of interest simultaneously across the region, assuming a sufficient number of sensors are available. However, it can be difficult and even dangerous to have humans manually place sensors and collect readings. Groups of autonomous mobile sensors under the control of an appropriate algorithm can address this issue by being able to move into position and gather data without human intervention.;In order to gain an accurate view of a region as a whole, it is important that the sensors be distributed to provide effective coverage. For fixed regions of known shape, the ideal positions for sensors can be computed in advance, with sensors simply moving to assign positions. However, if the shape of the region is not known in advance, or if the region changes its shape over time, then ideal positions will not be initially available, and must be identified by the autonomous sensors after they have already been placed and are in motion.;One means by which this can be accomplished is through a technique called swarming, in which individual elements coordinate their own behaviors based on local information in order to achieve a cohesive behavior for the entire group. If an appropriate swarming algorithm is used, mobile sensors can be made to seek out and settle in positions that are ideal for gathering data that will be useful for approximating the region as a whole.;In this dissertation, I first present an algorithm designed to achieve uniform mobile sensor coverage of an unknown region of interest using only local information. The algorithm is capable of scaling to different region sizes and shapes, dynamically adapting the behavior of the sensor nodes based on locally observed conditions. The algorithm divides nodes into two groups, boundary and interior, selected based on their positions within the swarm. Boundary nodes seek out the edge of the region of interest and distribute themselves evenly along it, while interior nodes use repulsive interactions to uniformly distribute themselves within the region. Uniformity between the boundary and interior is achieved through exchanging nodes between the two groups. Through simulation, I demonstrate the ability of the algorithm to adapt to a variety of regions, and analyze the effect that a number of control parameters have on the behavior of the swarm.;While a uniform distribution is sufficient to achieve complete coverage of a region, it may not be the optimal distribution for gathering data for interpolation. As an expansion of my work on generating uniform distributions, I present a system to generate non-uniform distributions using the concept of virtual coordinates, and show how changing the apparent positions of nodes can coerce a swarm to behave in a different manner without altering the underlying algorithm controlling them. I develop a technique to allow nodes to determine their relative location within a swarm based only on local communications by counting the number of local communication hops to the edge of the swarm, and to use that information to remap their radial distances from the center of the swarm. I present a remapping that will convert a 2D radial Chebyshev distribution into a uniform distribution in virtual coordinates. I adapt the uniform swarming algorithm to use this system of virtual coordinates, and demonstrate that the modified algorithm generates 2D Chebyshev distributions in real space. I simulate the exploration and measurement of regions of interest of a variety of shapes, and analyze the ability of both the uniform and Chebyshev algorithms to generate accurate maps of those regions through radial basis interpolation.