On Vehicle Localization: From Geometry to Topology
Monday, March 3, 2014 - 11:30am - 12:20pm
In this talk we will describe methodologies to localize both a single and a team of vehicles navigating in a complex environment without GPS. During the first part of the talk, we will consider the situation when vehicles (or a single vehicle navigating in an environment with multiple beacons) can measure their relative (inter-vehicle) distances. In this case, the problem can be posed as a distributed graph embedding problem. The convergence speed of this type of algorithms strongly depends on the spectral property of the underlying network (graph), and we will discuss a distributed clustering algorithm that can accelerate the distributed embedding problem for slowly varying networks. Next, we will consider situations where vehicle teams can only coarsely compare relative distance measurements. We will show that the problem can be posed, once again, as a graph embedding problem and demonstrate how this information can be fused with inertial sensors. Finally, we discuss the limiting case when a vehicle navigating in an environment, with multiple beacons, can coarsely localize itself by leveraging visibility (binary detection) information as well as a low-grade inertial sensor. Key to this final result is leveraging local homology computations to enable successful loop closure in a probabilistic filter. Initial experimental results for this last scenario will be presented.