| This dissertation contains work in novel algorithms which ensure robust estimation of physical phenomena. In the context of cooperative control of multi-agent networks, robustness refers to the fact that, despite the possibility of individual agent failures and the presence of noisy measurements, we wish to be able to characterize the network's performance at solving a given task (estimation). The contributions come from two problems of spatial estimation. The first problems motivation comes from spatial estimation tasks executed with unreliable sensors. Previous work has considered how to optimally deploy the unreliable sensors over an environment to robustly estimate the random field which they are measuring. For some problems, it has been shown that the optimal deployments correspond to agents forming clusters of a certain size and then deploying the clusters optimally assuming that one packet from each cluster reaches the center. Motivated by this result, our major contribution in this problem is a distributed algorithmic solution which exactly achieves those desirable network configurations. We also show the algorithms robustness to agent addition and subtraction as well as upper bound the completion time and required number of messages exchanged. The second problem considers a group of robotic drifters whose objective is to estimate the physical parameters (amplitude, wavenumber, frequency) that determine the dynamics of ocean internal waves. Internal waves are important because, as they travel, they displace small animals, such as plankton, larvae, and fish. While underwater, drifters do not have access to absolute position information and only rely on inter-vehicle measurements. Building on this data and the study of their dynamics under the flow induced by the internal wave, we design strategies that are able to characterize the internal wave. Because many wave models exist, we separately consider the tasks of estimating a single linear internal wave and a single nonlinear internal wave. We devise algorithms that perfectly determine the wave's parameters under noiseless measurements and also analyze the robustness to measurements corrupted by error. Since many parameter estimates may be obtained at different times, we also analyze a methodology for combining these estimates to decrease the final error. |
