1.3.2: Ergodic Control for Optimal Information Acquisition

In any exploratory process, information histories should be used to guide search strategies, even if that information history is absent. How should a search strategy respond to very diffuse information, potentially indicating very little or nothing is known about a given parameter of interest? In general, the controlled response of an autonomous agent needs to take the diffuse information into account in its planning and any update of the information. Applying this idea to the design of trajectories for search, the goal can be thought of as maximizing a function of the expected information that could be gained by carrying out that trajectory. The goal of the proposed research is to develop an active search process that incorporates information measures into trajectory design to estimate the state of continuous, time varying fields. Leveraging nonlinear optimal control theory, we will develop the tools necessary to select continuous-time trajectories for systems with nontrivial dynamics—for instance, systems with nonholonomic constraints or significant inertial effects. The proposed techniques use measures of ergodicity and the associated ergodic control to robustly explore for information while ensuring coverage of the informative subset of the statespace (as indicated by prior measurements or even the lack thereof). The developed methods will provide a synthesis technique for active sensing so that autonomous systems can optimize knowledge of continuous phenomena such as fluid or air flow fields, magnetic fields, electric fields, etc. Further, by developing trajectories that enable fast and accurate estimation of the state and evolution of such fields in local regions, the research can support forecasting and prediction. The proposed work leverages recent results in information-theoretic control theory. In particular, the development of ergodic metrics as a control measure is a fundamental starting point for the proposed work. The control synthesis techniques used in the proposed work build on the ergodic metrics by utilizing algorithms that are appropriate for the unique challenges ergodic metrics present. Lastly, experimental results indicate the feasibility of the approach in real-time, physical systems. Moreover, these same experiments indicate why alternative approaches—such as information maximization or entropy-based metrics—cannot be expected to perform well, motivating the need for ergodic search strategies.