Optimal Target Capture and Station Keeping Control of Mobile Agents without Global Position Information

The target capture problem, i.e., the problem of reaching a target zone, by a mobile robotic agent that cannot sense its own global position requires reactive motion control algorithms based on onboard sensor data. Although the existing solutions to the target capture problem provide robust convergence guarantees, they do not address the mobile agent's path and motion optimality. We address the agent path and motion optimality in target capture control and its extension to station keeping, i.e., steering the agent to a location that is pre-defined with respect to a set of beacons, in global positioning system (GPS)-denied environments. We formulate optimal control problems aiming to minimize the agent-target distance for target capture, and the difference of desired and actual agent-station distances for station keeping. We design and analyze a linear quadratic optimal control scheme involving a Luenberger observer based state estimator, for each of the target capture and station keeping problems. The proposed schemes outperform the previous approaches in numerical simulations in terms of agent path length and smoothness.