Control in Belief Space with Temporal Logic Specifications using Vision-based Localization

We present a solution for operating a vehicle without global positioning infrastructure while satisfying constraints on its temporal behavior, and on the uncertainty of its position estimate. The proposed solution is an end-to-end framework for mapping an unknown environment using aerial vehicles, synthesizing a control policy for a ground vehicle in that environment, and using a quadrotor to localize the ground vehicle within the map while it executes its control policy. This vision-based localization is noisy, necessitating planning in the belief space of the ground robot. The ground robot's mission is given using a language called Gaussian Distribution Temporal Logic (GDTL), an extension of Boolean logic that incorporates temporal evolution and noise mitigation directly into the task specifications. We use a sampling-based algorithm to generate a transition system in the belief space and use local feedback controllers to break the curse of history associated with belief space planning. To localize the vehicle, we build a high-resolution map of the environment by flying a team of aerial vehicles in formation with sensor information provided by their onboard cameras. The control policy for the ground robot is synthesized under temporal and uncertainty constraints given the semantically labeled map. Then the ground robot can execute the control policy given pose estimates from a dedicated aerial robot that tracks and localizes the ground robot. The proposed method is validated using two quadrotors to build a map, followed by a two-wheeled ground robot and a quadrotor with a camera for ten successful experimental trials.