Autonomous robotic exploration using a utility function based on R,nyi's general theory of entropy

In this paper we present a novel information-theoretic utility function for selecting actions in a robot-based autonomous exploration task. The robot's goal in an autonomous exploration task is to create a complete, high-quality map of an unknown environment as quickly as possible. This implicitly requires the robot to maintain an accurate estimate of its pose as it explores both unknown and previously observed terrain in order to correctly incorporate new information into the map. Our utility function simultaneously considers uncertainty in both the robot pose and the map in a novel way and is computed as the difference between the Shannon and the R,nyi entropy of the current distribution over maps. R,nyi's entropy is a family of functions parameterized by a scalar, with Shannon's entropy being the limit as this scalar approaches unity. We link the value of this scalar parameter to the predicted future uncertainty in the robot's pose after taking an exploratory action. This effectively decreases the expected information gain of the action, with higher uncertainty in the robot's pose leading to a smaller expected information gain. Our objective function allows the robot to automatically trade off between exploration and exploitation in a way that does not require manually tuning parameter values, a significant advantage over many competing methods that only use Shannon's definition of entropy. We use simulated experiments to compare the performance of our proposed utility function to these state-of-the-art utility functions. We show that robots that use our proposed utility function generate maps with less uncertainty and fewer visible artifacts and that the robots have less uncertainty in their pose during exploration. Finally, we demonstrate that a real-world robot using our proposed utility function is able to successfully create a high-quality map of an indoor office environment.