On the Bayes Filter for Shared Autonomy

The Bayes filter is the basis for many state-of-the-art robot localization algorithms. In the literature, its derivation typically requires the robot controls to be chosen independently of all other variables. However, this assumption is not valid for a robotic system that is to act purposefully. The contribution of this letter is twofold: We prove that the Bayes filter is also exact for an autonomous system that chooses the controls depending on any subset of all observable variables. We further show how to augment the filter if a human agent chooses controls on the basis of parts of the state space that are not directly accessible to the robot. In this case, modeling the agent's purpose improves the pose estimate as the control selection provides additional information about the hidden state space. A careful derivation of the Bayes filter then leads to an additional pseudo measurement update step. Simulation and real-world experiments with a teleoperated mobile robot as well as evaluations on the KITTI dataset show that the localization accuracy significantly improves if we augment a particle filter with the proposed pseudo measurement update. Finally, we present an analytical example for an augmented Kalman filter, which leads to a more accurate estimate than the standard Kalman filter.