Statistical decision theory for mobile robotics: theory and application

In this paper we pioneer a method which, given an input of mobile robot pose measurements by a sensor-based localization algorithm, produces a minimax risk fixed-size confidence set estimate for the pose of the agent. This work constitutes the first application to the mobile robotics domain of optimal fixed-size confidence-interval decision theory. The approach is evaluated in terms of theoretical capture probability and empirical capture frequency during actual experiments with the mobile agent. The method is compared to several other procedures including the Kalman filter (minimum mean squared error estimate) and the maximum likelihood estimator (MLE). The minimax approach is found to dominate all the other methods in performance. In particular, for the minimax approach, a very close agreement is achieved between theoretical capture probability and empirical capture frequency. This allows performance to be accurately predicted, greatly facilitating the design of mobile robotic systems, and delineating the tasks that may be performed with a given system