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Active Map Learning for Robots: Insights into Statistical Consistency

The problem of learning unknown environments in mobile robotics is called SLAM (Simultaneous Localization and Mapping). Furthermore, if the robot has to take some decision, it is called active SLAM or just exploration. The current SLAM methods are rooted on the strong probabilistic formulation in the form of Bayesian filters. There are extensions of this formulation in the field of decision making in uncertain environments that allows to solve the problem in an active and autonomous way, using, for example, MDPs (Markov Decision Processes). On the one hand, the huge dimensionality of the SLAM problem (temporal, spacial and statistical), make it mathematically intractable. There is no optimal solution. However, there are suboptimal solutions presented in the current literature based on approximations of the Extended Kalman Filter (EKF) or in sampling methods, like the Rao-Blackwellized Particle Filter (RBPF), but they suffer from certain statistical inconsistency that results in corrupt or totally wrong solutions in the long term. On the other hand, that huge complexity also implies that current MDPs techniques -value iteration, policy iteration and trees or gradients based policy searchonly provide partial solutions or they can only solve unrealistic toy problems. In this thesis, we analize the statistical properties of the SLAM problem and the most extended algorithms, especially their error sources. In this way, we investigate the applicability of second order linear approximations like the Unscented Kalman Filter (UKF), advanced sampling methods like the Marginal Particle Filter (MPF) or stochastic approximation based estimation. In theory, these algorithms outperform the statistical consistency of the previous ones, this is validated in the corresponding experiments. Additionally, we investigate more efficient policy search algorithms to solve the complex problem of decision making. In this way, we work with efficient global optimization algorithms for policy search. This work is highly related with active parameter learning using Gaussian processes.