Simultaneous planning localization and mapping: A hybrid Bayesian/ frequentist approach

In this paper, the problem of mapping and planning in an uncertain environment is studied. A hybrid Bayesian/ frequentist formulation of the simultaneous planning, localization and mapping (SPLAM) problem is presented wherein the environment is modeled as a stationary, spatially uncorrelated random process whose stationary probabilities are fixed but unknown, and have to be estimated as the autonomous system moves through the environment and makes observations using its sensors. The environmental random process is estimated using stochastic approximation algorithms. Under a certain "reliable sensor assumption", it is shown that the mapping algorithms converge with probability one, and that the convergence of the mapping algorithms is independent of the planning policy, as long as it is non-anticipative, akin to the celebrated "Separation Principle" in Classical Linear Control theory. Further, the computational burden of the mapping algorithms is significantly reduced when compared to Bayesian SPLAM techniques.