Conformative Filter: A Probabilistic Framework for Localization in Reduced Space

Algorithmic problem reduction is a fundamental approach to problem solving in many fields, including robotics. To solve a problem using this scheme, we must reduce the problem into another one for which solutions exist. The reduction function, which infers a conformation between the problem and the solution space, plays an important role in solution evaluation and is sometimes used to transform the solutions into the problem domain. We consider robot path planning in the context of algorithmic problem reduction where a reduction can be used to adapt a path (referred to as solution) generated by a human or other subsystem to environmental constraints that may differ from those at plan-generation time. Usually, solving these problems involves estimating the current state in the plan and trying to retrieve the solution. We develop a probabilistic framework for reduction-based path planning where the solutions can be obtained from localization into the plan by exploiting the Markov property. We name it Conformative Filter. The algorithm is an extension of Bayes' filter which tries to search for not only the solutions but also conformation between the environment and the plan. An implementation based on Localization and Expectation-maximization is discussed along with evaluation on navigation tasks using a set of actual hand-drawn maps of simulated environments. The results demonstrate applicability and effectiveness of the algorithm in such tasks and show that the proposed filter results in improved localization when compared with conventional approaches.