Conformative Filter : A Probabilistic Framework for Localization in Reduced Space Chatavut Viriyasuthee and Gregory Dudek Centre for Intelligent Machines McGill University Montreal, Quebec, Canada H3A 2A7 {pvirie,dudek}@cim.mcgill.ca Abstract— 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. I. I NTRODUCTION We are interested in path planning methods (and related techniques) where preliminary paths (so-called solutions) gen- erated by some subsystems are executed in environments that are different from that known when the planning was per- formed. In particular, we are interested using plans generated by humans on schematic maps in the form of hand-drawn sketches to control agents in real environments. Transforming schematic plans to real control actions involves 1) comparing the observed features in the environments to the plans, 2) iden- tifying the current steps, and 3) retrieving the actions. These three processes strongly resemble to the processes required to execute a single navigation loop in traditional robotic systems. In many cases and, in particular when humans use maps for planning, the plan and environment representation are necessarily highly abstracted and the plan is usually acquired through a reduction process that leaves some details from the environment abstract, inaccurate, or completely absent; thus the localization process and plan execution process very difficult. Many approaches have been proposed for navigation using potentially inaccurate maps, but they are usually limited by domain-specific assumptions which we wish to avoid. For example, Tomono et al. present an effective navigation approach in hybrid topological-metric maps [1]. They assume that the maps consist of many local islands of accuracy and connected by global relations corrupted by Gaussian noise between them. Setalaphruk et al. adopt topological maps to guide agents in limited environments such as corridor and hallway using a basic obstacle avoidance control [2]. Skubic et al. pose their idea on navigation using hand-drawn maps in object spaces [3]. Their approach is literally a version of reduction where they parse the environments into navigation states. By reduction, we refer to the process of converting an instance of problem into one another. It can also be used to retrieve a solution for the original problem by backward con- verting a solution from a similar problem whose the solution already exists or can be obtained effortlessly. Many ideas have been proposed under this scheme. Veloso presents a complete framework for storing and reusing past experience in newly- faced problems [4]. Plan reuse, repair, and adaption have been explored many times in previous decades [5], [6], though they were mostly limited to specific domains. Planning by reduction has a strong relation to case-based planning, where solutions to problems are found by exhaustive search from memory [7]. It is also related to using continuation methods akin to graduated non-convexity [8] to plan the solution in a simple domain and graduately transform the solution into the problem domain. Furthermore, some external constraints may be incorporated into the search procedure to identify good solutions as presented in [9]. Moreover, this idea can be regarded as learning by imitation [10], and it is also closely tied to the tracking problem regardless of retriving solutions. Some of sophisticated approaches in these areas are [11]– [13]. The most recent work that captures this concept has been deployed in multi-robot control [14]; it is inspired from the concept of registration in computer vision community. Notably, the idea of using computer vision mehods to interpret hand-drawn sketch maps and related them to the real world goes back to the classic work by Mackworth [15]. In this paper, we present a reduction-based algorithm for path planning in environments with the state transitions that satisfy the Markov property. The idea can also be expanded into other domains such as navigation using an inaccurate map, 2011 Canadian Conference on Computer and Robot Vision 978-0-7695-4362-8/11 $26.00 © 2011 IEEE DOI 10.1109/CRV.2011.11 24