This paper addresses the problem of simultaneous localisation and mapping (SLAM) by a mobile robot. An incremental SLAM algorithm is introduced that is derived from multigrid methods used for solving partial differential equations. The approach improves on the performance of previous relaxation methods for robot mapping because it optimizes the map at multiple levels of resolution. The resulting algorithm has an update time that is linear in the number of estimated features for typical indoor environments, even when closing very large loops, and offers advantages in handling non-linearities compared to other SLAM algorithms. Experimental comparisons with alternative algorithms using two well-known data sets and mapping results on a real robot are also presented.

Topological and metrical methods for representing spatial knowledge have complementary strengths. We present a hybrid extension to the Spatial Semantic Hierarchy that combines their strengths and avoids their weaknesses. Metrical SLAM methods are used to build local maps of small-scale space within the sensory horizon of the agent, while topological methods are used to represent the structure of large-scale space. We describe how a local perceptual map is analyzed to identify a local topology description and is abstracted to a topological place. The mapbuilding method creates a set of topological map hypotheses that are consistent with travel experience. The set of maps is guaranteed under reasonable assumptions to include the correct map. We demonstrate the method on a real environment with multiple nested large-scale loops.

Loop-closing has long been recognized as a critical issue when building maps of large-scale environments from local observations. Topological mapping methods abstract the problem of determining the topological structure of the environment (i.e., how loops are closed) from the problem of determining the metrical layout of places in the map and dealing with noisy sensors. A recently developed incremental topological mapping algorithm [1], [2] generates all possible topological maps consistent with the experienced sequence of actions and observations and the topological axioms. These are then ordered by a preference criterion such as minimality or probability, to determine the single best map for continued planning and exploration. This paper presents the planarity constraint and analyzes its impact on the search-tree of all topological maps consistent with (non-metrical) exploration experience. Experimental studies demonstrate excellent results even in artificial environments where loop-closing is particularly difficult due to large amounts of perceptual aliasing and structural symmetry.

In Simultaneous Localisation and Mapping (SLAM) the correspondence problem, specifically detecting cycles, is one of the most difficult challenges for an autonomous mobile robot. In this paper we show how significant cycles in a topological map can be identified with a companion absolute global metric map. A tight coupling of the basic unit of representation in the two maps is the key to the method. Each local space visited is represented, with its own frame of reference, as a node in the topological map. In the global absolute metric map these local space representations from the topological map are described within a single global frame of reference. The method exploits the overlap which occurs when duplicate representations are computed from different vantage points for the same local space. The representations need not be exactly aligned and can thus tolerate a limited amount of accumulated error. We show how false positive overlaps which are the result of a misaligned map, can be discounted. 1

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One of the most difficult problems in Simultaneous Localisation and Mapping (SLAM) is that of identifying and closing cycles. While localisation methods exist that can provide local consistency in a map, residual errors can grow unbounded in global metric maps. Topological maps are favoured by some because they do not have the global consistency problems however they too have difficult correspondence problems due to perceptual aliasing. In this paper we discuss our approach to closing cycles in a topological map. We use both a global metric map and the topological map itself to identify cycles in the topological map.

Two or more different entities that appear identical when observed in isolation are perceptually aliased. While the nature of perceptual aliasing is clearly general and its occurrence depends on the kind of entities and perceptual skills assumed, it originates a very practical problem when it comes to acquiring purposeful spatial representations, e.g., maps, of an unknown environment under exploration. If perceptual aliasing is taken into account, whenever a place is perceived as identical to one or more encountered earlier in the exploration, the following question must be addressed: “Is this place one of those visited earlier, or a totally new place (Was this a loop)?”. Different approaches to map-building handle (if that) this issue in a variety of ways. Our work takes place in the framework of the Spatial Semantic Hierarchy, which has proved relevant to a diverse body of research in AI, robotics and cognitive sciences. It represents spatial knowledge over different overlaying ontological levels, and allows topological map-building. In its current computational implementations, the complete set of topological hypotheses originated by perceptual aliasing is pruned by further exploration, and enforcing topological and common sense properties. Many such hypotheses, however, may survive due to symmetry in the environment or while the exploration is not complete, yielding a combinatorial explosion of possible maps. We believe that taming this proliferation is possible without giving up the complete account of all the possible hypotheses, by ranking them according to their inherent metrical plausibility. We propose to evaluate such a parameter from local metrical annotations, in a computationally economical fashion, and without building a single global metrical frame of reference, that would introduce the hard problem of enforcing global metrical consistency. The main contribution here is the novel perspective, purpose and way mathematical methods and spatial ontologies are employed and integrated.