The Spatial Semantic Hierarchy is a model of knowledge of large-scale space consisting of multiple interacting representations, both qualitative and quantitative. The SSH is inspired by the properties of the human cognitive map, and is intended to serve both as a model of the human cognitive map and as a method for robot exploration and map-building. The multiple levels of the SSH express states of partial knowledge, and thus enable the human or robotic agent to deal robustly with uncertainty during both learning and problem-solving. The control level represents useful patterns of sensorimotor interaction with the world in the form of trajectory-following and hill-climbing control laws leading to locally distinctive states. Local geometric maps in local frames of reference can be constructed at the control level to serve as observers for control laws in particular neighborhoods. The causal level abstracts continuous behavior among distinctive states into a discrete model ...

A framework for the qualitative representation of positional information in a two-dimensional space is presented. Qualitative representations use discrete quantity spaces, where a particular distinction is introduced only if it is relevant to the context being modeled. This allows us to build a flexible framework that accommodates various levels of granularity and scales of reasoning. Knowledge about position in large-scale space is commonly represented by a combination of orientation and distance relations, which we express in a particular frame of reference between a primary object and a reference object. While the representation of orientation comes out to be more straightforward, the model for distances requires that qualitative distance symbols be mapped to geometric intervals in order to be compared; this is done by defining structure relations that are able to handle, among others, order of magnitude relations; the frame of reference with its three components (distance system, s...

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Various relation-based systems, concerned with the qualitative representation and processing of spatial knowledge, have been developed in numerous application domains. In this article, we identify the common concepts underlying qualitative spatial knowledge representation, we compare the representational properties of the different systems, and we outline the computational tasks involved in relation-based spatial information processing. We also describe symbolic spatial indexes, relation-based structures that combine several ideas in spatial knowledge representation. A symbolic spatial index is an array that preserves only a set of spatial relations among distinct objects in an image, called the modeling space; the index array discards information, such as shape and size of objects, and irrelevant spatial relations. The construction of a symbolic spatial index from an input image can be thought of as a transformation that keeps only a set of representative points needed to define the relations of the modeling space. By keeping the relative arrangements of the representative points in symbolic spatial indexes and discarding all other points, we maintain enough information to answer queries regarding the spatial relations of the modeling space without the need to access the initial image or an object database. Symbolic spatial indexes can be used to solve problems involving route planning, composition of spatial relations, and update operations.

We present a general theory of topological maps whereby sensory input, topological and local metrical information are combined to define the topological maps explaining such information. Topological maps correspond to the minimal models of an axiomatic theory describing the relationships between the different sources of information explained by a map. We use a circumscriptive theory to specify the minimal models associated with this representation.

Wayfinding is part of everyday life. This study concentrates on the development of a conceptual model of human navigation in the U.S. Interstate Highway Network. It proposes three different levels of conceptual understanding that constitute the cognitive map: the Planning Level, the Instructional Level, and the Driver Level. This paper formally defines these three levels and examines the conceptual objects that comprise them. The problem treated here is a simpler version of the open problem of planning and navigating a multi-mode trip. We expect the methods and preliminary results found here for the Interstate system to apply to other systems such as river transportation networks and railroad networks.

Shortcomings of qualitative simulation and of quantitative simulation motivate combining them to do simulations exhibiting strengths of both. The resulting class of techniques is called semi-quantitative simulation. One approach to semi-quantitative simulation is to use numeric intervals to represent incomplete quantitative information. In this research we demonstrate semiquantitative simulation using intervals in an implemented semi-quantitative simulator called Q3. Q3 progressively refines a qualitative simulation, providing increasingly specific quantitative predictions which can converge to a numerical simulation in the limit while retaining important correctness guarantees from qualitative and interval simulation techniques. Q3's simulations are based on a technique we call step size refinement. While a pure qualitative simulation has a very coarse step size, representing the state of a system trajectory at relatively few qualitatively distinct states, Q3 interpolates newly expl...

In many applications in mobile robotics, it is important for a robot to explore its environment in order to construct a representation of space useful for guiding movement. We refer to such a representation as a map, and the process of constructing a map from a set of measurements as map learning. In this paper, we develop a framework for describing map-learning problems in which the measurements taken by the robot are subject to known errors. We investigate approaches to learning maps under such conditions based on Valiant’s probably approximately correct learning model. We focus on the problem of coping with accumulated error in combining local measurements to make global inferences. In one approach, the effects of accumulated error are eliminated by the use of local sensing methods that never mislead but occasionally fail to produce an answer. In another approach, the effects of accumulated error are reduced to acceptable levels by repeated exploration of the area to be learned. We also suggest some insights into why certain existing techniques for map learning perform as well as they do. The learning problems explored in this paper are quite different from most of the classification and boolean-function learning problems appearing in the literature. The methods described, while specific to map learning, suggest directions to take in tackling other learning problems.

Abstract. Many real-world applications involve the management of large amounts of time-dependent information. Temporal database systems maintain this information in order to support various sorts of inference (e.g., answering questions involving propositions that are true over some intervals and false over others). For any given proposition, there are typically many different occasions on which that proposition becomes true and persists for some length of time. In this paper, these occasions are referred to as time tokens. Many routine database operations must search through the database for time tokens satisfying certain temporal constraints. To expedite these operations, this paper describes a set of techniques for organizing temporal information by exploiting the local and global structure inherent in a wide class of temporal reasoning problems. The global structure of time is exemplified in conventions for partitioning time according to the calendar and the clock. This global structure is used to partition the set of time tokens to facilitate retrieval. The local structure of time;is exemplified in the causal relationships between events and the dependencies between planned activities. This local structure is used as part of a strategy for reducing the computation required during constraint propagation. The organizational techniques described in this paper are quite general, and have been used to support a variety of powerful inference mechanisms. Integrating these techniques into an existing temporal database system has increased, by an order of magnitude or more in most applications, the number of time tokens that can be efficiently handled.

In order to navigate through natural terrain an autonomous planetary rover must be able to sense its environment, plan and traverse a course through that environment, and react appropriately to unexpected situations as they appear. All this must be done while guiding the vehicle towards the goals that have been given to it by its operators on the Earth. This paper describes research at the Jet Propulsion Laboratory which concentrates on the planning and execution monitoring that must be carried out by the rover to ensure that a safe and efficient path is found and traversed correctly. In the next two decades, NASA is planning several missions involving an autonomous rover moving across