The Spatial Semantic Hierarchy
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
... ring 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 consisting of states linked by actions. The topological level introduces the external ontology of places, paths and regions by abduction, to explain the observed pattern of states and actions at the causal level. Quantitative knowledge at the control, causal and topological levels supports a "patchwork map" of local geometric frames of reference linked by causal and topological connections. The patchwork map can be merged into a single global frame of reference at the metrical level when sufficient information and computational resources are available. We describe the assumptions and guarantees behind the generality of the SSH across environments and sensorimotor systems. Evidence is presented from several partial implementations of the SSH on simulated and physical robots. Spatial Semantic Hierarchy DRAFT: February 18, 2000 3 Spatial Semantic Hierarchy DRAFT: February 18, 2000 7 ronment. The topological model of the environment is constructed by the nonmonotonic process of abduction, positing the minimal set of places and paths needed to explain the regularities observed among views and actions at the causal level. A topological network map, particularly one augmented with a hierarchical region structure, is much more effective for planning than the flat causal action model. The topological map can be augmented with quantitative attributes to improve planning further, but the ability to plan and act is not dependent on the availability of quantitative spatial knowledge. Section 4 describes the topological level in more formal detail in terms of first-order logic. The metrical level represents a global geometric map of the environment in a single frame of reference, which may be useful but is seldom essential. Quantitative spatial information is represented at each level of the hierarchy, from local analog maps at the control level, to action magnitudes at the causal level, to local headings and distances at the topological level. This is enough to represent a "patchwork metrical map" of local frames of reference linked by a topological network structure. Section 5 discusses the problem of unifying local frames of reference into a global metrical map, and when such a map is important. Section 6 describes a number of implementations of portions of the SSH framework on both simulated and physical robots, that demonstrate how multiple representations can work effectively together, and which have motivated revisions to the framework. Section 7 discusses practical issues of matching the general SSH framework to the sensors and effectors of a particular robot, and section 8 discusses a variety of related questions.