A Review of Kuiper s: Spatial Semantic Hierarchy

Transcription

1 A Review of Kuiper s: Spatial Semantic Hierarchy Okuary Osechas Comp-150: Behavior Based Robotics 4 November 2010

2 Outline Introduction 1 Introduction 2 Summary of ideas 3 Ontological Levels 4 Interfacing the real world 5 The causal level 6 The topological level 7 The metrical level 8 Conclusions Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

3 Introduction What is SSH The SSH is a model of knowledge of large-scale space Inspired by human cognitive map Hierarchical levels express states of partial knowledge Provides a way of handling a patchwork map of local geometric frames, linked by causal and topological connections......and of merging into single frame of reference Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

4 Introduction Author The author s experience in the field goes back many years PhD (Mathematics) from MIT, Thesis: Representing Knowledge of Large-Scale Space First publication on spatial knowledge A Model of the Acquisition of Spatial Knowledge Tufts University Working Papers in Cognitive Science, No. 11, February 1980 Professor at University of Michigan since Jan 2009 Was Assistant Professor at Tufts: Math dept, Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

5 Introduction Paper The paper collects the author s lifetime experience (up to 1999) in the representation of spatial knowledge Presentation of the SSH is very thorough 99 references in 43 pages Two goals: Describe multiple representations of the SSH, so they can be implemented Demonstrate that the representations can work together coherently and effectively Implicit Paradigm: An agent explores a previously unknown region and creates a representation for it Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

6 Outline Goals 1 Introduction 2 Summary of ideas 3 Ontological Levels 4 Interfacing the real world 5 The causal level 6 The topological level 7 The metrical level 8 Conclusions Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

7 Goals Organization The hierarchy is structured according to two criteria Ontological relations Qualitative vs. quantitative information Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

8 Goals The SSH is a model of knowledge of large-scale space Multiple interacting representations Different levels of increasing abstraction SSH The ultimate goal is a patchwork map of local geometries, linked by causal and topological connections Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

9 Goals Why this? Theoretical background for one question in our group project Trying to find an efficient, but generalizable answer to the question: What kind of information must be conveyed to a human, in order to most efficiently find a target? Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

10 Outline Ontological Levels 1 Introduction 2 Summary of ideas 3 Ontological Levels 4 Interfacing the real world 5 The causal level 6 The topological level 7 The metrical level 8 Conclusions Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

11 Ontological Levels Overview Five ontological levels are described 1 Sensory 2 Control 3 Causal 4 Topological 5 Metrical Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

12 Outline Real-world 1 Introduction 2 Summary of ideas 3 Ontological Levels 4 Interfacing the real world 5 The causal level 6 The topological level 7 The metrical level 8 Conclusions Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

13 Real-world Sensory The sensory and control levels deal with the continuous sensing of a continuous world This level is the only platform specific one Transition to causal level by abstracting continuous behavior to discrete states and actions Quantitative information is useful at every level, but: effective behavior is often possible with only qualitative knowledge. Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

14 Real-world Sensory The sensory level is the interface to the agent s sensory system Motion and exploration, guided by: Vision Range-sensing: Sonar Laser Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

15 Real-world Control The control level describes the world in terms of control laws Binding agent and environment into a dynamic system throughout a qualitatively uniform segment of environment Each law is coupled with conditions for: Appropriateness Conditions for termination Control laws blend over smoothly Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

16 Real-world Control Kuipers formulation is equivalent to a state-space representation Classic control laws formulated here Hybrid dynamic system Potential for interfacing with Kalman filter or particle filter SLAM Analog map Local way finding through behaviors This level may contain local geometric maps, to function as observers Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

17 Outline Causal 1 Introduction 2 Summary of ideas 3 Ontological Levels 4 Interfacing the real world 5 The causal level 6 The topological level 7 The metrical level 8 Conclusions Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

18 Causal Basics The causal level abstracts the continuous world and the agent s behavior Discrete model, consisting of: Sensory views Actions Causal relations among both Combined into schemas: V, A, V Two fundamental actions: Turn Travel Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

19 Causal Basics Views and actions are abstractions from the sensory/control level Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

20 Causal Schemas have two meanings Schemas Declarative: holds(v, s 0 ) holds(v, result(a, s 0 )) View V observed in state s 0, V will be observed if action A is taken in s 0 Procedural: holds(v, now) do(a, now) Stimulus-response pair An action sequence would look like this: V 0, A 0, V 1, A 1, V 2, A 2,..., V n 1, A n 1, V n Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

21 Causal Schemas The causal level can produce a view graph Nodes: views Edges: actions Humans have been shown to be able to build these graphs from purely visual information Difference to a topological map: distinguishability between places, based on views Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

22 Outline Topological 1 Introduction 2 Summary of ideas 3 Ontological Levels 4 Interfacing the real world 5 The causal level 6 The topological level 7 The metrical level 8 Conclusions Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

23 Topological Basics The topological level introduces the ontology of places, paths and regions Introducing relations between them: Connectivity Containment relations Constructed by [non-monotonic] abduction minimal set of places, paths and regions required to explain the sequence of observed views and actions Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

24 Topological Basics A toplogical network map is more effective for planning than the causal action model Particularly if map is augmented with hierarchical region structure Further refinement possible, using quantitative attributes Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

25 Topological Elements The elements in the topological map Elements: Place: zero dimensional; may lie on zero or more paths. A turn action preserves place Path: orientable one-dimensional subspace of the environment. A travel takes place along a path. May serve as boundary between regions Region: two-dimensional subspace of the environment Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

26 Topological Relations The topological relations between elements Represent: location of views, connection of places and paths, order of places on paths, and boundaries and membership of regions at(view,place) along(view,path,dir) on(place,path) order(path,place1,place2,dir) rightof, leftof (path,dir,region) in(place,region) Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

27 Topological Abstraction How to abduct from the causal level to the topological level Every view is observed at a place view place at(view, place) Turn actions preserve place V, (turnα), V place [ at(v, place) at(v, place) ] Travel actions preserve path and direction [ V, (travelδ), V δ 0 p 1, p 2 p1 1p 2 at(v, p 1 ) at(v, p 2 ) ] Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

28 Topological Wayfinding The topological level is useful for way-finding tasks Graph of places and paths can be searched blindly Where distance estimates exist: routes can be optimized With direction and heading information: heuristic search favors motion in direction of goal Abstracting complex way-finding probelms: simpler high-level problem, plus simpler connection problems at endpoints Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

29 Outline Metrical 1 Introduction 2 Summary of ideas 3 Ontological Levels 4 Interfacing the real world 5 The causal level 6 The topological level 7 The metrical level 8 Conclusions Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

30 Metrical Basics Global geometric map of the environment in a single frame of reference This representation may be useful, but seldom essential Quantitative spatial information more useful at each individual level: Control level analog map Causal level action magnitudes Topological level local headings and distances Enough to represent a patchwork map of local frames of reference, linked by topological network structure Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

31 Metrical Problems The main problems of having a map with a single frame of reference Exploring agent has useful states not representable as coordinates in single frame of reference (e.g. loop closing uncertainty) Time and cost of mapping algorithm: hierarchical structuring is more efficient than uniform 2-D occupancy grid (when dealing with large-scale space) Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

32 Metrical Patchwork Map Two options for a patchwork representation Feature mapping identifies environmental features by their sensory signature and assigns locations in a single frame Create loosely-coupled collection of local patch maps, with qualitative links between them Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

33 To complete our example: Metrical Patchwork Map Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

34 Outline Conclusions 1 Introduction 2 Summary of ideas 3 Ontological Levels 4 Interfacing the real world 5 The causal level 6 The topological level 7 The metrical level 8 Conclusions Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

35 Conclusions Summary Hopefully this talk conveyed the basic idea behind the SSH Implicitly, we talked about the interfaces between hierarchical levels: This is an important concept for DIY SSH Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36

36 Thank you! Bye bye have a good weekend Time for questions and discussion Osechas (BBR) Spatial Semantic Hierarchy Review 4 November / 36