Spatial Semantic Hierarchy (SSH)

1
Spatial Semantic Hierarchy (SSH)

• What is it? How is it related to robot
  localization and mapping?

2
Presentation Structure

• Overview of SSH
• Applications of SSH to robot localization and
  navigation
• Discussion

3
References

• 1 The Spatial Semantic Hierarchy, B. Kuipers,
  AI 119 (2000) pg 191-233
• 2 An intellectual History of the Spatial
  Semantic Hierarchy, B. Kuipers, in M. Jefferies
  and A. Yeap (Eds.), Robot and Cognitive
  Approaches to Spatial Mapping, Springer Verlag,
  2006
• 3 Local metrical and global topological maps
  in the Hybrid Spatial Semantic Hierarchy, B.
  Kuipers, J. Modayil, P. Beeson, M. MacMahon, and
  F. Savell, ICRA 2004.
• 4 Towards Autonomous Topological Place
  Detection Using the Extended Voronoi Graph, P.
  Beeson, N. K. Jong and B. Kuipers, ICRA 2005

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Types of spaces

• Visual Space
• Surrounding environment
• Large-scale Space
• Scale larger than the sensory horizon of the
  agent
• Graphical (Diagrammatic) Space
• Spatial layout and relations among symbols on
  paper

5
Overview of SSH

• A hierarchical description of a cognitive map,
  consisting of four different levels
• Each level defines its own ontology (i.e. types
  of objectsrelations among them)
• Each level is grounded in the ones below
• Low to high level knowledge organization
• Combines qualitative and quantitative information

6
SSH Structure
(copied from The Spatial Semantic Hierarchy
paper 1)
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Vertical Axis

• Sensory Level
• Control Level
• Causal Level
• Topological Level
• Metrical Level

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Horizontal Axis

• Qualitative
• Quantitative
• Continuous valued variables
• Analog models of space

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Control Level

• Provides an abstraction from the continuous
  sensory input and motor output to discrete states
  
• Agent representation includes a set of control
  laws, a selection method and termination
  conditions for each control law
• Agent, environment and control law form a
  continuous dynamical system

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States

• Locally distinctive state is a local maximum
  state with respect to a distinctiveness measure
• Possible distinctiveness measures
• equidistance from nearby obstacles (hill-climbing
  control law case)
• sudden change in trajectory (trajectory-following
  control law case)

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Control Laws

• Hill-climbing control laws bring the agent to a
  locally-distinctive state from any state within
  the local neighborhood
• Trajectory-following control laws bring the
  agent from one distinctive state to the
  neighborhood of the next

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Control law selection

• Many different strategies
• Rule-based system
• Decision-tree, based on sensory input
• Combination of multiple laws using fuzzy control,
  potential field methods etc.
• Smooth transitions between control laws can be
  implemented with weighted average of
  appropriateness measures.

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Local 2-D geometry (1)

• Different methods for map-building and
  localization
• Occupancy grids
• Split space into cells
• Each cell holds a number containing the
  probability of being occupied
• Sensory target map
• Identify and localize objects
• Size of the maps depends on the number of objects

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Local 2-D geometry (2)

• Model the path as a generalized cylinder
• Different characteristics of the cylinder might
  be known with different accuracy/confidence
• Good to incorporate weak metrical information
  with strong one

15
Guarantees at the control level

• Alternating trajectory-following and
  hill-climbing control laws using the following
  closure criteria
• For all states, there exist a trajectory-following
  control law (no dead ends)
• For all trajectory-following control laws
  executed at an appropriate state, there exist at
  least one hill-climbing control law available

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Causal Level

• Action A Sequence of control laws taking the
  agent from a distinctive state to another
• View V Description of the sensory input vector
  s(t)
• Schema A tuple (V,A,V)
• Declarative meaning/ Situation calculus
• Procedural meaning/ Stimulus-response pair
• Routine Set of schemas

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Situation Calculus (1) Overview

• First-order language extended with an extra
  situation argument
• Holds(V,s0) view V is observed in situation s0
• do function applies an action to a situation to
  yield a new situation
• result(A, s0) denotes the new situation after
  applying action A to situation s0

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Situation Calculus (2)

• Action representation
• Used in AI Planning
• Resulting planners are efficient if domain
  specific search control knowledge is used

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Action categorization

• Two (rough) categories turns and travels
• Turn Leaves the agent at the same place
• Travel Takes the agent from one place to another
• Also depends on the motor and sensor capabilities
  of the agent

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Topological Level

• Describes the environment as a collection of
• Places eq. to zero-dimensional points
• Paths eq. To one-dimensional subspaces (lines)
• Regions eq. two-dimensional subset of space, i.e.
  sets of places binded together
• Also exist topological relations and axioms
• Abduction is used to find places and paths from
  views and actions

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Hierarchy in Topological Level

• There are multiple topological maps with
  different granularity.
• Abstraction region represents the set of places
  that is abstracted to a single node in a higher
  level map
• Upward mapping Each node of the lower lvl
  corresponds to its abstraction region
• Downward mapping Inverse procedure

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Topological relations

• At(view, place) view seen at place
• Along(view, path, dir) view seen along path in
  direction dir
• On(place,path) place on path
• Order(path,place1, place2, dir) order on path
  from place1 to place2 is dir
• Right_of(path,dir, region)/left_of path facing
  direction dir has region on its right/left
• In(place, region) place is in region

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Metrical Level

• A global 2-D analog representation of the world
• Not necessary for the SSH to work
• Can lead to more accurate global localization,
  when perceptual aliasing (i.e. distinct places
  appear similar) is present

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Metrical Level Creation Problems

• Useful states of knowledge might not be
  expressible as global coordinates
• around the block and walking in circles
  problem
• High requirements in space and time
• Possible solution is to use a loosely-coupled
  collection of local patch maps

25
Extensions of SSH

• Combine large and small-scale perceptual space
• SSH treats perception as a black-box
• Better definition of distinctive states
• Hill-climbing is unnecessary in some cases
• Connect SSH with SLAM

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Hybrid Spatial Semantic Hierarchy

• Create a local perceptual map based on SLAM
  methods
• Use the local map for localization
• Identify gateways, i.e. places where control
  shifts from motion between places to localization
  within a neighborhood
• Identify path fragments connecting distinct
  places
• Create a local topology that describes how
  directed path segments join at a place

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Advantages of Hybrid SSH

• Hill-climbing not required
• More accurate identification of places using
  local topological and perceptual map

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Questions?
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Thank you