1. Spatial Semantic Hierarchy (SSH)
What is it? How is it related to robot localization and mapping?
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2. Presentation Structure
Overview of SSH
Applications of SSH to robot localization and navigation
Discussion
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3. CMSC828F-Perceptual Robotics
References
[1] “The Spatial Semantic Hierarchy”, B. Kuipers, AI 119 (2000) pg
[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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4. CMSC828F-Perceptual Robotics
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
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5. CMSC828F-Perceptual Robotics
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 objects+relations among them)
Each level is grounded in the ones below
Low to high level knowledge organization
Combines qualitative and quantitative information
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6. CMSC828F-Perceptual Robotics
SSH Structure
(copied from “The Spatial Semantic Hierarchy” paper [1])
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7. CMSC828F-Perceptual Robotics
Vertical Axis
Sensory Level
Control Level
Causal Level
Topological Level
Metrical Level
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8. CMSC828F-Perceptual Robotics
Horizontal Axis
Qualitative
Quantitative
Continuous valued variables
Analog models of space
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9. CMSC828F-Perceptual Robotics
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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10. CMSC828F-Perceptual Robotics
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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11. CMSC828F-Perceptual Robotics
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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12. CMSC828F-Perceptual Robotics
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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13. CMSC828F-Perceptual Robotics
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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14. CMSC828F-Perceptual Robotics
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
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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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16. CMSC828F-Perceptual Robotics
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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17. 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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18. CMSC828F-Perceptual Robotics
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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19. 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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20. CMSC828F-Perceptual Robotics
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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21. 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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22. 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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23. CMSC828F-Perceptual Robotics
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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24. 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
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25. CMSC828F-Perceptual Robotics
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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26. 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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27. Advantages of Hybrid SSH
Hill-climbing not required
More accurate identification of places using local topological and perceptual map
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28. CMSC828F-Perceptual Robotics
Questions?
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29. CMSC828F-Perceptual Robotics
Thank you
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