Spatial Semantic Hierarchy (SSH)

1. Spatial Semantic Hierarchy (SSH) What is it? How is it related to robot localization and mapping? CMSC828F-Perceptual Robotics

2. Presentation Structure • Overview of SSH • Applications of SSH to robot localization and navigation • Discussion CMSC828F-Perceptual Robotics

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 CMSC828F-Perceptual Robotics

4. 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 CMSC828F-Perceptual Robotics

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 objects+relations among them) • Each level is grounded in the ones below • Low to high level knowledge organization • Combines qualitative and quantitative information CMSC828F-Perceptual Robotics

6. SSH Structure (copied from “The Spatial Semantic Hierarchy” paper [1]) CMSC828F-Perceptual Robotics

7. Vertical Axis • Sensory Level • Control Level • Causal Level • Topological Level • Metrical Level CMSC828F-Perceptual Robotics

8. Horizontal Axis • Qualitative • Quantitative • Continuous valued variables • Analog models of space CMSC828F-Perceptual Robotics

9. 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 CMSC828F-Perceptual Robotics

10. 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) CMSC828F-Perceptual Robotics

11. 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 CMSC828F-Perceptual Robotics

12. 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. CMSC828F-Perceptual Robotics

13. 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 CMSC828F-Perceptual Robotics

14. 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 CMSC828F-Perceptual Robotics

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 CMSC828F-Perceptual Robotics

16. 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 CMSC828F-Perceptual Robotics

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 CMSC828F-Perceptual Robotics

18. Situation Calculus (2) • Action representation • Used in AI Planning • Resulting planners are efficient if domain specific search control knowledge is used CMSC828F-Perceptual Robotics

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 CMSC828F-Perceptual Robotics

20. 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 andaxioms • Abduction is used to find places and paths from views and actions CMSC828F-Perceptual Robotics

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 CMSC828F-Perceptual Robotics

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 CMSC828F-Perceptual Robotics

23. 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 CMSC828F-Perceptual Robotics

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 CMSC828F-Perceptual Robotics

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 CMSC828F-Perceptual Robotics

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 CMSC828F-Perceptual Robotics

27. Advantages of Hybrid SSH • Hill-climbing not required • More accurate identification of places using local topological and perceptual map CMSC828F-Perceptual Robotics

28. Questions? CMSC828F-Perceptual Robotics

29. Thank you CMSC828F-Perceptual Robotics