Introduction to Topological Navigation
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Transcript of Introduction to Topological Navigation
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Introduction toTopological Navigation
prof:S.ShiryPresenter:Masoomeh Bahreini
M.Sc Computer ScienceDepartment of Computer Eng. and IT
Amirkabir Univ. of Technology(Tehran Polytechnic)
winter1383
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Objectives
Definition of Navigation Fundemental functions of navigation Type of Navigation Topological Navigation
Vornoi Diagram Metric Navigation Summary Refrence AppendX
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Definition of Navigation
Robot navigation is one of the key issue in mobile robotics
It consists in driving a robot throgh a given environment,using the information from sensors
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Fundemental functions of navigation
Primary functions of navigation: Where am I?
Localization:relative or absolute
Where am I going? Usually defied by human operator or mission planner
What’s the best way to get there? Path planning:qualitative & quantitative
Where have I been? Map making
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Type of Navigation
Metrical Navigation Needs a geometric model of the world. Assumes exact sensor information. Allows a more precise navigation.
Topological Navigation Leads to a qualitative description of the navigation goals. Uses a flexible, easy to define, map. Not suitable for very precise applications.
Ideal Solution Merge both navigation models.
Metrical: local, more precise, navigation. Topological: global, less precise, navigation.
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Type of Navigation
metric map(quantitive) topologic map(qualitive)
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Type of Navigation
Navigation Topological vs Metric methods Metric methosd:
Potential fields
Topological methods: Waypoints Visibility graphs Vornoi Diagrams
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Topological Navigation
Steps of topological navigation Define topological map Costruct a Global map Sence
Sensors:vision,sonar,laser
Construct Local map Navigation
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Topological Navigation
Define &Construction global map The map should be useful to the application Amount of abstraction in modeling world
Can be represented as a directed graph where: Nodes: correspond to key-places in the map. Transitions: used to travel between key-places.
In robotic soccer, one could have: Nodes: field zones (half-field, penalty areas). Transitions: basic movements (turn left, move forward).
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Topological Navigation
Global Map (world model) Provided :user,robot(exploration) User map:unaccurate,not detailed the robots will have to be able to deal with
inaccuracies and lack of details that comes with the maps provided by users.
It does not require accurate metric and geometric information, and details about obstacles inside the environment can be omitted.
map can be given as a bitmap image,
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An Example of a Sketch Floor Map
Scale is unknown Scale is not uniform across the
map. Geometrical details are not
available. Details exact shapes of
the walls, shapes of intersections,…
Obstacles are left out of the map.
Topological Navigation
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Vornoi diagram
Let P = p1, p2, . . . , pn be a set of points in the 2 dimensional Euclidean plane. P is called the generators. partition the plane by assigning every point in the plane to its nearest point p.P. All those points assigned to pi form the Voronoi region V (pi), that is,V (pi) = {x : |pi - x| = |pj - x| .j = i}. note that some points do not have a unique nearest neighbor. The set of all points that have more than one nearest neighbor forms the Voronoi diagram V(P) A Voronoi vertex is a point p . V(P) that has more than 2 nearest neighbors and a Voronoi edge is a set of points that forms a boundary between Voronoi regions.
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Vornoi diagram
p1
p2 p2
p3
p1
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Vornoi diagramVornoi diagram with 2 points
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Vornoi diagramVornoi diagram with 3 points
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Vornoi diagramVornoi diagram of floor map
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Augmented Topological Map
a traditional topological map is a graph that represents connectivity between landmarks, without containing any metric or geometrical information.
+-intersection is a node connected with 4 arcs that extends approximately perpendicularly to each other.
T-intersection is a node that is connected with 3 arcs, with two of them perpendicular to the other.
Endpoint is a node that where the Voronoi diagram ends at a wall. Dead-end is a node that has 3 neighbors, and two of them are
Endpoints. Corner is a node that has 3 neighbors, and one of them is an
Endpoint. Generic node is a node that is not any of the above
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Topological map
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Map Localization
Essential step for navigation (topological or metrical).
In the topological case, it’s equivalent to identify in which node (of the graph) the robot is.
Might be expressed as a classification problem. current input map projection is compered to the projection
of global map Make use of k-nearest neighbour method to localize the
robot in a node/class.
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Map Localization
Method of matching Iconic:
use raw (or near raw) sensor readings Feature-based:
use features extracted from raw data Label and match corners, walls Less features, so less computations
Metric map-making relies on iconic localization Toplogical map-making relies on Feature-based localization
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Map Localization
Match between nodes Two nodes strictly match if
they have the same number of neighbors have the same attributes, without considering
diference of labels. For example, a Corner node v that has three neighbors v1,
v2, v3 with v2 as the Endpoint matches with a Corner node w that has three neighbors w1,w2,w3 with w1 as the Endpoint.
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Map Localization
Two nodes match if they are strictly match
or one of them is a generic node and they have the same number of neighbors
A generic node match everything that has the same number of neighbors as itself.
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Map Localization
Robot Pose a directed arc ij in a topological map that the robot is
moving on robot is somewhere between node i and j, and is
heading to node j.
Multiple Hypothesis Tracking.(MHT) Partially Observable Markov Process(POMP)
Given the last probality distribution and the current observation and action,calculate the probality of being in a state
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POMDP
It get states, actions, transitions,observations (a set of things that can be perceived by the
agent ) An observation function maps each state (or
sometimes state/action pair) to a probability distribution over observations
there are unobservable state variables it is important to estimate missing information
and to acquire better strategies that incorporate the prediction of environmental behaviors.
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Path Generation
Robot is aimed to sweep throgh all the reachable places of the terrain
Nodes of the graph considered as goals Use of search algorithms, applied to the graph.
Large Graphs: Define an heuristic. use A*
Find the shortest path from start node to a goal node.
Small Graphs simple search, so it’s not worthy to use an heuristic. reduce A* or breadth-first search.
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Path Following
Ideally, it corresponds to the sequential execution of the transitions defining the generated path.
Nevertheless…
Dynamic environment subject to sudden changes. Some transitions show more than 50% failures.
A failure detection and new path generation mechanism is needed.
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Topological Navigation using Occupancy Grid
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Topological Navigation using Occupancy Grid
Each cell of the occupancy grid contains a probality value which is an estimation that the representation position is occupied by some object
Occupancy grid can be viewd as a 2-d grayscale image of the environmentDigital image processing are valid approachesSkeletizationThinigVornoi diagram
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Topological Navigation using Occupancy Grid
Steps of map building Gloabal grid building Sensor interpretation
sonar
Integration over time Different sensors give different values for a grid cell because
of noise and changing viewpoint it’s important to integrate the conditional probalities of distinct moments
Pose estimation Local map is match with a global map
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Topological Navigation Using Landmark
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Topological Maps Use Landmarks A landmark is one or more perceptually distinctive
features of interest on an object or locale of interest
Natural landmark: configuration of existing features that wasn’t put in the environment to aid with the robot’s navigation (ex. gas station on the corner)
Artificial landmark: set of features added to the environment to support navigation (ex. highway sign)
Roboticists avoid artificial landmarks!
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Desirable Characteristics of Landmarks
Recognizable (can see it when you need to) Passive Perceivable over the entire range of where the robot
might need to view it Distinctive features should be globally unique, or at
least locally unique
Perceivable for the task (can extract what you need from it) ex. can extract relative orientation and depth
Be perceivable from many different viewpoints
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Global Map Construction without a predefiend map
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Topologial Navigation
Information required to represent each node must be gathered
a set of images P of the space where the robot will navigate
General enouph to represent all the areas of cs
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Principal Components Analysis
x2
x1
Use PCA (KL) to compress the information in P
Extraction of Eigenimages eigenvectors of the training
images covariance matrix:R = X XT
Use only the most significant components – higher eigenvalues.
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Construction Square Error
The number of eigenvalueChoose to represent
eigenspace
These expressions provide a criteria to choose the number of eigenvectores
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Map construction
PCA compute principle images Space after computation :principle space project each image in the principle space,
associating the projection with the node of graph
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Introduction to Metric Navigation
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Metric Navigation
A geometric map represent objects according to their absolute geometric relationships.
Localization A sensor-drived geometric map must be matched
against a global map of a large area
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Metric Localization(iconic)
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Summary
Map-based navigation is limited to laboratory setting with well-structured environment
Have not been tested extensively in real-world environment
Require a significant amount of processing and sencing
Higher level task can be performed by the robot after successful exploration.
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Summary
Localization and map making are intertwined Localization requires good maps Map making requires good localization
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Summary
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Future work
Sensor selection and sensor fusion for specific applications and environments.
Accurate and reliable algorithms for matching local maps to the stored map.
Good error models of sensors and robot motion. Good algorithms for integrating local maps into a
global map. Higher level task can be performed by the robot
after successful exploration
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Refrence
Vachirasuk Setalaphruk Atsushi Ueno Izuru Kume Yasuyuki Kono” Robot Navigation in Corridor Environments using a Sketch Floor Map”
Gon¸calo Neto, Hugo Costelha, Pedro Lima “Topological Navigation in Configuration Space Applied to Soccer Robots
Szabo, R. / Topological Navigation of Simulated Robots using Occupancy Grid, pp. 201 - 206, International Journal of Advanced Robotic Systems, Volume 1, Number 3 (2004), ISSN 1729-8806
J. Borenstein , H. R. Everett , and L. Feng Contributing authors: S. W. Lee and R. H. Byrne “Where am I?Sensors and Methods for Mobile Robot Positioning”
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Thanks for your Attention
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Appendix
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An example of vornoi
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Measurement type in Navigation
Relative Odometry
Absolute Active Beacons Landmark Recognition
Artificial Distinctive artificial landmarks are placed at known
locations in the environment 3 or more landmarks must be ‘in view’ to allow pose
estimation Detection these landmarks are easier for knowing size
and shape Natural
Distinctive features in the environment Vertical edges :doors,wall junction
Environment must be known in advance
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Measurement type in Navigation
Model Matching
Information acquired from sensors is compared to a map or world model of the environment
Geometric Represent the world in a global coordinate system
Toplogical Represent the world as a network of nodes and arcs