Introduction toTopological Navigation

prof:S.ShiryPresenter:Masoomeh Bahreini

M.Sc Computer ScienceDepartment of Computer Eng. and IT

Amirkabir Univ. of Technology(Tehran Polytechnic)

winter1383

Objectives

Definition of Navigation Fundemental functions of navigation Type of Navigation Topological Navigation

Vornoi Diagram Metric Navigation Summary Refrence AppendX

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

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

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.

Type of Navigation

metric map(quantitive) topologic map(qualitive)

Type of Navigation

Navigation Topological vs Metric methods Metric methosd:

Potential fields

Topological methods: Waypoints Visibility graphs Vornoi Diagrams

Topological Navigation

Steps of topological navigation Define topological map Costruct a Global map Sence

Sensors:vision,sonar,laser

Construct Local map Navigation

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).

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,

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

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.

Vornoi diagram

p1

p2 p2

p3

p1

Vornoi diagramVornoi diagram with 2 points

Vornoi diagramVornoi diagram with 3 points

Vornoi diagramVornoi diagram of floor map

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

Topological map

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.

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

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.

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.

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

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.

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.

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.

Topological Navigation using Occupancy Grid

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

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

Topological Navigation Using Landmark

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!

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

Global Map Construction without a predefiend map

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

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.

Construction Square Error

The number of eigenvalueChoose to represent

eigenspace

These expressions provide a criteria to choose the number of eigenvectores

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

Introduction to Metric Navigation

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

Metric Localization(iconic)

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.

Summary

Localization and map making are intertwined Localization requires good maps Map making requires good localization

Summary

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

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”

Thanks for your Attention

Appendix

An example of vornoi

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

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