planetary surface robotics enae 788u, spring 2005 u n i v e r s i t y o f maryland lecture 8 mapping...

Planetary Surface RoboticsENAE 788U, Spring 2005

U N I V E R S I T Y O F

MARYLAND

Lecture 8

Mapping5 April, 2005



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Quiz 5

1.What is the most significant integration error in dead reckoning?

2.State two requirements for a good landmark.

3.Give two examples of navigation in nature. Are these examples using dead-reckoning, landmarks, or other techniques?

4.What is perceptual aliasing? What are some methods to combat it?

5.Name one issue each with single position, and multiple position, belief representations.



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Overview

• Why do we map?• Spatial decomposition• Representing the robot• Current challenges



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Mapping

• Represent the environment around the robot• Impacted by robot position representation• Relationships

– Map precision must match application

– Precision of features on map must match precision of robots data (and hence sensor output)

– Map complexity directly affects computational complexity, and reasoning about localization and navigation

• Two basic approaches– Continuous

– Decomposition (discretization)



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Environment representation

• Continuous metric -> x, y, theta• Discrete metric -> metric grid• Discrete topological -> topological grid• Environmental modeling

– Raw sensor data• Large volume, uses all acquired information

– Low level features (e.g. lines, etc)• Medium volume, filters out useful information, still some ambiguities

– High level features (e.g. doors, car)• Low volume, few ambiguities, not enough information



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Continuous representation

• Exact decomposition of environment• Closed-world assumption

– Map models all objects

– Any area of map without objects has no objects in corresponding environment

– Map storage proportional to density of objects in environment

• Map abstraction and selective capture of features to ease computational burden



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• Match map type with sensing device– For laser ranger finder, may represent map as series of

infinite lines

– Fairly easy to fit laser range data to series of lines



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• In conjunction with position representation– Single hypothesis: extremely high accuracy

possible– Multiple hypothesis:

• Either, depict as geometric shape• Or, as discrete set of possible positions

• Benefits of continuous– High accuracy possible

• Dangers– Can be computationally expensive

– Typically only 2D



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Decomposition

• Capture only useful features of world• Computationally better for reasoning, particularly if

map is hierarchical



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Exact cell decomposition

• Model empty areas with geometrical shapes• Can be extremely compact (18 nodes in this figure)• Assumption: robot position within each area of free

space does not matter



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Fixed cell decomposition

• Tessellate world: discrete approximation• Each cell is either empty or full• Inexact (note loss of narrow passageway on right)



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Adaptive cell decomposition

• Multiple types of adaptation: quadtree, BSP, exact• Recursively decompose until a cell is completely free

or completely an object• Very space efficient compared to fixed cell approach



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Occupancy grid

• Typically fixed decomposition– Each cell is either filled or free

• Counter for cell: 0 indicates free, above a certain threshold is considered to be filled with an object

– Particularly useful with range-based sensors• If sensor strikes something in a cell, increase cell counter• If sensor goes over cell and strikes something else, decrease cell

counter (presuming is free space)

• By also discounting cell values over time, can deal with transient obstacles

– Disadvantages• Map size a function of size of environment and size of cell• Imposes a priori geometric grid on world



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Occupancy grid

• Darkness of cell proportional to cell counter value



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Topological decomposition

• Use environment features most useful to robots• A graph specifying nodes and the connectivity

between them– Nodes not of fixed size nor specify free space

– A node is an area the robot can recognize its entry to and exit from



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Topological example

• For this example, robot must be able to detect intersections between halls, and halls and rooms.



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Topological decomposition

• To robustly navigate with a topological map a robot– Must be able to localize relative to nodes

– Must be able to travel between nodes

– These constraints require the robot’s sensors to be tuned to the particular topological decomposition

• Major advantage is ability to model non-geometric features (like artificial landmarks) that benefit localization



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Map updates: occupancy grids

• Occupancy grid– Each cell indicates probability is free space and

probability is occupied

– Need method to update cell probabilities given sensor readings at time t

• Update methods– Sensor model

– Bayesian

– Dempster-Shafer



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Representing the robot

• How represent the robot itself on a map?• Point-robot assumption

– Represent the robot as a point

– Assume it is capable of omnidirectional motion

• Robot in reality is of nonzero size– Dilation of obstacles by robot’s radius

– Resulting objects are approximations

– Leads to problems with obstacle avoidance



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Current challenges

• Real world is dynamic• Perception still very error prone

– Hard to extract useful information

– Occlusion

• Traversal of open space• How to build up topology• Sensor fusion



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Summary

• Decomposition– Continuous

– Discrete

• Map updating– Bayes

– Dempster-Shafer

• Robot representation• Current challenges



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References

• “Introduction to Autonomous Mobile Robots”, R Siegwart and I Nourbaksh, Bradford

• “Mobile Robotics: A Practical Introduction”, U Nehmzow, Springer

• “Computational Principles of Mobile Robotics”, G Dudek, M Jenkin, Cambridge University Press

• “Introduction to AI Robotics”, R Murphy, Bradford• “Rover Localizaton Results for the FIDO Rover”, E

Baumgartner, H Aghazarian, A Trebi-Ollennu, SPIE Photinics East Conference, October, 2001.

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