Localization 1 Localization Navigation System Localization Where am

Localization (1)

Localization • Navigation System • Localization : Where am I ? – The robot must determine its position in the environment 2

Challenges of Localization • Mobile robot with GPS – GPS provides accuracy to within several meters – GPS cannot function indoors or in obstructed areas – The robot may need to identify its relative position to target humans – The robot may need to build an environmental model (map) that aids it in planning a path to the goal. • Practical Localization Problem – Building a map, then identifying the robot’s position relative to the map • Difficulties of Localization – Inaccuracy and incompleteness of sensors and effectors • Sensor noise • Sensor aliasing • Effector noise 3

Sensor Noise • Sources of sensor noise – Color CCD camera • Illumination • Picture jitter, signal gains, blooming, blurring … – Ultrasonic range finder • Surface • Interference between multiple sonar emitters • Solution – Multiple readings – Temporal fusion or multisensor fusion 4

Sensor Aliasing • Nonuniqueness of sensor readings (ex) narrow-beam range finders: ultrasonic or infrared • provides range information in a single direction without any additional data such as color, texture, and hardness • Even with multiple sensors, there is a many-to-one mapping from environmental states to the robot’s perceptual inputs. • Cannot distinguish between human and inanimate objects 5

Effector Noise • Mobile robot effectors (wheels / legs) introduce uncertainty about future states • In odometry (wheel sensors only) and dead reckoning (also heading sensors), the position update is based on proprioceptive sensors • Because the sensor measurement errors are integrated, the position error accumulates over time 6

Odometrc Error • Error sources 7

Odometric Error • Classification 8

Error Model for Odometry • A differential-drive robot : Incremental travel distance during a sampling time 9

Error Model for Odometry • Kinematics : traveled distance for the right and left wheel 10

Error Propagation Law 11

Error Propagation Law 12

Error Model for Odometry • Error model 13

Odometry Error • Growth of the pose uncertainty for straight-line movement 14

Odometry Error • Growth of pose uncertainty for circular movement 15

To Localize or Not to Localize • Map-based navigation vs. behavior-based navigation – Map-based navigation: localization-based solution – Behavior-based navigation: programmed solution 16

Behavior Based Navigation • Not includes localization and cognition stages – Left-wall following – Detection of target (room B) : (ex) color of carpet • Architecture • Advantage – Quick implementation • Disadvantages – Cannot directly scale to other environments – Time-consuming procedure 17

Map Based Navigation • Includes localization and cognition stages • Architecture • Advantages • Disadvantages – Localization by collecting sensor data, and updating some belief about its position w. r. t. a map of the environment – Map-based concept of position makes the system’s belief transparently to human operators – The human can give the robot a new map if the robot goes to a new environment – Time-optimal motion – Requires more development effort – If the map is wrong or the sensor values are incorrect, the robot’s behavior may be undesirable 18

Representation • Fundamental issue of map-based localization system – Map representation • What aspects of the environment are contained in the map ? • At what level of fidelity does the map represent the environment ? – Belief representation • Belief : robot’s possible position on the map • Does the robot identify a single unique position as its current position, or does it describe its position in terms of a set of possible solution ? • If multiple possible positions are expressed in a single belief, how are those multiple positions ranked ? • Effects on the system performance – Architectural complexity – Computational complexity – Localization accuracy 19

Belief Representation 20

Belief Representation • Single-hypothesis belief – The robot’s belief about position is expressed as a single unique point on the map – Advantage • Unique belief → no position ambiguity → facilitates decision making at the cognitive level (pathplanning) → facilitates position updating – Disadvantage • Often impossible to cover uncertainty due to effector and sensor noise 21

Belief Representation • Single-hypothesis belief a) real map b) line-based map c) grid-based map d) Topological map 22

Belief Representation • Multiple-hypothesis belief – The robot’s belief about position is expressed as a possibly infinite set of positions on the map – Advantage • The robot can explicitly cover uncertainty of its position due to effector/sensor noise and lack of sensor information. – Disadvantage • Complex decision-making at the cognitive level 23

Map Representation • Fundamental relationships – Precision of the map vs. precision of the robot’s application – Precision of the map vs. precision of the robot’s sensor – Complexity of the map vs. computational complexity of navigation • Map representation – Continuous representations – Decomposition 24

Map Representation 25

Map Representation: continuous representation • Continuous representation – Advantage • Potential for high accuracy – Disadvantage • High computational cost • Continuous line representation (EPFL) (a) Real map (b) Representation with a set of infinite lines 26

Map Representation: decomposition • Exact cell decomposition – Polygons – extremely compact representation: only 18 nodes – Particular position inside of free space does not matter – What matter is the robot’s ability to traverse from free space to adjacent area 27

Map Representation : decomposition • Fixed cell decomposition – Inexact nature – Narrow passages disappear 28

Map Representation : decomposition • Adaptive cell decomposition – The rectangle is decomposed into 4 identical rectangles • If interior of a rectangle lies completely in free space or obstacle, it is not composed further • Otherwise, it is recursively decomposed into 4 rectangles until some predefined resolution is attained White: outside of obstacle Black: inside of obstacle Gray: part of both regions 29

Map Representation : decomposition • Occupancy grid – – Popular version of fixed cell decomposition Grid: very small cells Grid value: hit count by range sensors Memory problem 30

Map Representation : decomposition • Topological decomposition – Graph representation: nodes & edges – Useful information for localization 31

Map Representation : decomposition 32