# Autonomous Navigation for Flying Robots -

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## Autonomous Navigation for Flying Robots

Lecture 2.3:. 2D Robot Example. Jürgen . Sturm. Technische. . Universität. . München. 2D . Robot. Robot is . located somewhere . in space. Jürgen Sturm. Autonomous Navigation for Flying Robots.

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## Presentation on theme: "Autonomous Navigation for Flying Robots"— Presentation transcript:

Slide1

Autonomous Navigation for Flying RobotsLecture 2.3:2D Robot Example

Jürgen

Sturm

Technische

Universität

München

Slide2

2D RobotRobot is located somewhere

in space

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Slide3

2D RobotRobot is located

somewhere in space

Robot pose:

Position

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Slide4

Robot PoseRobot is located somewhere in space

Robot pose:

Position

Robot pose represented as transformation matrix:

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Slide5

Robot PoseRobot is located at

Robot pose

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Slide6

Coordinate TransformationsRobot is located somewhere in space

Robot pose:

Position

What is the pose after moving 1m forward?How do we need to move to reach a

certain position?

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Slide7

Coordinate TransformationsRobot moves forward by 1mWhat is its position afterwards?

Point located 1m in front of the robot in local coordinates:

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Slide8

Coordinate TransformationsRobot moves forward by 1mWhat is its position afterwards?

Point located 1m in front of the robot in global coordinates:

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Slide9

Coordinate TransformationsWe transformed local to global coordinatesSometimes we need to do the inverse

How can we transform global coordinates into local coordinates?

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Slide10

Coordinate TransformationsWe transformed local to global coordinatesSometimes we need to do the inverse

How can we transform global coordinates into local coordinates?

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Slide11

Coordinate TransformationsNow consider a different motionRobot moves 0.2m forward,

0.1m sideward and turns by 10deg

Euclidean transformation:

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Slide12

Coordinate System TransformationsNow consider a different motionRobot moves 0.2m forward,

0.1m sideward and turns by 10deg

After this motion, the robot pose becomes

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Slide13

Coordinate System TransformationsNote: The order matters!

Compare:

Move

1m forward, then turn 90deg left

Turn 90deg left, then move 1m forward

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1.

2

.

Slide14

Robot OdometryHow can we estimate the robot motion?

Control-based

models predict the estimated motion from the issued control commands

Odometry

-based

models are used when systems are equipped with distance sensors (e.g., wheel encoders)Velocity-based

models have to be applied when no wheel encoders are given

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Slide15

Mathematical

procedure to determine

the present location of a vehicleAchieved by calculating the current pose of the vehicle based on

the estimated/measured velocities and the elapsed time

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Slide16

Motion ModelsEstimating the robot pose based

on the issued

controls

(

the previous

locationMotion model

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Slide17

ExerciseGiven:

IMU readings from real flight of

Ardrone

quadrotorHorizontal speed in the local frame

Yaw angular speedWanted: Position and orientation in global frame

Integrate these values to get robot pose

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Slide18

Lessons Learned2D poseConversion between local and global coordinates

Concatenation of (robot) motions

Robot

odometry

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