Lecture 23 2D Robot Example Jürgen Sturm Technische Universität München 2D Robot Robot is located somewhere in space Jürgen Sturm Autonomous Navigation for Flying Robots ID: 794602
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Autonomous Navigation for Flying RobotsLecture 2.3:2D Robot Example
Jürgen
Sturm
Technische
Universität
München
Slide22D RobotRobot is located somewhere
in space
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Autonomous Navigation for Flying Robots
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Slide32D RobotRobot is located
somewhere in space
Robot pose:
Position
Orientation (yaw angle/heading)
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Autonomous Navigation for Flying Robots
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Slide4Robot PoseRobot is located somewhere in space
Robot pose:
Position
Orientation (yaw angle/heading)
Robot pose represented as transformation matrix:
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Autonomous Navigation for Flying Robots
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Slide5Robot PoseRobot is located at
Robot pose
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Autonomous Navigation for Flying Robots
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Slide6Coordinate TransformationsRobot is located somewhere in space
Robot pose:
Position
Orientation (yaw angle/heading)
What is the pose after moving 1m forward?How do we need to move to reach a
certain position?
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Slide7Coordinate TransformationsRobot moves forward by 1mWhat is its position afterwards?
Point located 1m in front of the robot in local coordinates:
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Autonomous Navigation for Flying Robots
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Slide8Coordinate TransformationsRobot moves forward by 1mWhat is its position afterwards?
Point located 1m in front of the robot in global coordinates:
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Autonomous Navigation for Flying Robots
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Slide9Coordinate 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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Slide10Coordinate 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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Slide11Coordinate TransformationsNow consider a different motionRobot moves 0.2m forward,
0.1m sideward and turns by 10deg
Euclidean transformation:
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Autonomous Navigation for Flying Robots
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Slide12Coordinate 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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Autonomous Navigation for Flying Robots
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Slide13Coordinate 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
.
Slide14Robot 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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Slide15Dead ReckoningIntegration of odometry is
also called dead reckoning
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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Slide16Motion ModelsEstimating the robot pose based
on the issued
controls
(
or IMU readings) and
the previous
locationMotion model
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Slide17ExerciseGiven:
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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Slide18Lessons Learned2D poseConversion between local and global coordinates
Concatenation of (robot) motions
Robot
odometry
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