Lecture 43 Kinematics and Dynamics Jürgen Sturm Technische Universität München Kinematics Describes the motion of rigid bodies Position Velocity Acceleration Jürgen Sturm ID: 199697
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Autonomous Navigation for Flying RobotsLecture 4.3 :Kinematics and Dynamics
Jürgen
Sturm
Technische
Universität
MünchenSlide2
KinematicsDescribes the motion of rigid bodiesPosition
Velocity
Acceleration
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Autonomous Navigation for Flying Robots
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Example: 1D KinematicsState
Action
Time constant
Linear process model
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Autonomous Navigation for Flying Robots
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DynamicsActuators induce forces and torquesForces induce linear accelerationTorques induce angular acceleration
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Autonomous Navigation for Flying Robots
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Forces and AccelerationsForces are vectors and can be summed up
Important forces (for us
): Gravity
, thrust, friction
Forces induce accelerations
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massSlide6
Torques and Angular AccelerationsForce on a lever induces a torque (“turning force”)
Forces are vectors and
can
be summed up
Torque results in angular acceleration
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i
nertial matrixSlide7
Dynamics of a QuadrotorEach propeller induces force and torque by accelerating air
Gravity pulls quadrocopter downwards
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Vertical AccelerationThrust
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Vertical and Horizontal AccelerationThrust
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Vertical and Horizontal AccelerationThrustAcceleration
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attitudeSlide11
Pitch (and Roll)Attitude changes when opposite motors generate unequal thrustInduced torqueInduced angular acceleration
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Side view of
quadrotorSlide12
YawEach propeller induces torque due to rotation and the interaction with the airInduced torqueInduced angular
acceleration
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Lessons LearnedRigid body kinematics: Position, velocity, acceleration
Dynamics:
Forces and torques
Application to
quadrotors
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