Download - Lecture 03 - Kinematics and Control
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Introduction to RoboticsKinematics
CSCI 4830/7000September 13, 2010
Nikolaus Correll
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Last week’s exercise
• Suspension stability
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Last week’s exercise
• Statically vs. dynamically stable gaits
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Last week’s exercise
• Dynamically stable motions
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Last week’s exercise
• Sinuoidal motions for gait generation
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Today
• Forward kinematic• Inverse kinematics• Feedback position control• Mobility• Steerability
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Kinematics Intro
• How does a robot move?
• Reference frames
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Forward Kinematics
• Given– Wheel speeds– Wheel radius– Axle length
• Required– Speed in robot coords– Speed in world coords
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Inverse Kinematics
• Given– Desired speed in world
coordinates• Required– Set-speed in robot coordinates– Wheel-speed
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Wheel kinematic constraints
• Wheel HAS to roll• Wheel cannot slide
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Robot kinematic constraints
• Only standard wheels impose constraints– Fixed– Steerable
• Castor, Swedish and Spherical wheels do not
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Maneuverability
• Robot moves along x, y and theta• Degree of mobility: number of
parameters the robot can change just with its wheels
• Degree of steerability: how many independently steered wheels?
• Maneuverability = mobility + steerability= Degrees of freedom a robot can
manipulate
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Maneuverability
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Examples
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Motion Control
Open-Loop vs. Closed Loop
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Motion Control
• Calculate forward and rotational speed from position error
• Easier: express error in polar coordinates
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Example
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Homework
• Reading– Chapter 4: up to including 4.1.7
• Exercise– Program a way-point following robot