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