Introduction to RoboticsKinematics

CSCI 4830/7000February 1, 2010

Nikolaus Correll

Last week’s exercise

• Suspension stability

• Statically vs. dynamically stable gaits

Last week’s exercise

• Dynamically stable motions

• Sinuoidal motions for gait generation

Today

• Forward kinematic• Inverse kinematics• Feedback position control• Mobility• Steerability

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

Motion Control

Motion Control

• Calculate forward and rotational speed from position error

• Easier: express error in polar coordinates

Example

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

Homework

• Reading– Chapter 4: up to including 4.1.7

• Exercise– Program a way-point following robot