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Kinematics describes motion without considering its causes. From a video of a tennis match, for example, you can reconstruct the ball’s path without knowing its mass or the forces of gravity and drag. A wheeled robot’s kinematic model relates its linear and angular velocities to changes in its pose (x,y,θ)(x, y, \theta). For a robot arm, the model determines the end-effector pose from joint angles and their rates without considering the torques that cause the motion. This chapter uses the representations from the motion algebras chapter: poses and twists, the exponential map, and the Lie groups SE(2) and SE(3). It starts by connecting that theory to software and estimation, then builds the kinematics of a wheeled robot and of a six-axis arm. Dynamics adds the masses, forces and torques.

Lie III: applications

Connect Lie theory to software libraries and estimation on manifolds, then compare the product of exponentials with Denavit-Hartenberg.

Wheeled robots

Develop kinematic models for wheeled mobile robots using chapter 13 of Lynch and Park.

AR4 arm kinematics

Follow a six-axis example from Denavit-Hartenberg parameters through forward and inverse kinematics to motor steps.

AR4 kinematics lab

Build FK and IK from the as-built URDF, then reconcile the results with the DH model.

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References

  • Modern Robotics Videos (Northwestern University), companion video lectures to Kevin Lynch and Frank Park’s Modern Robotics: Mechanics, Planning, and Control.
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