Skip to main content
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

Wheel types, the chassis as a planar rigid body, and the two families of wheeled robots, following chapter 13 of Lynch and Park.

Omnidirectional robots

Wheel speeds from the body twist for omniwheels and mecanum wheels, checked against a mecanum robot in simulation.

Nonholonomic robots

The differential-drive model, its no-slip assumption on ice, and wheel odometry.

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.

​
References

  • Modern Robotics Videos (Northwestern University), companion video lectures to Kevin Lynch and Frank Park’s Modern Robotics: Mechanics, Planning, and Control.
Found an error on this page? Report an issue.