Essential Kinematics for Autonomous Vehicles

Abstract

A short tutorial on Homogeneous Transforms is presented covering the triple interpretation of a homogeneous transform as an operator, a coordinate frame, and a coordinate transform. The operator/transform duality is derived and its use in the Denavit Hartenberg convention is explained. Forward, inverse, and differential kinematics are derived for a simple manipulator to illustrate concepts. A standard set of coordinate frames is proposed for wheeled mobile robots. It is shown that the RPY transform serves the same purpose as the DH matrix in this case. It serves to interface with vehicle position estimation systems of all kinds, to control and model pan/tilt mechanisms and stabilized platforms, and to model the rigid transforms from place to place on the vehicle. Forward and inverse kinematics and the Euler angle rate to the angular velocity transform are derived for the RPY transform. Projective kinematics for ideal video cameras and laser rangefinders, and the imaging Jacobian relating world space and image space is derived. Finally, the kinematics of the Ackerman steer vehicle is presented for reference purposes. This report is both a tutorial and a reference for the transform used in the RANGER vehicle controller. It is both because the models keep evolving and it was necessary to provide the tools, mechanisms, and discipline required to continue the evolution.