Motion in the global coordinates

This chapter considers the models of motion in global coordinates system (in two and three dimensions) such that the robot has complete information about the robot’s location and velocity with respect to the origin. Such information is provided by permanent access to global positioning system or to hovering cameras. In particular, the chapter introduces the concept of configuration space and also considers transformations of vehicle coordinates; turning radius, instantaneous velocity center, rotation, and translation matrices. The most common configuration for mobile robots is the Hilaretype robot (known also as differential steering). The mobile platform is governed by the rotational velocity (and direction) of each wheel. Commonly, one assumes a no-slip between the wheels and the floor during the whole motion. The chapter provides a short review of the quadrotor’s dynamics. It presents a simple proportional-derivative controller for stabilizing the quadrotor. The chapter further describes a trajectory tracking control scheme.