Time and Motion

Abstract

In the previous chapter we learnt how to describe the pose of objects in 2- or 3-dimensional space. This chapter extends those concepts to objects whose pose is varying as a function of time.

For robots we wish to create a time varying pose that the robot can follow, for example the pose of a robot’s end-effector should follow a path to the object that it is to grasp. Section 3.1 discusses how to generate a temporal sequence of poses, a trajectory, that smoothly changes from an initial pose to a final pose.

Section 3.2 discusses the concept of rate of change of pose, its temporal derivative, and how that relates to concepts from mechanics such as velocity and angular velocity. This allows us to solve the inverse problem – given measurements from velocity and angular velocity sensors how do we update the estimate of pose for a moving object. This is the principle underlying inertial navigation.