Dynamics and Control

In this chapter we consider the dynamics and control of a serial-link manipulator. Each link is supported by a reaction force and torque from the preceding link, and is subject to its own weight as well as the reaction forces and torques from the links that it supports.

Section 9.1 introduces the equations of motion, a set of coupled dynamic equations, that describe the joint torques necessary to achieve a particular manipulator state. The equations contains terms for inertia, gravity and gyroscopic coupling. The equations of motion provide insight into important issues such as how the motion of one joint exerts a disturbance force on other joints, how inertia and gravity load varies with configuration, and the effect of payload mass. Section 9.2 introduces real-world drive train issues such as gearing and friction. Section 9.3 introduces the forward dynamics which describe how the manipulator moves, that is, how its configuration evolves with time in response to forces and torques applied at the joints by the actuators, and by external forces such as gravity. Section 9.4 introduces control systems that compute the joint forces so that the robot end-effector follows a desired trajectory despite varying dynamic characteristics or joint flexibility.