ABSTRACT
This chapter provides background on some established control methods that are available for holonomic robotic systems. It presents the dynamics for a robot manipulator and several assumptions/properties associated with those dynamics. The chapter focuses on feedback mechanisms that yield ultimate boundedness or asymptotic stability of the tracking error. There are unique challenges that emerge when describing the control objectives in the task-space of the robot. Given the fact that the usefulness of robots is generally derived from establishing a desirable pose of the robot end-effector with respect to the environment, it is often best to formulate control objectives for the robotic system in the task-space. A potential exists for an over- or underdetermined problem based on the task-space objective and the number of actuated joints in the robot. The control objective for many robotic applications is best described in the task-space or Cartesian-space where the relationship between the robot and external objects is relevant.
