Chapter 3

PID Control in Task Space

Abstract

Task space (or Cartesian space) is defined by the position and orientation of the end-effector of a robot. Joint space is defined by a vector whose components are the translational and angular displacements of each joint of a robotic link. In this chapter, linear PID in the task-space is proposed. The sufficient conditions for asymptotic stability are simple and explicit. The linear PID gains can be selected with these conditions directly. When the measurement of velocities it is not available, a velocity observer (position filter) is applied. The local asymptotic stability of the linear PID control with an observer is proven. The analysis provides explicit conditions for choosing the linear ...

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