Time Optimal Control

Abstract

The most important job of industrial robots is moving between two points rest-to-rest. Minimum time control is what we need to increase industrial robots productivity. The objective of time-optimal control is to transfer the end-effector of a robot from an initial position to a desired destination in minimum time. Consider a system with the following equation of motion:

$$ \dot x = f(x(t),Q(t)) $$

(14.1)

where Q is the control input, and x is the state vector of the system

$$ x = \left[ {\begin{array}{*{20}c} q \\ {\dot q} \\ \end{array} } \right]. $$

(14.2)

The minimum time problem is always subject to bounded input such as

$$ \left| {Q\left( t \right)} \right| \leqslant Q_{Max} . $$

(14.3)