On singular time-optimal control along specified paths

Abstract

This paper presents a general necessary condition for singular time optimal control of robotic manipulation moving along specified paths. Early work by Bobrow-Dubowsky (1985) and Shin-McKay (1985) ignored the issue of singular control, assuming bang-bang acceleration along the path. Recent work by Shiller-Lu (1992) has shown that the time optimal control can be singular if one of the equations of motion reduces to a velocity constraint. This paper derives a more general necessary condition for singular control. It is also proven that singular control cannot exist if the set of admissible controls is strictly convex, as is demonstrated for a two-link planar manipulator with elliptical actuator constraints.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>