A new optimization algorithm for singular and non-singular digital time-optimal control of robots

Time-optimal controls for 2-link robots are often of bang-bang type. Many algorithms to solve time-optimal robot control problems a-priori assume the optimal control to be bang-bang. Industrial robots very often have 5 or 6 links and then the associated time-optimal controls are usually singular. This paper presents a new algorithm that enables computation of both bang-bang and singular time-optimal controls for robots. The algorithm uses both the conjugate gradient and Gauss-Newton method to enhance its efficiency and does not require state-parameterization, which introduces additional errors. The algorithm is used to compute time-optimal controls for an industrial 5-link robot model including gravity and viscous friction.

1 Introduction

Motion time of an articulated manipulator plays a crucial role in the productivity of robots in industrial applications. We focus in this paper on the point-to-point time-optimal control problem (PTPTOC): find the control that brings the manipulator from the initial position to the final position in minimum time, while taking into account the dynamics of the robot, constraints on the torques, friction and gravity. The robot model can be written in state-space, with the angular position and velocity as states. The PTPTOC can then be formulated as a nonlinear optimal control problem with free final time, final state constraints and bounded controls.