Minimum-time anti-swing motion planning of cranes using linear programming

Abstract

A novel method to solve the minimum-time anti-swing motion planning problem for cranes based on the use of linear programming is proposed. It is shown that its solution can be obtained by solving a sequence of fixed-time maximum-range linear programming problems. A convergence proof is presented. A classical kinematical model for which the trolley acceleration is the control variable is used. The crane motion equations are discretized in time assuming that the control variable is piecewise constant. Inequality constraints on both trolley speed and acceleration are included to represent physical bounds associated to the electromechanical driving system. The load and the trolley are required to be at rest both at the initial and at the final times. The load cable length as a function of time is assumed given. The ease of both the formulation and the solution of the problem is in contrast with the traditional two-point boundary value problem associated to the Pontryagin's minimum principle. Copyright © 2012 John Wiley & Sons, Ltd.