||The problem of minimum-time anti-swing motion planning of cranes with uncertainty
in the hoisting speed of the load cable is addressed. The crane is modeled as a
trolley-pendulum system for which the trolley acceleration is the control variable. A previously
existing method that uses linear programming to solve the problem in the absence of
uncertainties has been extended in order to take the uncertainty in the hoisting speed into
account. Constraints that impose that the sensitivity of both the load angle and load angular
speed with respect to the uncertain parameter to be zero at the final point of the path are
included in the linear programming formulation.