Trolley and Hoisting Motion Planning of Cranes Using Linear Programming

[摘要] A new numerical method to obtain a suboptimal solution of the minimum-time anti-swing motion planning problem for cranes based on the use of linear programming is proposed. Both the trolley and the hoisting motions are the problem unknowns. A classical kinematical nonlinear model for which the trolley acceleration and the hoisting speed are the control variables is used. The crane motion equations are discretized in time assuming that the control variables are piecewise constant. Inequality constraints on state and control variables are included in order to represent physical bounds associated to the electromechanical driving system. Equality constraints are added in to represent the requirement that both the load and the trolley be at rest at the end points of the trolley path. The proposed algorithm consists in the repetition of two steps: (i) an approximation of the hoisting motion is fixed and a corresponding suboptimal trolley motion is computed; (ii) first-order corrections on both the hoisting and the trolley motions are computed based on a linearized model of the system. In spite of the nonlinear dynamics, both steps are reduced to solving Linear Programming problems. A convergence proof of the algorithm is presented. The ease of both the formulation and the solution of the problem contrasts with the traditional two-point boundary value problem associated to the Pontryagin’s minimum principle...

[学科分类] 自动化工程

[关键词] Motion planning ;Minimum-time control ;Anti-swing control ;Crane control ;Linear programming