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

机译：使用线性编程的起重机最小时间防摆运动计划

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摘要

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.
机译：提出了一种基于线性规划的求解起重机最小时间防摆运动计划的新方法。结果表明，可以通过解决一系列固定时间的最大范围线性规划问题来获得其解。提出了收敛证明。使用经典运动学模型，其中小车加速度是控制变量。假设控制变量为分段常数，那么起重机的运动方程会及时离散。包括对台车速度和加速度的不平等约束，以代表与机电驱动系统相关的物理界限。货物和手推车在开始和结束时都必须处于静止状态。假定负载电缆的长度是时间的函数。与庞特里亚金极小原理相关的传统两点边值问题形成对比和解决问题的简便性。

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