PDF《带有状态约束的双摆效应吊车轨迹规划》

第31 卷第

7 期2014 年7月控制理论与应用Control Theory &

Applications Vol.

31 No.

7 Jul.

2014 带带带有 有 有状 状 状态 态 态约 约 约束 束 束的 的 的双 双 双摆 摆 摆效 效 效应 应 应吊 吊 吊车 车 车轨 轨 轨迹 迹 迹规 规 规划 划划DOI: 10.7641/CTA.2014.40054 孙宁, 方勇纯? , 钱哲 (南开大学 机器人与信息自动化研究所, 天津 300071;

南开大学 天津市智能机器人技术重点实验室, 天津 300071) 摘要: 对于欠驱动吊车而言, 已有方法大都将负载摆动视为单摆进行处理. 然而当吊钩质量相比负载质量不可忽 略或负载体积较大时, 负载会绕吊钩产生第二级摆动, 出现双摆效应, 使系统的摆动特性更为复杂, 欠驱动度更高, 其控制更具挑战性;

此外, 现有方法均无法保证系统的暂态控制性能. 针对这些问题, 本文提出了一种基于轨迹规划 的消摆定位控制方法. 具体而言, 本方法所规划的台车轨迹具有解析表达式, 且充分考虑系统安全性(摆动幅值)及 台车运动的物理约束;

通过构造新颖的平坦输出信号, 将施加在台车运动和两级摆动上的约束/指标转化为对平坦 输出的约束, 从而将轨迹规划转化为凸优化问题. 该方法能够保证整个过程中系统两级摆动的角度、角速度, 台车 的速度、加速度、加加速度均保持在设定范围内. 通过与已有方法进行仿真对比, 可见本方法不仅简单易行, 且在 工作效率与摆动抑制方面均具有更为良好的控制性能. 关键词: 吊车;

双摆效应;

轨迹规划;

状态约束 中图分类号: TP273 文献标识码: A Motion planning for cranes with double pendulum effects subject to state constraints SUN Ning, FANG Yong-chun?, QIAN Yu-zhe (Institute of Robotics and Automatic Information System, Nankai University, Tianjin 300071, China;

Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300071, China) Abstract: For underactuated cranes, most existing methods treat the payload swing as that of a simple pendulum. However, when the hook mass is not negligible compared with the payload mass or the payload size is large, the payload will rotate around the hook, which exhibits double-pendulum effects and complicates the swing dynamics. Consequently, an extra underactuation degree appears, making the control problem much more challenging. Additionally, currently available approaches cannot guarantee the desired transient control performance. To deal with these problems, a trajectory planning- based control method is presented. Speci?cally, the planned trajectory has an analytical expression and takes full account of the system safety and physical constraints. An elaborate differential ?at output signal is created, and the constraints/ indices imposed on the trolley motion and payload swing are equivalently transformed to some new constraints on the ?at output, which converts the trajectory planning task into a convex optimization problem. The proposed method ensures the swing angles/angular velocities and the trolley velocity/acceleration/jerk to be always within prescribed bounds. Simulation results show that, in comparison with existing methods, the proposed approach is convenient for implementing and achieving superior control performance in terms of both working ef?ciency and swing suppression. Key words: cranes;

double pendulum effects;

motion planning;

state constraints

1 引引引言 言言(Introduction) 对于桥式吊车系统而言, 其工作效率在很大程度 上受制于负载的摆动, 尤其是当台车到达目标点后停 止运行时负载的残余摆动. 大幅摆动将增大负载与工 作空间中其他货物甚至工作人员发生碰撞的可能性, 造成安全隐患. 同时, 残余摆动的存在给操作人员的 落吊操作带来了较大的困难, 而在自然情况下(如空气 阻力的作用下), 负载摆动的衰减往往需要很长的时 间, 严重降低了系统的工作效率. 当负载质量集中且 远大于吊钩质量时, 其摆动主要呈现单摆特性(即单级 摆动). 此时, 操作人员可依靠长期积累的经验, 通过 控制台车的运动对负载的摆动加以抑制. 但人工操作 的方式不仅效率低下、 定位精度差, 还易发生误操作, 造成安全事故. 此外, 当吊钩质量相比负载质量不可 忽略, 或负载不能视为质点时, 负载与吊钩之间会产 生相对摆动, 呈现出复杂的两级摆动特性, 即双摆效 收稿日期: 2014?1?20;