带有状态约束的双摆效应吊车轨迹规划

Motion planning for cranes with double pendulum effects subject to state constraints

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.

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 planningbased control method is presented.Specifically,the planned trajectory has an analytical expression and takes full account of the system safety and physical constraints.An elaborate differential flat 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 flat 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 efficiency and swing suppression.