On Trajectory Planning for a Cable-driven Gangue Sorting Robot
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摘要: 依据矸石分拣过程和特点,提出一种柔索驱动拣矸机器人的抓取轨迹规划方案。建立柔索驱动拣矸机器人运动学模型,仿真分析验证了模型的正确性,为末端抓斗的运动轨迹是否符合索长变化规律提供判定依据。根据矸石与皮带运输机同步运动的特性、矸石仓位置及拣矸机器人工作空间几何中心受力最佳等条件,将末端抓斗的抓取轨迹规划为启动段、准备段、抓矸段和置矸段;并针对各段不同的运动特点,采用S型速度曲线和五次多项式组合的轨迹规化方法,对末端抓斗的四段运动进行规划。对规划的轨迹方案进行仿真,结果表明,末端抓斗的运动轨迹、速度和加速度连续,索长变化光滑连续,且轨迹参数能适应矸石在皮带运输机上的不同分布情况。Abstract: According to the process and characteristics of the gangue sorting, a grasping trajectory planning scheme for the cable-driven gangue sorting robot was proposed. The kinematic model of the cable-driven gangue sorting robot was firstly expounded, and the accuracy of the model was verified by simulation, which provided a basis for judging whether the trajectory of the end grab conforms to the change rule of the cable length. According to the characteristics of synchronous movement of the gangues and belt conveyor, the position of the gangue bin and the workspace geometric center, the grasping trajectory of the end grab was then planned four sections, namely as start, preparation, gangue grab, and gangue disposal sections. According to the different motion characteristics of the above sections, the S-type velocity curve, quintic polynomial and the combination of both were used to plan the motion of the end grab. The planned trajectory scheme was finally simulated and analyzed. The results showed that the trajectory, velocity and acceleration of the end grab were continuous, the change of cable length was smooth and continuous, and the trajectory parameters determined by the above method could adapt to the different distribution of gangue on the belt conveyor.
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表 1 各段轨迹规划方法
Table 1. Trajectory planning method for each stage
阶段 方向 采用的轨迹规划方法 启动段CD x 五次多项式 y S型速度曲线 z 无位移 准备段DE x 无位移 y S型速度曲线 z 无位移 抓矸段EF x 五次多项式 y 五次多项式 z 五次多项式 抓矸段FG x 无位移 y S型速度曲线 z 五次多项式 置矸段GD x 五次多项式 y 五次多项式 z 无位移 表 2 五次多项式轨迹规划参数
Table 2. Quintic polynomial trajectory planning parameters
阶段 五次多项式参数 $q_0/{\rm{m}}$ $\dot q_0/({\rm{m\cdot s}}^{-1}) $ $\ddot q_0/({\rm{m\cdot s}}^{-2}) $ $q_t/{\rm{m}} $ $\dot q_t/({\rm{m\cdot s}}^{-1}) $ $\ddot q_t/({\rm{m\cdot s}}^{-2}) $ CD $x_c=0 $ $\dot x_c=0 $ $\ddot x_c=0 $ $ x_D=0 $ $\dot x_D=0 $ $\ddot x_D=0 $ EF $x_E =0.25 $ $\dot x_E =0 $ $\ddot x_E =0 $ $ x_F =1 $ $\dot x_F =0 $ $\ddot x_F =0 $ $y_E=0 $ $\dot y_E=1 $ $\ddot y_E=0 $ $y_F=1-\sqrt {5} $ $\dot y_F=-1 $ $\ddot y_F=0 $ ${\textit{z}}_E=1.5 $ $\dot {\textit{z}}_E=0 $ $\ddot {\textit{z}}_E=0 $ $ {\textit{z}}_F=1.8 $ $\dot {\textit{z}}_F=0 $ $\ddot {\textit{z}}_F=0 $ FG $ {\textit{z}}_F=1.8 $ $\dot {\textit{z}}_F=0 $ $\ddot {\textit{z}}_F=0 $ ${\textit{z}}_G= 1.5$ $\dot {\textit{z}}_G= 0$ $\ddot {\textit{z}}_G= 0 $ GD $ x_G= 1 $ $\dot x_G= 0 $ $\ddot x_G= 0 $ $\dot x_D= 0.25 $ $\dot x_G= 0 $ $\ddot x_G= 0 $ $ y_G= 0 $ $\dot y_G=-1 $ $\ddot y_G=0 $ $ y_D=\sqrt{5}-1 $ $\dot y_D= 1$ $\ddot y_D= 0 $ 表 3 i = 0.25 m时
${\rm{ S}}$ 型速度曲线规划段参数Table 3. Parameters of S-type velocity curve planningstage when i=0.25
阶段 S型速度曲线规划参数 $ {v_{\max }}/( {{\rm{m\cdot s}}}^{-1} ) $ $ a/( {{\rm{m}}\cdot{{\rm{s}}^{-2}}} ) $ $ J/( {{\rm{m}}\cdot{{\rm{s}}^{-3}}} ) $ $ CD $ $ {v_{y\max }} = 1 $ $ {a_y} = \sqrt 5 $ $ {J_y} = 5 $ $ DE $ $ {v_{y\max }} = 1 $ $ {a_y} = \sqrt 5 $ $ {J_y} = 5 $ $ FG $ $ {v_{y\max }} = - 1 $ $ {a_y} = - \sqrt 5 $ $ {J_y} = - 5 $ 表 4 i = 0时
五次多项式规划调整参数 Table 4. Parameters of quintic polynomial planning stage when i=0
阶段 五次多项式参数 $ {q_0} $/${\rm{m}} $ $ \dot q_0 $/$ ( {{\rm{m\cdot s}}}^{-1} ) $ $ \ddot q_0 $/$ ( {{\rm{m}}\cdot{{\rm{s}}^{-2}}} ) $ $ {q_t} $/$ {\rm{m}} $ $ \dot q_t $/$ ( {{\rm{m\cdot s}}}^{-1} ) $ $ \ddot q_t $/$ ( {{\rm{m}}\cdot{{\rm{s}}^{-2}}} ) $ CD x方向无位移,无需五次多项式规划 EF $ {x_E} = 0 $ $ {\dot x _E} = 0 $ $ {\ddot x _E} = 0 $ $ {x_F} = 0 $ $ {\dot x _F} = 0 $ $ {\ddot x _F} = 0 $ GD $ {x_G} = 0 $ $ {\dot x _G} = 0 $ $ {\ddot x _G} = 0 $ $ {x_D} = 0 $ $ {\dot x _D} = 0 $ $ {\ddot x _D} = 0 $ -
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