Modeling of Kinematics of Continuous Robot via Plane Circular Method and Experimental Study
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摘要: 针对当前连续型机器人的运动学逆解求解复杂、低效这一问题，提出了一种基于平面圆弧法的运动学建模方法，其具有运动学逆解求解简单、高效的特点。利用该方法在平面内拟合连续型机器人的弯曲运动形状，建立其运动学模型，分析其驱动空间、关节空间和操作空间的映射关系，并描述其工作空间。分析连续型机器人在平面内弯曲形状的几何约束，建立关节空间变量之间的数学关系，降低求解复杂逆运动学问题的难度。对机器人末端执行器的位置和驱动线长度变化曲线进行仿真分析，求解逆运动学的有效解，并研制原理样机进行样机实验，实验表明该运动学模型的正确性以及逆运动学求解方法的有效性。Abstract: In order to solve the problem that the inverse kinematics solution of continuous robot is complex and inefficient, a kinematics model based on the plane circular method is proposed, which has the characteristics of simple and efficient for inverse kinematics solution. The method is used to fit the shape of the bending motion of the continuous robot in the plane and the kinematics model for the continuous robot is presented. The mapping relationship between the drive space, joint space and operation space are analyzed and the workspace is described. The geometric constraints of the curved shape in the plane of the continuous robot are analyzed, and the mathematical relationship between the joint space variables is established to reduce the difficulty of the complex inverse kinematics problems. The position of end-effector and the change of drive line length are simulated and the effective solution of the inverse kinematics is solved. The correctness of the kinematics model and the effectiveness of the inverse kinematics solution are verified by using the prototype experiment.
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Key words:
- continuous robot /
- inverse kinematics /
- plane circular method /
- prototype experiment
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图 3 柔性臂单圆弧弯曲运动几何模型
Figure 3. Geometric model of single circular arc bendingmotion of a flexible arm
图 6 柔性臂双圆弧弯曲运动几何模型
Figure 6. Geometric model of double circular arc bendingmotion of a flexible arm
图 7 双圆弧曲线几何关系示意图
Figure 7. Schematic diagram of geometric relationship of double arc curves
图 8 双圆弧曲线形状下末端执行器几何模型
Figure 8. Geometric model of an end effector in double arccurve shape
图 10 单圆弧曲线柔性臂末端执行器位置变化曲线
Figure 10. Position change curve of end effector of a flexible arm with single circular arc curve
图 11 柔性臂第一段关节组驱动线长度变化曲线
Figure 11. Length variation curve of driving line of the first joint group of a flexible arm
图 12 柔性臂第二段关节组驱动线长度变化曲线
Figure 12. Length variation curve of driving line of the second joint group of a flexible arm
图 13 双圆弧曲线柔性臂末端执行器位置变化曲线
Figure 13. Position change curve of end effector of doublecircular arc flexible arm
图 14 双圆弧弯曲第二段关节组驱动线长度变化曲线
Figure 14. Length change curve of driving line of the second joint group of double arc bending
图 15 连续型柔性臂平面内弯曲运动试验
Figure 15. In plane bending motion test of continuous flexible arm
图 16 随机取得16个目标点的直线距离误差曲线
Figure 16. Straight line distance error curve of 16 target points at random
图 17 平面y = 345内目标点直线距离误差曲线
Figure 17. Straight line distance error curve of target points in plane y = 345
表 1 4种工况下的绳长变化量
Table 1. Rope length variation under four working conditions
mm 参数 工况1 工况2 工况3 工况4 $\Delta {l_{11}}$ 2.077 14.616 −12.9 8.01 $\Delta {l_{12}}$ 2.077 −14.616 −0.9 2.70 $\Delta {l_{13}}$ −2.077 −14.616 12.9 −8.01 $\Delta {l_{14}}$ −2.077 14.616 0.9 −2.70 $\Delta {l_{21}}$ 20.98 25.698 25.16 −30.98 $\Delta {l_{22}}$ 20.98 −25.698 1.75 −10.32 $\Delta {l_{23}}$ −20.98 −25.698 −25.16 30.98 $\Delta {l_{24}}$ −20.98 25.698 −1.75 10.32 $\Delta {l_{31}}$ 30.979 30.401 46.77 −52.73 $\Delta {l_{32}}$ 30.979 −30.401 3.26 −17.57 $\Delta {l_{33}}$ −30.979 −30.401 −46.77 52.73 $\Delta {l_{34}}$ −30.979 30.401 −3.26 17.57 
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表 2 4种工况下仿真值与实际值
Table 2. Simulation values and actual values underfour working conditions
mm 工况 参数值 x轴 y轴 z轴 1 仿真值 402.3 398.6 0 实际值 403.0 394.0 −4.0 误差 0.7 4.6 4.0 2 仿真值 345.3 0 501.3 实际值 354.0 −8.5 503.0 误差 9.3 8.5 1.7 3 仿真值 400.0 230.0 200.0 实际值 407.5 240.0 201.0 误差 7.5 10.0 1.0 4 仿真值 300.0 −300.0 −150.0 实际值 310.0 −299.0 −148.0 误差 10.0 1.0 2.0
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