Forward Kinematics and Workspace Analysis of Screw Theory of Seven-DOF Dual-arm Robot
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摘要: 机器人关节空间与工作空间的关系是通过正向运动学方程建立的,正向运动学分析是实现轨迹规划和控制的关键。介绍了比D-H参数法计算简单、描述全面的旋量理论法,应用指数积公式分别对七自由度和六自由度双臂机器人的单臂进行运动学分析并建立正向运动学方程。利用ADAMS进行运动仿真,对比发现:仿真结果与通过正向运动学方程求解的数据接近,误差不超过3 mm,验证了结合旋量理论建立的正向运动学方程的正确性;利用MATLAB软件进行工作空间分析,通过工作空间云图对比,得出七自由度双臂机器人有着更大的工作空间,表明拥有肩部关节的七自由度双臂机器人具有更好的运动学性能。Abstract: The relationship between robot joint space and working space is established by the forward kinematics equations. The forward kinematics analysis plays a key role in realizing the trajectory planning and control. The screw theory, which is simpler and more comprehensive than the D-H parameter method, is introduced. The kinematic analysis of the seven-DOF single-arm robot and the six-DOF dual-arm robot is carried out with the Product of Exponentials. The forward kinematics equation is established. The ADAMS software is applied for motion simulation. It is found that the simulation results are close to those obtained with the forward kinematics equation and that the error is less than 3 mm. The correctness of the forward kinematics equation established by combining the screw theory is verified. The MATLAB software is used to analyze the workspace. The comparison of the working space cloud map shows that the seven-DOF dual-arm robot has a larger workspace and that the seven-DOF double-arm robot with shoulder joints has a better kinematics performance.
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Key words:
- dual-arm robot /
- screw theory /
- product of exponentials /
- forward kinematics /
- software simulation /
- errors /
- workspace
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表 1 六自由度双臂机器人右臂各关节角取值及末端位移理论值与实际值
时间/s 1 2 3 θ1/(°) -30 -60 -60 θ2/(°) -30 -60 -60 θ3/(°) 30 45 45 θ4/(°) 30 75 75 θ5/(°) 30 60 60 θ6/(°) 45 0 0 px/mm 72.5 98.9 98.9 py/mm 220.4 88.1 88.1 pz/mm -40.2 -23.1 -23.1 px1/mm 70.2 101.9 101.9 py1/mm 218.4 89.8 89.8 pz1/mm -39.5 -22.1 -22.1 注:px, py, pz为理论值; px1, py1, pz1为实际值。 表 2 七自由度双臂机器人右臂各关节角取值及末端位移理论值与实际值
时间/s 1 2 3 θ1/(°) 30 -15 -15 θ2/(°) -30 -60 -60 θ3/(°) -30 0 0 θ4/(°) 30 45 45 θ5/(°) 30 -15 -15 θ6/(°) 30 60 60 θ7/(°) 45 0 0 px/mm 46.4 18.5 18.5 py/mm 226.3 243.6 243.6 pz/mm -84.6 122.2 122.2 px2/mm 44.5 20.5 20.5 py2/mm 224.3 245.2 245.2 pz2/mm -84.5 122.1 122.1 注:px, py, pz为理论值; px2, py2, pz2为实际值。 -
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