A Solving Method for Inverse Kinematics of Space 3R Manipulator based on Singular Trajectory Theory
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摘要: 针对机器人逆运动学多解问题，提出一种基于奇异轨迹线的多模块径向基神经网络的求解方法。根据奇异轨迹线理论，将关节空间严格划分成只具有单逆解的多个关节子空间区域，然后通过正向运动学，使各个关节子空间映射到同一工作空间，以获得多组工作空间位置相同但是关节区域不同的训练样本，每组训练样本只含单逆解。在多模块径向基神经网络结构中，每个子模块分别负责学习一组训练样本，从而将逆运动学多解求取问题转化为各个子模块对神经网络权值的训练问题，通过神经网络结构中的多个模块逆解预测，实现了机器人逆运动学的多解计算。算例表明基于奇异轨迹线的多模块神经网络能够正确输出多组逆解，满足求解精度要求，在逆运动学多解求取中具有较好的推广价值。Abstract: Aiming at the multi-solution problem of robot inverse kinematics, a solution method of multi-module radial basis function network based on singular trajectory is proposed. According to the singular trajectory theory, the joint space is strictly divided into multiple joint subspace regions with only single inverse solution. Then, through forward kinematics, each joint subspace is mapped to the same workspace to obtain multiple sets of training samples with the same working space but different joint regions. Each training sample only contains a single inverse solution. In a multi-module radial basis neural function network structure, each sub-module is responsible for learning a set of training samples. Therefore, the inverse kinematics multiple solution problem is transformed into the training problem of neural network weights of each sub-module. Multi-solution calculation of robot inverse kinematics is realized by inverse solution prediction of multiple modules in neural network structure. The example shows that multi-module neural networks based on singular trajectories can correctly output multiple sets of inverse solutions, moreover, it satisfies the requirements of solving accuracy and has a good generalization value in the inverse kinematics solution.
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Key words:
- robots /
- singular trajector /
- multitasking /
- radial basis function networks
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表 1 6自由度机器人的DH参数
关节转角
θi/(°)连杆距离
di/m连杆长度
ai/m连杆扭角
αi/(°)θ1 0 0 90 θ2 0 0.431 8 0 θ3 0.15 0.020 3 -90 θ4 0.431 8 0 90 θ5 0 0 -90 θ6 0 0 0 
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表 3 两个随机点的多模块神经网络逆解及误差
空间位置点 (0.22, 0.27, 0.14) (0.36, 0.40, 0.42) LD RBF逆解 (3.592, 3.867, 2.372) (3.651, 3.130, 3.351) 位置 (0.191, 0.259, 0.144) (0.361, 0.373, 0.432) 绝对误差E (0.029, 0.012, 0.004) (0.001, 0.027, 0.012) LU RBF逆解 (3.575, 1.656, 0.822) (3.633, 1.699, -0.111) 位置 (0.226, 0.270, 0.103) (0.359, 0.362, 0.441) 绝对误差E (0.006, 0.000, 0.037) (0.001, 0.038, 0.021) RD RBF逆解 (1.341, -0.857, 0.873) (1.150, 0.066, -0.355) 位置 (0.213, 0.254, 0.106) (0.372, 0.462, 0.437) 绝对误差E (0.007, 0.016, 0.034) (0.012, 0.062, 0.017) RU RBF逆解 (1.412, 1.653, 2.424) (1.088, 1.352, 3.335) 位置 (0.196, 0.273, 0.158) (0.376, 0.395, 0.390) 绝对误差E (0.025, 0.003, 0.018) (0.016, 0.005, 0.030)
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表 4 多模块神经网络4组预测逆解平均绝对误差
位型逆解 θe1 θe2 θe3 RU 0.067 7 0.007 6 0.021 3 RD 0.009 1 0.030 5 0.006 0 LU 0.026 0 0.016 9 0.009 2 LD 0.019 3 0.011 0 0.004 7
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