For analyzing the characteristics of complex mechanical system, topology contravariant mapping was described among the trajectories location space of manipulator and multivariate state space which included trajectory of the displacement, velocity and acceleration. It was realized multivariate information and decoupling transformation for the manipulator trajectory space. Based on the multivariable characteristics, the function of Sobolev space was established, which was monitoring multivariate state space of manipulator. The results of the method are effective agreement with the experimental observation.%为了分析复杂机械系统的特征,利用拓扑反变映射,将建立的复杂机械系统信号空间变换到目标变量特征空间,实现对复杂机械系统的多特征表述和解耦变换.然后,针对多特征特点建立Sobolev空间函数,对复杂机械系统特征进行分析监测.最后把该方法应用到机械手特征监测中,验证理论方法的有效性.
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