Dynamic modelling and PFL-based trajectory tracking control for underactuated cable-driven truss-like manipulator

In recent years,an innovative underactuated robot was developed,named as underactuated cable-driven trusslike manipulator(UCTM),to be suitable in aerospace applications.However,there has been strong consensus that the stabilization of planar underactuated manipulators without gravity is a great challenge since the system includes a second order nonholonomic constraint and most classical control methods are not suitable for this kind of system.Furthermore,the complexity of the truss-like structure results in tremendous difficulty of computational complicacy and high nonlinearity during dynamic modelling in addition to controller design.It is paramount to solve these difficulties for UCTM's future applications.To solve the above difficulties,this paper presents a dynamic modelling method for UCTM and a trajectory tracking control method based on partial feedback linearization(PFL)that fulfills the control goal of moving UCTM from its original position to a desired position by tracking a given trajectory of the joint angles.To achieve this,a model equivalent method is proposed to make UCTM equivalent with a three-link manipulator in the sense of dynamic behavior.Then the Lagrangian equation combined with complex vector method is proposed in the dynamic modelling process of UCTM,which simplifies the derivation procedure.Based on the established dynamic model,a coordinate transformation method is proposed to transform the control force matrix into the conventional form of an underactuated system,so that the control force can be separated from the unactuated term.The PFL method in combination with the LQR control method is then proposed to realize the targets that the joint angles can track given desired trajectory.Simulation experiments are conducted to verify the correctness and effectiveness of the proposed methods.

Causality Analysis of Futures Sugar Prices in Zhengzhou Based on Graphical Models for Multivariate Time Series

This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series.We construct a partial correlation graph at first which is an undirected graph.For every undirected edge in the partial correlation graph,the measures of linear feedback between two time series can help us decide its direction,then we obtain the mixed graph.Using this method,we construct a mixed graph for futures sugar prices in Zhengzhou（ZF）,spot sugar prices in Zhengzhou（ZS） and futures sugar prices in New York（NF）.The result shows that there is a bi-directional causality between ZF and ZS,an unidirectional causality from NF to ZF,but no causality between NF and ZS.