On The Trajectory Planning And Motion Control Of A Cable-Driven Gangue Sorting Robot

At present,there are many disadvantages in the coal gangue separation method,and the separation of the gangues from raw coals is an indispensable link in the efficient and clean utilization of coal resources.Therefore,separation of the coals and gangues restricts the development of the coal industry.Using robots for the separation of the coals and gangues is an effective way to solve the problem and to realize the automatic sorting of coals and gangues’fast,accurately and stably.In this paper,combining with the advantages of cable-driven parallel robots,a cable-driven gangue sorting robot is proposed,and furthermore,the sorting trajectory planning and trajectory tracking control are studied.The main contents are as follows:(1)The kinematics model of the cable-driven gangue sorting robot is established by using the vector closure principle,The simulation results show that the cable length curve conforms to the geometric characteristics of the end grab trajectory.The Newton-Euler method is used to establish the dynamic model of the robot,and it is pointed out that the dynamic model cannot solve the problem of flexible cable tension directly due to the redundant driving.It lays a foundation for the research on sorting trajectory planning and trajectory tracking control of cable-driven gangue sorting robot.(2)It is well-known that the dynamic model of the robot cannot directly solve the cable tensions because of the redundant driving,And therefore the cable tension optimization for robot is established,in which the minimum cable tension(preload)and the maximum bearing capacity of the cable are taken as linear constraints,and the minimum variance of the cable tensions is taken as the optimization objective.And furthermore the minimum cable tension equivalent surface is solved based on the minimum cable tensions.The cable tension is greater than the minimum cable tension in the envelope space of the end-grab,which can ensure the smooth operation of the end-grab.The simulation results show that the method is effective and reliable to optimize the cable tension.When the end-grab of the robot is in the equivalent surface formed by the minimum cable tension,the cable tension changes continuously and stably,which can meet the stability requirements.(3)Due to the movement characteristics of the gangues,the position of the gangue bin and the optimal force of the geometric center of the workspace of the robot,the sorting path of the end-grab has special requirements and high accuracy requirements.According to the advantages of the Cartesian space trajectory planning,the sorting trajectory planning of the end-grab of the robot is carried out from the Cartesian space,and the sorting trajectory of the end-grab is planned as the starting section,the preparation section,the grab section and the gangue section,And moreover according to the different motion characteristics of each segment,the four-segment motion of the end grab is planned by using the S-type velocity curve and the five-degree polynomial trajectory planning method.The simulation of the planned trajectory scheme shows that the sorting trajectory is located in the minimum cable tension equivalent surface.The four segments of the trajectory are connected smoothly.The sorting trajectory corresponds to continuous velocity and acceleration,and the change of cable length is smooth and continuous.The trajectory parameters can adapt to the different distribution of gangue on the belt conveyor.(4)Considering the unidirectional force characteristics of the cables,it is difficult to avoid the influence of external interference,including external impact load,a fuzzy robust adaptive trajectory tracking control system for the cable-driven gangue sorting robot is designed against the external interferences based on the dynamic model.Based on Lyapunov stability theory,it is proved that the control system is stable.The simulation of the designed control system shows that the trajectory tracking effect is good,and the cable tensions satisfy the unidirectional force characteristics of the cables.As a result,the control strategy is feasible and effective.