Equivalent Position Workspace for a Coal Gangue Picking Robot and Its Application to Stability Analysis: A Descriptive Study

The separation of gangues from coals is of key important for green mining. Robotic separation of coals and gangues based on the machine vision system, which is called a coal gangue picking robot with an end-grab driven by four cables, is developed in this study. The proposed robots possess highly dynamic performance of the gangue pick-and-place operation, such as a high payload-to-weight ratio, as well as a high positioning accuracy. For using cable actuation in the robots, there are not only the advantages but also problems come from it. One most critical issue is the stability of the robot, and furthermore, the stability is directly related to whether the target gangues can be successfully sorted. It is noted that the stability of the robots is associated with a particular position where a family of cable tensions is required to make the end-grab be in equilibrium. As a result, in order to learn more about the stability of a coal gangue picking robot, this research focuses on the equivalent position workspace, within which a coal gangue picking robot has the same stability. First, the kinematic and kinetostatic models of the robot are presented in order to analyze their influence on the coal gangue picking robot's stability. Furthermore, based on convex optimization theory, a non-iterative polynomial-based optimization algorithm with the proper optimal objective function is proposed, in which the cable with the smallest cable tension at any posture is determined. Then three position performance indices are provided to demonstrate the significant effects of end-grab positions on the stability of the coal gangue picking robot in a given workspace zone. In addition, the Equivalent Position Workspace (EPW), a new workspace, is added. Finally, simulation data are used to correct the theoretical relationship between the two performance indices and the stability. For coal gangue robotic separation, the research has significant guiding relevance and practical utility.