Stability Analysis of a Reconfigurable and Mobile Cable-Driven Parallel Robot

Abstract

This paper presents a stability analysis based on the Zero Moment Point (ZMP) concept during the reconfiguration of a Cable-Driven Parallel Robot (CDPR) using three mobile bases. Each mobile base can be driven forward and backward, and it has a crane that can be moved up and down, to which a cable connected to the end effector is attached. The ZMP should stay within the designated support boundaries to prevent the robot from tumbling. Therefore, the next positions of the cable exit point are changed by applying two reconfiguration schemes to the robot: 1) changing the mobile base position and 2) altering the crane length. Kinetostatic models of both reconfiguration schemes are formulated such that the wrench matrix is expressed to compute the cable tensions. A fifth-degree polynomial test trajectory is defined to be followed by the end-effector. When executing a prescribed trajectory, the sequence of the mobile base position and the crane length are optimized by continuously considering the robot stability based on ZMP. Without reconfiguration, the mobile cranes cannot handle high cable tensions without tipping over. By performing two reconfiguration schemes, the whole system can be constantly maintained in equilibrium, and the robot's workspace can be enlarged; therefore, the tipping over can eventually be avoided. An experimental setup is built to demonstrate and validate the mathematical models of both reconfiguration scenarios.