Descriptor modeling and response analysis of two rigid-flexible cooperative arms

In this paper, a descriptor dynamic model for a two-cooperative rigid-flexible link manipulators system which holds a rigid object in a horizontal workspace is derived. When a system of multi manipulators grasps an object, they form a closed chain that its equations consist of some algebraic constraints as well as dynamic equations. These algebraic constraints can cause impulsive behaviors in the system response and must be considered in modeling and control. Moreover, some of these algebraic constraints are dependent to each other and must be neglected in order to reach to the minimal form of the model. In this paper, a dynamic model for a rigid-flexible link manipulator which is derived in many literatures based on Lagrange equation and assumed mode method is considered. Then, the Minimal constraints equations of the system are derived. The closed chain motion of manipulators and constraints are linearized around the rigid-body motion, and a linearized dynamic descriptor model of the system which is the absolute description of the whole system is obtained. Finally, by using descriptor system theory, the behavior of the system is investigated. To evaluate the proposed method, a simulation was performed on a two-cooperative flexible-link manipulator system.