Dynamic modeling and control of a multi‐robot system for assembly of flexible payloads with applications to automotive body assembly

Abstract

The field of multi-robot control has almost exclusively addressed issues that are of relevance to the manipulation of payloads that are rigid. A number of studies have examined the multi-robot manipulation of rigid payloads with one or more lower-pair joints such as hand tools, i.e., pliers. In this work, we examine certain modeling and control aspects associated with the assembly of flexible payloads with a multi-robot system. While this particular problem is of a general nature, our work is motivated by the particular problem presented by the assembly of automotive bodies from sheet metal parts. State of the art assembly of automotive bodies involves the use of a great number of costly hardware fixtures that are used to orient and clamp each piece of bent sheet metal prior to robot welding. Currently under development, a new assembly technology called flexible fixtureless assembly is being designed to replace fixtures with robotic technology. Each robot grasps one piece of sheet metal, and correctly positions and orients the part to mate them to permit a third robot to weld them. The assembly process is complicated by the fact that the sheet metal parts are flexible, cannot be permanently deformed during mating and must be positioned to within a relatively small position tolerance. This article describes work performed to model the dynamics of a multi-robot system consisting of two robot manipulators bringing sheet metal parts of an automotive body into contact. This dynamic model is used as a tool to facilitate the investigation of control strategies for the execution of this task. To adequately model the system, the sheet metal parts are first discretized into finite shell elements. The flexible payload dynamics are derived via the Lagrangian formulation and combined with the robot dynamics to form one robot-payload system. The system equations are first simplified by making use of some of the properties of the assembly process. This allows certain of the interaction effects between flexible and rigid body coordinates to be ignored. Contact between the sheet metal payloads during the mating process is modeled with an exponential barrier function. Application of Guyan reduction leads to a lower order dynamic model of the sheet metal payloads and a simplified dynamic model of the two robot system suitable for numerical simulation. The model developed is then used to investigate several candidate control methods for the mating of two sheet metal parts. Simulation results are presented for proportional and derivative control with gravity compensation, computed torque control, and master slave hybrid position force control. Simulation results reveal that all three control methods are able to achieve contact force and position stability. Adequate performance of the proportional and derivative control demonstrates that standard industrial controls implemented in commercial robots may be used to control robots for fixtureless assembly tasks. © 1996 John Wiley & Sons, Inc.