This paper addresses methods of control of a multi-robot system designed for the assembly of flexible sheet metal parts. The work begins with the dynamic modeling of two robots and their sheet metal payloads. Recognizing that the flexible sheet metal states are practically unobservable, since none of the sheet metal parts will be instrumented, a practical control algorithm is proposed based on the rigid body dynamics of the robot and payloads. Stability analysis is carried out using the theory of singularly perturbed dynamic systems to determine the effect of the "rigid" feedback on the flexible system. Experimental results are given to illustrate the dynamic response of the two robot system, while carrying out the assembly operation with the two robots under force control. The experiments are performed with two 6-DOF commercial industrial robots.

Many sophisticated robot controls are formulated with nonlinear Jacobian transformations, which are dependent on task geometry, as integral components of the control law. Under laboratory conditions, these controls are typically implemented with these nonlinear, task geometry dependent transformations analytically derived and hard-coded in controller software. A change in task geometry implies a change in controller software, a cumbersome exercise that severely restricts the versatility of such controls. In this brief paper, we propose a simple, yet effective algorithm to circumvent this implementation problem. Using only geometric information of the task, the required nonlinear task geometry dependent Jacobian transformations are approximated numerically. While seemingly trivial, this methodology implies that given new task geometry data, these sophisticated task based controls can be utilized without tedious derivation and coding of controller software, a process that effectively renders such controls of little utility in an industrial setting. To illustrate the algorithm proposed, two examples are given with experimental results of one example to contrast the performance of the proposed algorithm with that using hard-coded transformations.