# Multi-Robot Trajectory Planning and Position/Force Coordination Control in Complex Welding Tasks
## 1 Introduction  
With the complication and diversification of industrial production tasks, multi-robot cooperative systems have demonstrated stronger operational capabilities, more flexible system structures, and stronger collaboration capabilities. Therefore, multi-robot collaboration has become an important challenge for robot control. Multi-robot collaboration has been applied in many fields such as handing, assembly, welding, etc. The application of this paper is focused on the welding field. In arc welding, the traditional welding workstation consisting of \"welding robot + positioner\" is not able to meet the current demand for small-volume, customized, flexible, and automated production. Multi-robot cooperative welding adopts a universal and high-degree of freedom handing robot instead of a low-degree of freedom positioner, which can effectively improve the flexibility of welding tasks and welding automation. Arc welding is a complex system that contains both pose constraints and wrench constraints, the use of multi-robot systems for arc welding has many advantages, but it also brings more complex control problems. Two of the most critical issues are the trajectory planning in the multi-robot collaboration process and the coordinated control of position/force among multi-robot. For the trajectory planning of multi-robot systems, the current research issues include motion constraints, control methods for cooperative motion, and implementation of multi-robot cooperative systems. (1) For the motion constraint problem of multi-robot systems, the main task is to derive the end-effector of robot pose, velocity and acceleration constraints. For example, the idea is first pointed out in [1] that when two or more robots grah a common object, the robot end-effector is subject to kinematic constraints, and gives the speed constraint relationship of the multi-robot end-effector when the multi-robot is holding an object and rotates around its center. The pose, speed and acceleration constraints of the end-effector in the case of two robots grasp the common object, operate a pair of pliers and grah an object with a ball joint are deduced in [2; 3]. The concept of absolute motion when the two robots cooperatively clamp the workpiece is proposed in [4]. The multi-robot cooperated trajectory planning approach based on the closed kinematic chain model is proposed in [5]; (2) For the control methods of collaborative movements, a method of establishing a constraint model with differential algebraic equations which using feedback linearization is addressed in [6]. The common control methods of general differential algebraic systems is summarized base on the above idea in [7]; (3) The realization for multi-robot collaboration system, the problem of trajectory planning and programming of general multi-robot cooperative system are analyzed. Such as ABB MultiMove function, KUKA RoboTeam function, Yaskawa independence/collaboration function, FANUC cooperative action function, etc. Although the above research has given a certain impetus to the kinematics constraints and trajectory planning, the current multi-robot coordination tasks are relatively simple and most of them are focus on the coordination of dual robots. The above trajectory planning method is not scalable and feasible for multi-robot collaboration to accomplish specific tasks in a more complex and unstructured environment. Multi-robot trajectory planning is the basis for completing the welding tasks, there are not only pose constraints, but also the wrench constraints in the process of welding displacement. Therefore, multi-robot position/force coordination control is another key issue in the cooperative welding process. Research methods for multi-robot position/force coordination control include master/slave control, hybrid motion/force control, synchronization control and impedance control. (1) Master/slave control. The control idea is to define one of the robotic arms as the master arm and the other as the valve arm.