Trajectory planning for coordinated motion of a robot and a positioning table. I. Path specification

Coordinating the tool (robot) and workpiece (positioning table) motion in continuous manufacturing processes such as sealing, welding, and laser cutting offers several advantages over the motion of only the tool or workpiece. Better utilization of the speed and workspace characteristics of the two devices and improvement in tracking accuracy at sharp corners in the path are some of the merits of this approach. In coordinated motion, the two devices are simultaneously moved to track a given path, and two strategies are developed for coordinating their motion, where each is dependent on the given path information. The first strategy is applicable to any type of path and resolves the motion by splitting the displacement between any two points on the path into segments moved by the robot and the table. The robot and the table move in opposite directions in this strategy. The second strategy is applicable to sharp cornered paths and resolves the given path into two smooth paths. The first path is a double clothoid curve, whereas the second path is a tangential straight line path. The table executes a local motion around the corner in this strategy, whereas the robot is moved at all times. The uniqueness of this strategy in constructing the original corner path is proved. The proposed strategies are shown to be applicable to other coordinated motion systems