Time-Optimum Trajectories for Robots With Multiple End-Effectors
Aggressive throughput performance of automated tools for semiconductor and flat-panel-display manufacturing applications have led to development of substrate-handling robots with multiple end-effectors. For maximum throughput levels, a method for calculating a time-optimum substrate transfer trajectory without causing any of the substrates carried by the robot to slide, and without violating other prescribed constraints, is required. This paper presents an algorithm which provides the required functionality with desirable computational efficiency and reliability. The key idea is to identify the set of fundamental trajectory shapes which cover all possible combinations of constraints for a given category of moves, e.g., moves along a straight line or along a circular arc, decompose the fundamental shapes into segments where a single constraint is active, and determine the time-optimum motion profiles in the segments. The fundamental shapes for each of the categories are found as simplified versions of the generic shape which corresponds to the case when all of the constraints are active. Each of the shapes has a set of conditions associated with it to determine whether the shape can be used for a particular move. An example comparison of a motion profile generated based on pre-defined time-optimum shapes with a conventional s-curve trajectory demonstrates that the present algorithm produces substantially faster motion, resulting in an improved throughput performance of the robot.