Abstract: A method and apparatus involving the application of an algorithm used for finding the time optimal trajectory for torque limited Industrial Robots, to achieve the operation of Cluster Tool Robots in an improved manner by modifying the applied algorithm through adding two additional constraints, i.e., jerk (the rate of change of acceleration) and the acceleration seen by the load. This modification renders it possible to create a robot arm trajectory that minimizes travel time by minimizing the excitation of uncontrolled resonances and avoiding command of an acceleration that would exceed the force of friction between a substrate holder on the end of the arm and a substrate held thereon by friction.

Abstract: A method and apparatus involving the application of an algorithm used for finding the time optimal trajectory for torque limited Industrial Robots, to achieve the operation of Cluster Tool Robots in an improved manner by modifying the applied algorithm through adding two additional constraints, i.e., jerk (the rate of change of acceleration) and the acceleration seen by the load. This modification renders it possible to create a robot arm trajectory that minimizes travel time by minimizing the excitation of uncontrolled resonances and avoiding command of an acceleration that would exceed the force of friction between a substrate holder on the end of the arm and a substrate held thereon by friction.