Time optimal trajectory for cluster tool robots

Apparatus for operating a workpiece handling tool with a friction-type workpiece holder, said apparatus minimizes time required for a motor-driven, articulated arm of said tool to travel a set distance to a final end point by maximizing an average velocity over the set distance while avoiding an excitation of uncontrolled resonances and a command of an acceleration that would exceed a frictional force between an end effector at an end of the arm and a workpiece supported thereon, comprising:

• means for determining points of a trajectory of arm travel, including a start end point, while limiting a travel velocity and acceleration by constraints of:
• acceleration at the workpiece, such that a horizontal acceleration at the workpiece is equal to a coefficient of a static friction between the end effector multiplied by the gravity acceleration;
• and
• jerk rate, such that excitation of resonances in the arm is minimized;
• and wherein
• said determining means comprises means for finding trajectory points by moving from one dynamic state to a next dynamic state and selecting, as points on the trajectory, dynamic states that do not violate said constraints and maximize the average velocity of arm travel over the set distance.

A method of operating a substrate handling tool with a friction-type substrate holder, said method minimizes time required for a motor-driven, articulated arm of said tool to travel a set distance to a final end point from a start end point by maximizing an average velocity over the set distance while avoiding an excitation of uncontrolled resonances and a command of an acceleration that would exceed a frictional force between an end effector at the end of the arm and a substrate supported thereon, comprising the steps of:

• determining points of a trajectory of arm travel, limiting a travel velocity and acceleration by constraints comprising:
• acceleration at the substrate, such that a horizontal acceleration at the substrate is equal to a coefficient of a static friction between the substrate and the end effector multiplied by the gravity acceleration;
• and
• jerk rate, such that excitation of resonances in the arm is minimized;
• and
• finding points of the trajectory by determining the dynamic states thereof by the steps comprising:
• STEP 1:
• determining and storing the values of the maximum acceleration that does not violate any of said constraints and the maximum deceleration that does not violate any of said constraints;
• STEP 2:
• evaluating a point on the trajectory using the criterion that such a point has a valid dynamic state if the maximum acceleration is greater than the maximum deceleration, in accordance with said stored values;
• STEP 3:
• if a point being evaluated on the trajectory has a valid dynamic state, then going to STEP 5 wherein the maximum acceleration is applied at said point;
• STEP 4:
• if a point being evaluated on the trajectory does not have a valid dynamic state, then going back down the states found until the last point the maximum acceleration was applied is found, and applying the maximum deceleration instead, and determining a next dynamic state by going to STEP 6;
• STEP 5:
• applying the maximum acceleration, and determining a next dynamic state by going to STEP 6;
• and
• STEP 6:
• if a final end point of the trajectory has not been passed then determining a next dynamic state by going to STEP 2, otherwise END.