Time optimal trajectory for cluster tool robots

Apparatus for operating a workpiece handling tool, having a friction-type workpiece holder disposed at the end of a motor-driven, articulated arm of said tool, with maximum workpiece throughput by minimizing the time required for said workpiece holder to travel a set distance from a start end point to a final end point with a workpiece supported thereon, comprising:

• means for moving from one dynamic state to a next dynamic state of said workpiece holder;
• and
• means for determining points of trajectory of arm travel by evaluating successive dynamic states of said workpiece holder, said determining means comprising:
• means for selecting as said points of said trajectory dynamic states where the maximum velocity of said workpiece holder is maintained while limiting the horizontal acceleration and deceleration of a workpiece supported thereon so as not exceed the frictional force between said workpiece and said workpiece holder;
• and
• means for choosing the final dynamic state with said workpiece holder at one of said start end point and said final end point and at a lower velocity than said maximum velocity.

A method of operating a substrate handling tool, having a friction-type substrate holder disposed at the end of a motor-driven, articulated arm of said tool, with maximum substrate throughput, which method minimizes the time required for said substrate holder to travel a set distance to a final end point from a start end point with a substrate supported thereon, comprising the steps of:

• determining points of trajectory of arm travel by determining the dynamic states thereof by the steps comprising:
• STEP 1:
• determining and storing the values of the maximum acceleration and the maximum deceleration that does not exceed the horizontal frictional force between said substrate and said holder;
• 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 said start end point or said final end point of the trajectory has not been passed then determining a next dynamic state by going to STEP 2, otherwise END.