Method for controlling redundantly actuated machines for cutting a pattern of disconnected contours

1. A method for controlling a machine according to pattern of disconnected contours, wherein the machine includes redundant actuators, comprising:

generating a set of initial trajectories from the pattern, wherein each initial trajectory corresponds to one of the disconnected contours, or a path from an exit point of one contour and an entry point of a next contour;

determining a set of costs for the set of initial trajectories, wherein the determining comprises generating a set of possible costs to make one path between two contours by considering multiple initial conditions for states of fast and slow actuators;

determining a sequence of final trajectories based on the set of costs;

determining a set of commands for controlling the machine according to the sequence of final trajectories, wherein the steps are performed in a processor.

2. The method of claim 1 , wherein a particular trajectory represents an operation of the machine proceeding from the exit point with an exit velocity to an entry point with an entry velocity according to a shape of the contour to be cut, and dynamics of the machine.

3. The method of claim 1 , wherein the set of initial trajectories includes at least one trajectory representing an operation of the machine along the contour with non-zero velocities at corresponding exit and entry points, and at least one trajectory representing the operation between different contours with non-zero velocities at the corresponding exit and/or entry points.

4. The method of claim 1 , wherein the costs minimize a time to machine the pattern.

5. The method of claim 1 , wherein the costs minimize an energy to machine the pattern.

6. The method of claim 1 , wherein the costs minimize a jerk when machining the pattern.

7. The method of claim 1 , wherein the costs are a weighted combination of an energy, a time, and a jerk when machining the pattern.

8. The method of claim 1 , wherein the costs are determined according to an operator, wherein the operator includes a minimum, a maximum, an average, a mean or combinations thereof.

9. The method of claim 1 , wherein the machine includes a slow and a fast actuator, and wherein the paths are generated only by the slow positioning subsystem.

10. The method of claim 1 , further comprising:

optimizing the set of final trajectories to obtain optimized trajectories.

11. The method of claim 10 , wherein optimizing uses a Christofides procedure.

12. The method of claim 10 , wherein the optimizing minimizes a total traveling distance of slow actuators.

13. The method of claim 1 , wherein the set of costs are minimized by solving a traveling salesman problem.

14. The method of claim 1 , wherein the set of costs are determined by ensuring a fast actuator starts at a neutral position.

15. The method of claim 1 , wherein the set of costs are determined by ensuring a fast actuator starts and ends at a neutral position.

16. The method of claim 10 , further comprising:

storing states of the sequence of final trajectories in a memory; and

optimizing a local neighborhood of the sequence of final trajectories.

17. A system for controlling a machine according to pattern of disconnected contours, comprising:

a fast actuator and a slow actuator; and

a processor for

generating a set of initial trajectories from the pattern, wherein each initial trajectory corresponds to one of the disconnected contours, or a path from an exit point of one contour and an entry point of a next contour;

determining a set of costs for the set of initial trajectories, wherein the set of costs are determined by ensuring a fast actuator starts at a neutral position;

determining a sequence of final trajectories based on the set of costs; and

determining a set of commands for controlling the machine according to the sequence of final trajectories.

18. A method for controlling a machine according to pattern of disconnected contours, wherein the machine includes redundant actuators, comprising:

generating a set of initial trajectories from the pattern, wherein each initial trajectory corresponds to one of the disconnected contours, or a path from an exit point of one contour and an entry point of a next contour;

determining a set of costs for the set of initial trajectories;

determining a sequence of final trajectories based on the set of costs;

determining a set of commands for controlling the machine according to the sequence of final trajectories, wherein the machine includes a slow and a fast actuator, and wherein the paths are generated only by the slow actuator, wherein the steps are performed in a processor.

19. A method for controlling a machine according to pattern of disconnected contours, wherein the machine includes redundant actuators, comprising:

generating a set of initial trajectories from the pattern, wherein each initial trajectory corresponds to one of the disconnected contours, or a path from an exit point of one contour and an entry point of a next contour;

determining a set of costs for the set of initial trajectories;

determining a sequence of final trajectories based on the set of costs;

optimizing the set of final trajectories to obtain optimized trajectories, wherein the optimizing minimizes a total traveling distance of slow actuators; and

determining a set of commands for controlling the machine according to the sequence of optimized trajectories, wherein the steps are performed in a processor.

20. A method for controlling a machine according to pattern of disconnected contours, wherein the machine includes redundant actuators including a slow actuator and a fast actuator, comprising:

generating a set of initial trajectories from the pattern, wherein each initial trajectory corresponds to one of the disconnected contours, or a path from an exit point of one contour and an entry point of a next contour;

determining a set of costs for the set of initial trajectories ensuring the fast actuator starts and ends at a neutral position;

determining a sequence of final trajectories based on the set of costs; and

determining a set of commands for controlling the machine according to the sequence of final trajectories, wherein the steps are performed in a processor.