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

Abstract

A method controls a machine with redundant actuators according to pattern of disconnected contours, wherein the machine includes redundant actuators by first generating a set of initial trajectories from the pattern. 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. A set of costs for the set of initial trajectories is determined. A sequence of final trajectories is determined based on the set of costs. Then, a set of commands is generated for controlling the machine according to the sequence of final trajectories.

Claims

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.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic of a laser cutting machine with dual actuators that uses embodiments of the invention;

(2) FIG. 2 is a schematic of an exemplar pattern of disconnected contours on which embodiments of the invention operate;

(3) FIG. 3A is a flow chart of a method for controlling a machine according to a pattern of disconnected contours according to some embodiments of the invention;

(4) FIG. 3B is a flow chart of a procedure to optimize trajectories; and

(5) FIG. 4 is a schematic of moving time depending on the position of the fast and slow actuators at the beginning of the trajectory;

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(6) As shown in FIG. 1, an example laser cutting machines 1 allows on-the-fly cutting or other type of machining, that is without stopping to turn the cutter on or off. This enables faster processing, but also poses a much more complicated planning problem, because the straight traverses for such machine can be suboptimal. The laser cutting machine is suitable for controlling a position of a beam, produced by a laser 10 on a work-piece 11. The laser cutting machine includes redundant actuators, i.e., a first actuator and a second actuator, such that a laser beam travels along, a first direction 20. However, the principles of the invention can be employed by any type of redundant actuators.

(7) The laser cutting machine includes a slow actuator, i.e., a platform 12 configured to move along the first direction 20. The platform is moved by a motion system 22 for moving the platform in a plane parallel to the work-piece. In one embodiment, the motion system 22 includes a first prismatic joint facilitating a first motion of the platform along the first direction 20.

(8) The laser cutting machine also includes a fast actuator, i.e., a galvano mirror assembly 13 arranged on the platform 12, such that the motion of the platform along the first direction 20 causes a motion of the galvano mirror assembly along the first direction. The platform actuator is a slow actuator having high inertia. The galvano actuator is a fast actuator having low inertia.

(9) For example, the motion of the platform is along the direction 20. Also, an operation of the galvano mirror assembly directs the laser beam to the work-piece along at least a second direction 30. The galvano mirror assembly is arranged on the platform such that the second direction is fixed with respect to the first direction 20, which allows directing the laser beam concurrently along the first direction and along the second direction. In various embodiments, the position of the laser beam on the work-piece can be approximated by a vector sum 40 of the first motion, and the second motion. The motion of the platform and the operation of the galvano mirror assembly are controlled by a controller 50. The control module 50 can be implemented using a processor connected to memory and input/output interfaces by buses as known in the art. The controller uses a motion planning module 60. The input to the controller is a numerical code, and the output is motion commands for the laser machine.

(10) FIG. 2 shows an example pattern 200 of disconnected contours, such as the contours 210, 212, 214, 216, and 218, which can be used for cutting the material of the work-piece. Because the pattern includes the disconnected contours, the machining alternates with repositioning, e.g., after a cut the machine turns off the cutter, traverse to a new location along a path, i.e., a trajectory from one contour to the next, and then turn the cutter back on to continue the machining. Accordingly, cutting trajectories, i.e., the trajectories of cutting along the contour, such as contour 226, can alternate with traverse paths, i.e., the trajectory for repositioning the cutter to a new contour without cutting, such as the path 225.

(11) End points of each trajectory are an exit point of starting the path from the contour and an entry point for entering the trajectory into the net contour. The endpoints are located on one of the contours of the pattern. Typically, the endpoints of the cutting trajectory are on the same contour, e.g., points 222 and 224 of the trajectory 226. However, the endpoints of the traverse paths are typically on different contours, e.g., points 222 and 228 of the trajectory 225. Each endpoint can be the exit point, the entry point, or both.

(12) FIG. 3A shows a system and method for controlling a machine according to a pattern of disconnected contours. A set of initial trajectories 345 is generated 205 from the pattern 200. Each initial trajectory corresponds to one of the disconnected contours in the pattern, or a path from an exit point of one contour and an entry point of a next contour. The initial trajectories may not be optimally sequenced. Therefore, a set of costs 315 is determined 310 for the set of initial trajectories. The costs can be optimized costs 316 as described in detail below.

(13) The costs are used to determine 320 a sequence of final trajectories 325. The final trajectories can be optimized trajectories 326. The sequence of trajectories can be used to determine 330 a set of commands 335 for controlling 50 the machine 1.

(14) The steps of the method can be performed in a processor 300 connected to memory and input/output interface by buses as known in the art.

(15) A particular trajectory can represents 370 an operation of the machine proceeding from an exit point of one contour with an exit velocity 375 to an entry point of a next contour with an entry velocity 373 according to a shape 363 of the contour to be cut, and dynamics 365 of the machine 1. Typically, the set of initial trajectories includes at least one trajectory representing an operation along the contour with non-zero velocities at corresponding exit and entry points, e.g., the trajectory 226 of FIG. 2, and at least one trajectory representing the operation between different contours with non-zero velocities at the corresponding exit and entry points, e.g., the path 225 of FIG. 2.

(16) Determining Costs

(17) In redundant laser processing machines, the position of a laser spot along an X and Y axis is a function of the redundant actuators, e.g., fast and slow actuators:
x.sub.laser spot=.sub.x(x.sub.fast,x.sub.slow)
y.sub.laser spot=.sub.y(y.sub.fast,y.sub.slow)

(18) In some embodiments, the relationship between the laser spot position and the positions of the fast and slow actuators can be approximated using a linear function.

(19) As a result of this redundancy, cutting trajectories and traverse paths can be realized with a combination of positions of the fast and slow actuators. The motion planning procedure 60, i.e., the method 300, controls the two actuators in a way to minimize the time to move along the trajectories, while ensuring that all actuators remain within their operational and physical limits.

(20) As shown in FIG. 4, the moving time depends on the position of the fast and slow actuators at the beginning of the trajectory. As shown in FIG. 4, slow actuator trajectories 420, 430 are both feasible trajectories, assuming that the difference between the cutting contour 410 and the slow actuator trajectory can be covered by the fast actuator. Both trajectories 420 and 430 represent the minimum-time solutions given the initial and final conditions.

(21) In one embodiment, to determine the costs, it is assumed that the fast actuator is positioned at a neutral position at the beginning of each trajectory and the laser spot position is realized by the slow actuator (trajectory 420 in FIG. 4). This assumption removes the extra degrees of freedom in the system and allows us to determine the set of costs for different trajectories.

(22) To ensure the validity of this assumption, a set of constraints is used in the trajectory generation unit, which requires the fast actuator to return to its neutral position at the end of each trajectory. This assumption may return, suboptimal costs, as the trajectory generator is limited to a set of possible trajectories where the fast actuator is forced to be located at its neutral position at the beginning and at the end of each trajectory. Therefore, the costs can be optimized when the entire trajectory is known.

(23) In another embodiment, the optimized costs 316 can be determined according to an optimization operator, e.g., minimum, maximum, average, mean, etc. and combination thereof, applied to the costs 315.

(24) For example, the system can determine relative positions of the actuators by considering a large set of possible past paths contained within a neighborhood of likely transition locations.

(25) The embodiments can generate a set of possible costs related to making one particular transition path between two contours, and many possible computations can be applied to determine the cost actually used within the TSP graph. For example, an average of the potential times required to make the transition, or the minimal potential time required, among others. This embodiment of computing costs can produce a better trajectory, but also requires more time to determine than assuming the neutral position.

(26) In one embodiment, the determination of the costs can be made more efficient by assuming that the traverse paths without cutting are generated by the slow actuator only. This assumption is based on the fact that the traverse path are generally smoother than the cutting trajectories, and the time associated with these paths are not significantly affected by only using the slow actuator. This can be considered in combination with any of the two above described embodiments, and it forces the machine to operate as a non-redundant laser cutting machine while moving along a traverse path.

(27) The set of optimized costs 316 can be used to determine 320 the sequence of optimized trajectories 326, for example, by using a Christofides procedure, as is known in the art. The goal of the Christofides procedure is to find a solution to the instances of the traveling salesman problem where edge weights satisfy a triangle inequality.

(28) Although the sequence of trajectories 325 defines an entire trajectory that is capable of cutting out the pattern, the sequence of trajectories is not likely to be an optimal entire trajectory that minimizes the time required to cut the pattern. As such, the sequence of trajectories 325 is optimized to improve the entire trajectory.

(29) Optimize Sequence of Trajectories.

(30) As shown in FIG. 3B, an optimization procedure 380 can change a current trajectory and determine when the change improves the current trajectory. If an improvement is made, then the change is applied, and the improved trajectory becomes an optimized trajectory 326.

(31) Various alternatives to this optimization procedure allow for various trajectories or trajectory meta-data 381 to be stored during the optimization to allow back-tracking. Local search techniques 382 can also be applied.

(32) The optimization procedure, unlike when optimizing the set of costs, is able to determine precisely an optimal relative position of the dual actuators 383, as the entire trajectory is known for both the current best trajectory as well as the trajectory with the considered change. As a result, it is no longer required to force the fast actuator to be located at its neutral position at the beginning of each trajectory, or to assume that the traverse paths are performed by the slow actuator only. This allows us to determine precisely an optimal trajectory for the redundantly actuated laser cutting, machine including the relative positions of the actuators.

(33) When performing the optimization, it is not usually necessary to re-evaluate the entire trajectory to determine the benefit of the current trajectory, as local changes often only affect the relative actuator positions for a limited neighborhood of motions. As such, information about the laser cutting machine state, e.g., the states of the slow and fast actuators 384, can be stored in a memory and used to determine the changes for only a small neighborhood of trajectories 386 around a proposed change to the current trajectory. If the change improves the current trajectory, then the current trajectory, including the updated state of the laser cutting machine in the memory is replaced.

(34) In the embodiments described above, we formulate the system for optimizing the time required for a redundantly actuated system to execute part or all of a trajectory. Other embodiments that minimize or maximize other functions are also possible and covered under the embodiments. For example, one can minimize 385 a total traveling distance of the slow actuators, or minimize the jerk of the fast or slow actuators, among many other formulations.

(35) Although the invention has been described by way of examples of preferred embodiments, it is to be understood that various other adaptations and modifications can be made within the spirit and scope of the invention. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.