System and method for controlling redundant actuators with different dynamics

A method for controlling a joint motion of redundant actuators including a first actuator and a second actuator to position a controlled parameter according to a reference trajectory including a sequence of points defining positions of the controlled parameter of the system as a function of time, wherein the redundant actuators are part of a laser processing machine such that the controlled parameter is a position of a laser spot on a workpiece processed by the laser processing machine, wherein the second actuator is configured to direct the laser spot at different locations on the workpiece, and wherein the first actuator is configured to move the second actuator relative to the workpiece, wherein steps of the method are performed by a processor connected to a memory storing the reference trajectory and coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor carry out at least some steps of the method comprising:

• determining, for an axis of control, an envelope bounding a first trajectory of the first actuator with respect to the reference trajectory in at least the axis of control and time domains, wherein the envelope is centered on the reference trajectory with a width not greater than a range of the second actuator;
• determining the shortest trajectory traversing the envelope along the time domain to produce the first trajectory of the first actuator, wherein determining the first trajectory comprises:
• determining a forward-looking trajectory and a backward-looking trajectory moving the first actuator only when required by the shape of the envelope, wherein the forward-looking trajectory moves the first actuator between two neighboring stationary positions as soon as possible, and wherein the backward-looking trajectory moves the first actuator between the two neighboring stationary positions as late as possible;
• and
• selecting the first trajectory within a region flanked by the forward-looking and the backward-looking trajectories as a monotonic function of time;
• determining a second trajectory of the second actuator based on a difference between the reference trajectory and the positions the second actuator with respect to the reference trajectory governed by the first trajectory enabling the joint motions of the first actuator and the second actuator to position the controlled parameter of the system along the reference trajectory;
• and
• causing the first actuator to move according to the first trajectory and causing the second actuator to move according to the second trajectory.

A non-transitory computer readable storage medium embodied thereon a program executable by a processor for performing a method for controlling a joint motion of redundant actuators including a first actuator and a second actuator to position a controlled parameter according to a reference trajectory including a sequence of points defining positions of the controlled parameter of the system as a function of time, wherein the redundant actuators are part of a laser processing machine such that the controlled parameter is a position of a laser spot on a workpiece processed by the laser processing machine, wherein the second actuator include a galvano mirror assembly to direct the laser spot at different locations on the workpiece, and wherein the first actuator is a platform configured to move in a plane to position the galvano mirror assembly relative to the workpiece, the method comprising:

• determining, for an axis of control, an envelope bounding a first trajectory of the first actuator with respect to the reference trajectory in at least the axis of control and time domains, wherein the envelope is centered on the reference trajectory with a width not greater than a range of the second actuator;
• determining the shortest trajectory traversing the envelope along the time domain to produce the first trajectory of the first actuator, wherein determining the first trajectory comprises:
• determining a forward-looking trajectory and a backward-looking trajectory moving the first actuator only when required by the shape of the envelope, wherein the forward-looking trajectory moves the first actuator between two neighboring stationary positions as soon as possible, and wherein the backward-looking trajectory moves the first actuator between the two neighboring stationary positions as late as possible;
• and
• selecting the first trajectory within a region flanked by the forward-looking and the backward-looking trajectories as a monotonic function of time;
• determining a second trajectory of the second actuator based on a difference between the reference trajectory and the positions the second actuator with respect to the reference trajectory governed by the first trajectory enabling the joint motions of the first actuator and the second actuator to position the controlled parameter of the system along the reference trajectory;
• and
• causing the first actuator to move according to the first trajectory and causing the second actuator to move according to the second trajectory.