Control of redundant laser processing machines

A method for controlling an operation of a laser processing machine with redundant actuators including a first actuator and a second actuator to place a laser beam along a reference trajectory by joint motions of the first actuator and the second actuator, wherein the method uses a processor coupled to a memory storing a model of the reference trajectory, constraints of the laser processing machine including physical constraints of a structure of the laser processing machine, constraints on the reference trajectory including constraints on a rate of change of the reference trajectory, constraints on a range of motion of the first actuator, and constraints on a range of motion of the second actuator, wherein a composition of the range of motion of the first actuator and the range of motion of the second actuator represent a range of possible positions of the laser beam controlled by the first or the second actuators, wherein the range of motion of the first actuator is greater than the range of motion of the second actuator, wherein the processor is coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor carry out steps of the method, comprising:

• determining, using the processor, a feasible region for states of the first actuator and states of a reference trajectory of the first actuator, wherein the feasible region is defined by the constraints of the laser processing machine, the constraints on the reference trajectory, and the constraints on the range of motion of the second actuator, wherein the states of the first actuator include positions and velocity of the first actuator, wherein the states of the reference trajectory of the first actuator include positions of the reference trajectory of the first actuator;
• selecting, using the processor, a subset of the feasible region forming a convex region of the states of the first actuator and the states of the reference trajectory of the first actuator, such that for any state of the first actuator and any state of the reference trajectory of the first actuator within the subset, there is an admissible control maintaining the state of the first actuator within the subset of the feasible region for admissible future states of the reference trajectory, wherein the admissible future states of the reference trajectory are determined according to the model of the reference trajectory and the constraints on the reference trajectory, wherein the model of the reference trajectory includes a position and a rate of change of the reference trajectory represented by states of the model of the reference trajectory, inputs to the model of the reference trajectory, or combination thereof;
• selecting, using the processor, a first admissible control action maintaining the state of the first actuator within the subset of the feasible region;
• determining, using the processor, a second admissible control action based on a difference between the state of the reference trajectory and the state of the first actuator controlled by the first admissible control action;
• and
• controlling, using the processor, the first actuator using the first admissible control action and controlling the second actuator using the second admissible control action to jointly place the laser beam on the reference trajectory.