Movement apparatus with decoupled position controllers

1. A method for operating a movement apparatus having a first assembly and a second assembly, the first assembly including a first base and several first permanent-magnet arrangements, the first permanent-magnet arrangements being connected to the first base via respectively assigned actuators such that they are each configured to move as a whole relative to the first base in at least one degree of freedom by the respectively assigned actuator, the second assembly including a second base and a second permanent-magnet arrangement, the second permanent-magnet arrangement being arranged firmly relative to the second base, the method comprising:

providing at least two position controllers, each with a single scalar controlled variable and with a single scalar correcting variable, the single scalar controlled variable being, in each instance, one of six possible degrees of freedom with regard to a relative position between the first assembly and the second assembly, the single scalar correcting variable representing one of (i) a force and (ii) a torque that has been assigned to the one of six possible degrees of freedom,

computing desired positions of the actuators at least one of (i) from the single scalar correcting variables and (ii) using tables of values; and

setting the actuators to the desired positions.

2. The method according to claim 1 , wherein the at least two position controllers are continuous linear controllers.

3. The method according to claim 1 , wherein the at least two position controllers comprise six position controllers.

4. The method according to claim 1 , wherein:

each actuator is configured to be adjusted by a respective electric current;

wherein a respective position controller of the at least two position controllers is assigned to each actuator,

the single scalar controlled variable of the respective position controller is a position of the respectively assigned actuator,

the single scalar correcting variable of the respective position controller is, at least indirectly, the respective electric current.

5. The method according to claim 1 further comprising:

providing a position-determination apparatus; and

determining, with the position-determination apparatus, a vector of actual relative positions between the first assembly and the second assembly.

6. The method according to claim 5 , the determining the vector of actual relative positions further comprising:

measuring, with the position-determination apparatus, the vector of actual relative positions between the first assembly and the second assembly.

7. The method according to claim 1 , the computing the desired positions of the actuators further comprising:

computing the desired positions of the actuators from the single scalar correcting variables by solving a non-linear system of equations.

8. The method according to claim 7 further comprising:

computing, within bounds of the solving of the non-linear system of equations, a scalar error parameter one of (i) from actual relative positions between the first assembly and the second assembly and predetermined desired relative positions between the first assembly and the second assembly and (ii) from a vector of the single scalar correcting variables and a vector of desired correcting variables,

optimizing the scalar error parameter within the bounds of the solving of the non-linear system of equations.

9. The method according to claim 8 , wherein:

the optimizing the scalar error parameter is executed iteratively;

the at least two position controllers operate in a time-discrete manner with a fixed time pulse; and

all iterative steps of the optimizing the scalar error parameter are executed within one time pulse of the at least two position controllers.

10. The method according to claim 9 , wherein a vector of the desired positions of the actuators from an immediately preceding time pulse of the at least two position controllers is used as starting value of the optimizing the scalar error parameter.

11. The method according to claim 1 , wherein:

one of (i) the first assembly comprises a plurality of first assemblies and (ii) the second assembly comprises a plurality of second assemblies; and

the method is executed separately one of (i) for each first assembly in the plurality of first assemblies and (ii) for each second assembly in the plurality of second assemblies.

12. A movement apparatus comprising:

a first assembly including a first base and several first permanent-magnet arrangements, the first permanent-magnet arrangements being connected to the first base via respectively assigned actuators such that they are each configured to move as a whole relative to the first base in at least one degree of freedom by the respectively assigned actuator; and

a second assembly including a second base and a second permanent-magnet arrangement, the second permanent-magnet arrangement being arranged firmly relative to the second base,

wherein at least two position controllers are provided, each with a single scalar controlled variable and with a single scalar correcting variable, the single scalar controlled variable being, in each instance, one of six possible degrees of freedom with regard to a relative position between the first assembly and the second assembly, the single scalar correcting variable representing one of (i) a force and (ii) a torque that has been assigned to the one of six possible degrees of freedom,

wherein desired positions of the actuators are computed from the single scalar correcting variables,

wherein the actuators are set to the desired positions.

13. A movement apparatus according to claim 12 further comprising:

the at least two position controllers.