Systems and methods for controlling a Lorentz-force-based apparatus

1. A system comprising:

a conductive coil, wherein at least a portion of the conductive coil is oriented along a first direction and orthogonal to a second direction;

a magnetic field generation structure that generates a magnetic field through the portion of the conductive coil along a third direction orthogonal to the first direction and the second direction;

a force constant compensator that:

receives an electrical current command to alter a relative location of the conductive coil and the magnetic field; and

adjusts the electrical current command based on at least one physical characteristic of the system that affects a relationship between electrical current in the conductive coil and resulting force between the conductive coil and the magnetic field along the second direction; and

a coil driver that generates, in response to the adjusted electrical current command, a first electrical current in the conductive coil to generate a first force between the conductive coil and the magnetic field along the second direction.

2. The system of claim 1 , wherein the at least one physical characteristic of the system comprises at least one physical characteristic of the conductive coil.

3. The system of claim 2 , wherein the at least one physical characteristic of the conductive coil comprises a dynamic physical characteristic of the conductive coil.

4. The system of claim 3 , wherein:

the dynamic physical characteristic of the conductive coil comprises an electrical resistance of the conductive coil relative to a temperature of the conductive coil;

the system further comprises a temperature sensor that provides a temperature reading; and

the force constant compensator adjusts the electrical current command based on the temperature reading.

5. The system of claim 1 , wherein the at least one physical characteristic of the conductive coil comprises a static physical characteristic of the conductive coil.

6. The system of claim 5 , wherein the system further comprises a memory storing a data structure specifying the relationship between electrical current in the conductive coil and resulting force between the conductive coil and the magnetic field along the second direction.

7. The system of claim 1 , wherein the portion of the conductive coil defines a portion of a spherical surface.

8. The system of claim 1 , wherein the magnetic field generation structure comprises a pair of magnets positioned on opposing sides of the portion of the conductive coil along the third direction.

9. The system of claim 1 , wherein:

the conductive coil comprises a first conductive coil;

the system further comprises:

a second conductive coil, wherein at least a portion of the second conductive coil is oriented along the second direction within the magnetic field; and

a body that holds the first conductive coil and the second conductive coil;

the electrical current command comprises a first electrical current command;

the force constant compensator:

receives a second electrical current command to alter a relative location of the second conductive coil and the magnetic field; and

adjusts the second electrical current command based on at least one physical characteristic of the system that affects a relationship between electrical current in the second conductive coil and resulting force between the second conductive coil and the magnetic field along the first direction; and

the coil driver generates, in response to the adjusted second electrical current command, electrical current in the second conductive coil to generate a second force between the second conductive coil and the magnetic field along the first direction.

10. The system of claim 9 , further comprising:

a detection subsystem that determines a location of the first conductive coil relative to the magnetic field and a location of the second conductive coil relative to the magnetic field; and

a force-to-current converter that:

receives a first force command to alter a relative location of the first conductive coil and the magnetic field;

receives a second force command to alter a relative location of the second conductive coil and the magnetic field;

issues, in response to the first force command, the first electrical current command based on the determined location of the first conductive coil relative to the magnetic field; and

issues, in response to the second force command, the second electrical current command based on the determined location of the second conductive coil relative to the magnetic field.

11. The system of claim 10 , wherein the detection subsystem determines the location of the first conductive coil relative to the magnetic field and the location of the second conductive coil relative to the magnetic field by determining a location of a first mechanical structure connected to the magnetic field generation structure relative to a location of a second mechanical structure connected to the body.

12. The system of claim 11 , wherein:

the system further comprises a plurality of distance sensors;

each distance sensor measures a distance between the distance sensor and at least one of the first mechanical structure and the second mechanical structure; and

the detection subsystem determines the location of the first conductive coil relative to the magnetic field and the location of the second conductive coil relative to the magnetic field based on the measured distances.

13. The system of claim 12 , wherein the detection subsystem generates:

a first translational position vector and a first rotational position vector indicating the location of the first conductive coil relative to the magnetic field based on the measured distances; and

a second translational position vector and a second rotational position vector indicating the location of the second conductive coil relative to the magnetic field based on the measured distances.

14. The system of claim 13 , wherein:

the first force command comprises a first translational force vector and a first rotational torque vector;

the second force command comprises a second translational force vector and a second rotational torque vector;

the first electrical current command is based on the first translational position vector, the first rotational position vector, the first translational force vector, and the first rotational torque vector; and

the second electrical current command is based on the second translational position vector, the second rotational position vector, the second translational force vector, and the second rotational torque vector.

15. The system of claim 14 , further comprising:

a platform mechanically coupled to one of the body and the magnetic field generation structure; and

a tracking controller that generates the first force command and the second force command based on an indication of a present orientation of the platform relative to a desired orientation of the platform.

16. The system of claim 15 , wherein:

the system further comprises a directional sensor that senses the present orientation of the platform; and

the detection subsystem generates, based on the sensed present orientation of the platform, the indication of the present orientation of the platform relative to the desired orientation of the platform.

17. The system of claim 15 , wherein the force-to-current converter also generates the first electrical current command and the second electrical current command based on the indication of the present orientation of the platform relative to the desired orientation of the platform.

18. A method comprising:

generating a magnetic field through at least a portion of a conductive coil, wherein:

the conductive coil is oriented along a first direction and orthogonal to a second direction; and

the magnetic field is directed along a third direction orthogonal to the first direction and the second direction;

receiving an electrical current command to alter a relative location of the conductive coil and the magnetic field;

adjusting the electrical current command based on at least one physical characteristic of a system including the conductive coil that affects a relationship between electrical current in the conductive coil and resulting force between the conductive coil and the magnetic field along the second direction; and

generating, in response to the adjusted electrical current command, a first electrical current in the conductive coil to generate a first force between the conductive coil and the magnetic field along the second direction.

19. The method of claim 18 , wherein the at least one physical characteristic of the system comprises at least one physical characteristic of the conductive coil.

20. A system comprising:

a plurality of subassemblies, wherein each subassembly comprises a conductive coil, wherein at least a portion of the conductive coil is oriented along a first direction and orthogonal to a second direction; and

for each subassembly, a magnetic field generation structure that generates a magnetic field through the portion of the conductive coil, wherein the magnetic field is directed along a third direction orthogonal to the first direction and the second direction;

a stator assembly comprising a base and:

the plurality of subassemblies, wherein each of the plurality of subassemblies is connected to the base; or

the magnetic field generation structures, wherein each of the magnetic field generation structures is connected to the base;

a rotor assembly comprising a platform and:

the plurality of subassemblies, wherein each of the plurality of subassemblies is connected to the platform; or

the magnetic field generation structures, wherein each of the magnetic field generation structures is connected to the platform;

a force constant compensator that, for each subassembly:

receives an electrical current command to alter a location of the rotor assembly relative to the stator assembly; and

adjusts the electrical current command based on at least one physical characteristic of the system that affects a relationship between electrical current in the conductive coil and resulting force between the conductive coil and the magnetic field along the second direction; and

a coil driver that, for each subassembly:

supplies, in response to the adjusted electrical current command, first electrical current to the conductive coil to move a corresponding magnetic field generation structure along the second direction relative to the subassembly; or

supplies, in response to the adjusted electrical current command, first electrical current to the conductive coil to move the subassembly along the second direction relative to a corresponding magnetic field generation structure.