System and method for collision avoidance using virtual boundaries

1. A computer-assisted device comprising:

a repositionable arm configured to support an instrument; and

a control unit comprising one or more processors, the control unit being coupled to the repositionable arm, wherein the control unit is configured to:

determine a position and an orientation, the position and the orientation being of the repositionable arm or of the instrument;

determine, based on the position and the orientation, a plurality of first virtual boundaries around the repositionable arm or the instrument;

determine a second virtual boundary around an object;

determine a tip force on a distal end of the instrument based on a first overlap between the second virtual boundary and a virtual boundary of the plurality of first virtual boundaries; and

apply the tip force as a first feedback force on the instrument or the repositionable arm.

2. The computer-assisted device of claim 1 , wherein to determine the tip force based on the first overlap, the control unit is configured to:

map a first overlap force to a virtual torque on a joint of the repositionable arm; and

determine the tip force based on the virtual torque.

3. The computer-assisted device of claim 1 , wherein to determine the position and the orientation the control unit is configured to:

determine a joint position for each of one or more joints of the repositionable arm; and

determine the position and the orientation from each joint position.

4. The computer-assisted device of claim 1 , wherein the control unit is further configured to:

apply haptic feedback to an input control based on the tip force, the control unit being configured to receive movement commands for the instrument from the input control.

5. The computer-assisted device of claim 4 , wherein the control unit is further configured to determine the haptic feedback based on a difference between a first commanded position of the instrument due to application of the first feedback force on the instrument and a second commanded position of the instrument determined from the input control.

6. The computer-assisted device of claim 1 , wherein to determine the tip force on the distal end of the instrument the control unit is configured to:

determine an overlap force on the repositionable arm due to the first overlap between the second virtual boundary and a virtual boundary of the plurality of first virtual boundaries; and

determine the tip force on the distal end of the instrument based on the overlap force.

7. The computer-assisted device of claim 1 , wherein the plurality of first virtual boundaries comprises a plurality of convex hulls that approximates a physical geometry of the repositionable arm.

8. The computer-assisted device of claim 1 , wherein the plurality of first virtual boundaries are determined only for portions of the repositionable arm or the instrument proximal to a body opening or a remote center of motion, wherein the instrument is inserted into the body opening, and wherein the remote center of motion is of the repositionable arm or the instrument.

9. The computer-assisted device of claim 6 , wherein a magnitude of the overlap force is determined based on a maximum overlap of the first overlap, a surface area of the first overlap, or a volume of the first overlap.

10. The computer-assisted device of claim 1 , wherein the first feedback force is superimposed on forces applied to the instrument as a result of movement commands received from an input control.

11. The computer-assisted device of claim 1 , wherein the first feedback force opposes motion of the repositionable arm that is likely to cause a collision between the repositionable arm and the object.

12. A method of collision avoidance, the method comprising:

determining, by a control unit, a position and an orientation, the position and the orientation being of a repositionable arm or of an instrument, the repositionable arm being configured to support the instrument;

determining, by the control unit based on the position and the orientation, a plurality of first virtual boundaries around the repositionable arm or the instrument;

determining, by the control unit, a second virtual boundary around an object;

determining, by the control unit, a tip force on a distal end of the instrument based on a first overlap between the second virtual boundary and a virtual boundary of the plurality of first virtual boundaries; and

applying, by the control unit, the tip force as a first feedback force on the instrument or the repositionable arm.

13. The method of claim 12 , wherein determining the tip force based on the first overlap comprises:

mapping a first overlap force to a virtual torque on a joint of the repositionable arm; and

determining the tip force based on the virtual torque.

14. The method of claim 12 , wherein determining the position and the orientation comprises:

determining a joint position for each of one or more joints of the repositionable arm; and

determining the position and the orientation from each joint position.

15. The method of claim 12 , further comprising:

applying, by the control unit, haptic feedback to an input control based on the tip force, the control unit being configured to receive movement commands for the instrument from the input control.

16. The method of claim 12 , further comprising:

determining, by the control unit, an overlap force on the repositionable arm due to a second overlap between a second one the plurality of first virtual boundaries and a virtual boundary of another repositionable arm;

determining, by the control unit, a second tip force on the distal end of the instrument based on the overlap force; and

applying, by the control unit, the second tip force as a second feedback force on the instrument or the repositionable arm.

17. A non-transitory machine-readable medium comprising a plurality of machine-readable instructions which when executed by one or more processors are adapted to cause the one or more processors to perform a method comprising:

determining a position and an orientation, the position and the orientation being of a repositionable arm or of an instrument, the repositionable arm being configured to support the instrument;

determining, based on the position and the orientation, a plurality of first virtual boundaries around the repositionable arm or the instrument;

determining a second virtual boundary around an object;

determining a tip force on a distal end of the instrument based on a first overlap between the second virtual boundary and a virtual boundary of the plurality of first virtual boundaries; and

applying the tip force as a first feedback force on the instrument or the repositionable arm.

18. The non-transitory machine-readable medium of claim 17 , wherein determining the tip force based on the first overlap comprises:

mapping a first overlap force to a virtual torque on a joint of the repositionable arm; and

determining the tip force based on the virtual torque.

19. The non-transitory machine-readable medium of claim 17 , wherein determining the position and the orientation comprises:

determining a joint position for each of one or more joints of the repositionable arm; and

determining the position and the orientation from each joint position.

20. The non-transitory machine-readable medium of claim 17 , wherein:

the method further comprises applying haptic feedback to an input control based on the tip force; and

movement commands for the instrument are received from the input control.