Null space control for end effector joints of a robotic instrument
The disclosed embodiments relate to systems and methods for a surgical tool or a surgical robotic system. One example method includes providing a redundant degree of freedom (DoF) for an end effector joint of one DoF by driving the joint with two actuators, calculating a position displacement of the joint to effect a desired end effector movement in response to an input command, calculating a first movement of the two actuators based on the position displacement of the joint and a second movement of the two actuators based on a second control objective in a null space corresponding to the redundant DoF, and driving the joint according to the first movement and the second movement to effect the desired end effector movement while accomplishing the second control objective in the null space.
1. A robotic method comprising:
providing a redundant degree of freedom (DoF) for an end effector joint of one DoF by driving the joint with two actuators;
calculating a position displacement of the joint to effect a desired end effector movement in response to an input command;
calculating a first movement of the two actuators based on the position displacement of the joint and a second movement of the two actuators based on a second control objective in a null space corresponding to the redundant DoF; and
driving the joint according to the first movement and the second movement to effect the desired end effector movement while accomplishing the second control objective in the null space,
wherein the joint is an articulation wrist coupled to two actuators through cables,
wherein the second control objective is maintaining a minimum tension on the cables, and
wherein the minimum tension is maintained by a control system having an error signal based on a first torque of one of the two actuators and a second torque of the other of the two actuators.
2. The robotic method of claim 1 , further comprising:
calculating the error signal (e) according to:
e =max(τ min +τ 1 ,τ min −τ 2 ),
wherein τ min is the minimum tension, τ 1 is the first torque, and τ 2 is the second torque.
3. The robotic method of claim 1 , wherein the null space corresponding to the redundant DoF for the articulation wrist is described as a vector [−1, 1] or [−1, 1] T .
4. The robotic method of claim 3 , wherein the null space corresponding to the redundant DoF for the articulation wrist provides a relationship between the first movement of the two actuators and the second movement of the two actuators.
5. The robotic method of claim 3 , wherein a relationship between the first movement of the two actuators [θ m1 1 ,θ m2 1 ] and the second movement of the two actuators [θ m1 2 , θ m2 2 ] includes [θ m1 1 , θ m2 1 ] T =[θ m1 2 , θ m2 2 ] T +[−1, 1] T , where k is a constant number.
6. The robotic method of claim 1 , wherein a physical displacement of the joint (θ j ) is provided by:
θ
j
=
a
+
1
2
(
θ
m
1
+
θ
m
2
)
b
,
based on a first position (θ m1 ) for a first actuator and a second actuator position (θ m2 ) for a second actuator, and at least one property constant includes first constant a and second constant b.
7. A robotic method comprising:
providing a redundant degree of freedom (DoF) for an end effector joint of one DoF by driving the joint with two actuators;
calculating a position displacement of the joint to effect a desired end effector movement in response to an input command;
calculating a first movement of the two actuators based on the position displacement of the joint and a second movement of the two actuators based on a second control objective in a null space corresponding to the redundant DoF;
driving the joint according to the first movement and the second movement to effect the desired end effector movement while accomplishing the second control objective in the null space,
wherein the joint is a closure jaw joint of the end effector, wherein the second control objective is providing a certain torque at the closure jaw joint, wherein the certain torque is maintained by a control system having an error signal based on a first torque of one of the two actuators and a second torque of the other of the two actuators.
8. The robotic method of claim 7 , further comprising:
calculating the error signal (e) according to:
e=−τ 1 +τ 2 ,
wherein τ 1 is the first torque, and τ 2 is the second torque.
9. The robotic method of claim 7 , wherein a physical displacement of the joint (θ j ) is provided by:
θ
j
=
∑
i
=
0
n
a
i
[
1
2
*
(
θ
m
1
+
θ
m
2
)
]
i
,
based on a first position (θ m1 ) for a first actuator and a second actuator position (θ m2 ) for a second actuator, and a i is a constant coefficient from a tool calibration process.
10. The robotic method of claim 7 , wherein the null space corresponding to the redundant DoF for the closure jaw joint is described as a vector [1, −1] or [1, −1] T .
11. The robotic method of claim 10 , wherein the null space corresponding to the redundant DoF for the closure jaw joint provides a relationship between the first movement of the two actuators and the second movement of the two actuators.
12. The robotic method of claim 11 , wherein the relationship between the first movement of the two actuators [θ m1 1 ,θ m2 1 ] and the second movement of the two actuators [θ m1 2 , θ m2 2 ] includes [θ m1 1 , θ m2 1 ] T =[θ m1 2 ,θ m2 2 ] T +k[1, −1] T , where k is a constant number.
13. The robotic method of claim 1 , further comprising:
determining a projection of a control signal for the position displacement of the joint to a vector for the null space, wherein the projection represents the second control objective.
14. An apparatus to provide a control objective using a null space of a redundant degree of freedom of a surgical tool, the apparatus comprising:
a tool driver including a plurality of actuators providing a redundant degree of freedom (DoF) for an end effector joint of one DoF; and
one or more processors configured to:
provide a redundant degree of freedom (DoF) for an end effector joint of one DoF by driving the joint with two actuators;
calculate a position displacement of the joint to effect a desired end effector movement in response to an input command;
calculate a first movement of the two actuators based on the position displacement of the joint and a second movement of the two actuators based on a second control objective in a null space corresponding to the redundant DoF; and
generate a joint command for the joint according to the first movement and the second movement to effect the desired end effector movement while accomplishing the second control objective in the null space,
wherein the joint is an articulation wrist coupled to two actuators through cables,
wherein the second control objective is maintaining a minimum tension on the cables, and
wherein the minimum tension is maintained by a control system having an error signal based on a first torque of one of the two actuators and a second torque of the other of the two actuators.
15. The apparatus of claim 14 , wherein the error signal (e) is calculated according to:
e =max(τ min +τ 1 ,τ min −τ 2 ),
wherein τ min is the minimum tension, τ 1 is the first torque, and τ 2 is the second torque.
16. The apparatus of claim 14 , wherein the null space corresponding to the redundant DoF for the articulation wrist is described as a vector [−1, 1] or [−1, 1] T .
17. The apparatus of claim 14 , wherein the null space corresponding to the redundant DoF for the articulation wrist provides a relationship between the first movement of the two actuators and the second movement of the two actuators.
18. The apparatus of claim 14 , wherein a relationship between the first movement of the two actuators [θ m1 1 , θ m2 1 ] and the second movement of the two actuators [θ m1 2 , θ m2 2 ] includes [θ m1 1 , θ m2 1 ] T =[θ m1 2 θ m2 2 ] T +k[−1,1] T , where k is a constant number.
19. A non-transitory computer readable medium including instructions to cause one or more processors to perform:
identifying a redundant degree of freedom (DoF) for an end effector joint of one DoF by driving the joint with a plurality of actuators;
calculating a position displacement of the joint to effect a desired end effector movement in response to an input command;
calculating a first movement of the plurality of actuators based on the position displacement of the joint and a second movement of the plurality of actuators based on a second control objective in a null space corresponding to the redundant DoF; and
driving the joint according to the first movement and the second movement to effect the desired end effector movement while accomplishing the second control objective in the null space,
wherein the joint is a closure jaw joint of the end effector, wherein the second control objective is providing a certain torque at the closure jaw joint, wherein the certain torque is maintained by a control system having an error signal based on a first torque of one of the plurality of actuators and a second torque of another of the plurality of actuators.