Systems and methods for tracking a path using the null-space
Devices, systems, and methods for providing a desired movement of one or more joints of a manipulator arm having a plurality of joints with redundant degrees of freedom while effecting commanded movement of a distal end effector of the manipulator. Methods include defining a constraint, such as a network of paths, within a joint space defined by the one or more joints and determining a movement of the plurality of joints within a null-space to track the constraints with the one or more joints. Methods may further include calculating a reconfiguration movement of the joints and modifying the constraints to coincide with a reconfigured position of the one or more joints. Various configurations for devices and systems utilizing such methods are provided herein.
1. A method for moving a manipulator assembly that is adapted to support a tool that includes a tool tip, the manipulator assembly comprising a proximal portion coupled to a base, and a plurality of joints between the tool tip and the base, the plurality of joints having sufficient degrees of freedom to allow a range of differing joint states for a given state of the tool tip, and the method comprising:
defining a position-based constraint of one or more joints of the plurality of joints within a joint space of the plurality of joints, the position-based constraint including one or more paths corresponding to a desired movement of the one or more joints within the joint space of the plurality of joints;
calculating a tracking movement of the plurality of joints so as to move one or more positions of the one or more joints of the plurality of joints towards the position-based constraint, wherein calculating the tracking movement of the plurality of joints comprises calculating joint velocities of the plurality of joints from joint-velocity directions that correspond to the tool tip not moving; and
driving the plurality of joints according to the calculated tracking movement.
2. The method of claim 1 , wherein the joint-velocity directions that correspond to the tool tip not moving are within a null space of a Jacobian of the manipulator assembly.
3. The method of claim 1 , further comprising:
receiving a manipulation command to move the tool tip with a desired tool-tip movement;
calculating a tool-tip displacing movement of the plurality of joints to effect the desired tool-tip movement, wherein calculating the tool-tip displacing movement of the plurality of joints comprises calculating joint velocities of the plurality of joints from joint-velocity directions that correspond to the tool tip moving; and
driving the plurality of joints according to the calculated tool-tip displacing movement so as to effect the tool-tip displacing movement concurrently with the tracking movement.
4. The method of claim 3 , wherein the joint-velocity directions that correspond to the tool tip not moving are within with a null space of a Jacobian of the manipulator assembly, and the joint-velocity directions that correspond to the tool tip moving are within a null-perpendicular space of the Jacobian.
5. The method of claim 1 , wherein a first path of the one or more paths of the position-based constraint has at least one dimension and is defined within a subspace of the joint space of the plurality of joints by at least two joints of the plurality of joints.
6. The method of claim 1 , wherein the one or more paths of the position-based constraint include a network of piecewise continuous paths within the joint space of the plurality of joints.
7. The method of claim 1 , wherein calculating the tracking movement comprises:
defining a potential field between one or more calculated positions of the one or more joints of the plurality of joints and the one or more paths of the position-based constraint, wherein an increasing potential of the potential field corresponds to an increasing distance between the one or more calculated positions and the one or more paths;
determining from the potential field a potential between the one or more calculated positions and the one or more paths; and
calculating the tracking movement by using the potential to determine a direction from the one or more calculated positions towards the one or more paths.
8. The method of claim 1 , wherein calculating the tracking movement comprises:
determining a first movement of the plurality of joints within the joint space of the plurality of joints by evaluating a potential function of the one or more joints of the position-based constraint; and
determining the joint velocities of the plurality of joints for the tracking movement by projecting the first movement of the plurality of joints onto a null space of a Jacobian of the manipulator assembly.
9. A system comprising:
a manipulator assembly that is adapted to support a tool that includes a tool tip, the manipulator assembly comprising a proximal portion coupled to a base, and a plurality of joints between the tool tip and the base, the plurality of joints having sufficient degrees of freedom to allow a range of differing joint states for a given state of the tool tip;
one or more processors operably connected to the manipulator assembly, the one or more processors being configured to perform operations including:
defining a position-based constraint of one or more joints of the plurality of joints within a joint space of the plurality of joints, the position-based constraint including one or more paths corresponding to a desired movement of the one or more joints within the joint space of the plurality of joints;
calculating a tracking movement of the plurality of joints so as to move one or more positions of the one or more joints of the plurality of joints towards the position-based constraint, wherein calculating the tracking movement of the plurality of joints comprises calculating joint velocities of the plurality of joints from joint-velocity directions that correspond to the tool tip not moving; and
causing the manipulator assembly to drive the plurality of joints according to the calculated tracking movement.
10. The system of claim 9 , wherein the joint-velocity directions that correspond to the tool tip not moving are within a null space of a Jacobian of the manipulator assembly.
11. The system of claim 9 , further comprising:
an input device for receiving a manipulation command to move the tool tip with a desired tool-tip movement, the input device being operably connected to the one or more processors, wherein the operations of the one or more processors further comprise:
calculating a tool-tip displacing movement of the plurality of joints to effect the desired tool-tip movement, wherein calculating the tool-tip displacing movement of the plurality of joints comprises calculating joint velocities of the plurality of joints from directions that correspond to the tool tip moving; and
causing the manipulator assembly to drive the plurality of joints according to the calculated tool-tip displacing movement so as to effect the tool-tip displacing movement concurrently with the tracking movement.
12. The system of claim 11 , wherein the joint-velocity directions that correspond to the tool tip not moving are within with a null space of a Jacobian of the manipulator assembly, and the joint-velocity directions that correspond to the tool tip moving are within a null-perpendicular space of the Jacobian.
13. The system of claim 9 , wherein a first path of the one or more paths of the position-based constraint has at least one dimension and is defined within a subspace of the joint space of the plurality of joints by at least two joints of the plurality of joints.
14. The system of claim 9 , wherein the one or more paths of the position-based constraint include a network of piecewise continuous paths within the joint space of the plurality of joints.
15. The system of claim 9 , wherein calculating the tracking movement comprises:
defining a potential field between one or more calculated positions of the one or more joints of the plurality of joints and the one or more paths of the position-based constraint, wherein an increasing potential of the potential field corresponds to an increasing distance between the one or more calculated positions and the one or more paths;
determining from the potential field a potential between the one or more calculated positions and the one or more paths; and
calculating the tracking movement by using the potential to determine a direction from the one or more calculated positions towards the one or more paths.
16. The system of claim 9 , wherein calculating the tracking movement comprises:
determining a first movement of the plurality of joints within the joint space of the plurality of joints by evaluating a potential function of the one or more joints of the position-based constraint; and
determining the joint velocities of the plurality of joints for the tracking movement by projecting the first movement of the plurality of joints onto a null space of a Jacobian of the manipulator assembly.
17. The system of claim 9 , wherein a distal portion of the manipulator assembly includes a tool holder that releasably supports the tool, the tool including an elongate shaft extending distally to the tool tip, and the shaft pivoting about a remote center of motion during a surgical procedure associated with the tool.
18. A non-transitory readable memory storing a processor-implemented program for moving a manipulator assembly that is adapted to support a tool that includes a tool tip, the manipulator assembly comprising a proximal portion coupled to a base, and a plurality of joints between the tool tip and the base, the plurality of joints having sufficient degrees of freedom to allow a range of differing joint states for a given state of the tool tip, and the processor-implemented program including instructions that, when executed by one or more processors, cause the one or more processors to perform operations comprising:
defining a position-based constraint of one or more joints of the plurality of joints within a joint space of the plurality of joints, the position-based constraint including one or more paths corresponding to a desired movement of the one or more joints within the joint space of the plurality of joints;
calculating a tracking movement of the plurality of joints so as to move one or more positions of the one or more joints of the plurality of joints towards the position-based constraint, wherein calculating the tracking movement of the plurality of joints comprises calculating joint velocities of the plurality of joints from joint-velocity directions that correspond to the tool tip not moving; and
driving the plurality of joints according to the calculated tracking movement.
19. The readable memory of claim 18 , wherein the operations further comprise:
receiving a manipulation command to move the tool tip with a desired tool-tip movement;
calculating a tool-tip displacing movement of the plurality of joints to effect the desired tool-tip movement, wherein calculating the tool-tip displacing movement of the plurality of joints comprises calculating joint velocities of the plurality of joints from joint-velocity directions that correspond to the tool tip moving, the joint-velocity directions that correspond to the tool tip not moving being within with a null space of a Jacobian of the manipulator assembly, and the joint-velocity directions that correspond to the tool tip moving being within a null-perpendicular space of the Jacobian; and
driving the plurality of joints according to the calculated tool-tip displacing movement so as to effect the tool-tip displacing movement concurrently with the tracking movement.
20. The readable memory of claim 18 , wherein the operations further comprise:
defining a potential field between one or more calculated positions of the one or more joints of the plurality of joints and the one or more paths of the position-based constraint, wherein an increasing potential of the potential field corresponds to an increasing distance between the one or more calculated positions and the one or more paths;
determining from the potential field a potential between the one or more calculated positions and the one or more paths; and
calculating the tracking movement by using the potential to determine a direction from the one or more calculated positions towards the one or more paths.