For teleoperation of a surgical robotic system, the control of the surgical robotic system accounts for a limited degree of freedom of a tool in a surgical robotic system. A projection from the greater DOF of the user input commands to the lesser DOF of the tool is included within or as part of the inverse kinematics. The projection identifies feasible motion in the end-effector domain. This projection allows for a general solution that works for tools having different degrees of freedom and will converge on a solution.

A medical system includes a manipulator arm including a movable distal portion, a proximal portion coupled to a base, and joints between the distal portion and the base. A processor coupled to the manipulator arm performs operations including calculating a first movement of the joints in a null-space of a Jacobian of the manipulator arm, the first movement being calculated in accordance with a first objective for arm-to-patient collision avoidance. The operations further include calculating a second movement of the joints in the null-space, the second movement being calculated in accordance with a second objective for arm-to-arm collision avoidance, and combining at least the first and second movements into a combined movement in a manner allowing the first objective to overpower the second objective, and driving the joints to effect the combined movement.

A medical system includes a manipulator arm including a movable distal portion, a proximal portion coupled to a base, and joints between the distal portion and the base. A processor coupled to the manipulator arm performs operations including calculating a first movement of the joints in a null-space of a Jacobian of the manipulator arm, the first movement being calculated in accordance with a first objective for arm-to-patient collision avoidance. The operations further include calculating a second movement of the joints in the null-space, the second movement being calculated in accordance with a second objective for arm-to-arm collision avoidance, and combining at least the first and second movements into a combined movement in a manner allowing the first objective to overpower the second objective, and driving the joints to effect the combined movement.

A method for moving a manipulator arm. The manipulator arm includes a movable distal portion, a proximal portion coupled to a base, and joints between the distal portion and the base. The method involves calculating a first movement of the joints in accordance with a first objective. The method further involves calculating a second movement of the joints in accordance with a second objective. The first and the second movements are in a null-space of a Jacobian of the manipulator arm. The method also involves determining a combined movement of the joints by combining the first and second movements while limiting an overall magnitude of the combined movement without changing a direction of the combined movement, and/or combining the first and second movements while limiting a magnitude of the combined movement degree-of-freedom by degree-of-freedom. The method further involves driving the joints to effect the combined movement of the joints.

A robot has a vertical 6-axis articulated arm having an offset arm having a fifth axis and length link, and mutually linking fourth and sixth axes. The fourth and sixth axes shaft centers are parallel. The articulated arm has a head portion designated as a control point. A position and an orientation targeted to the control point is processed by an inverse transform to calculate angles of the axes. A provisional target position of the sixth axis is obtained by subtracting the link length from a target position of the sixth axis. The link length to the provisional target position is given zero to perform the inverse transform process. Processed results are evaluated. Until a difference between a calculated sixth-axis angles and provisionally decided sixth-axis angles becomes equal to or less than a predetermined value, processes started from the angle provisional decision of the sixth axis are repeatedly performed.

A method for moving a manipulator arm. The manipulator arm includes a movable distal portion, a proximal portion coupled to a base, and joints between the distal portion and the base. The method involves calculating a first movement of the joints in accordance with a first objective. The method further involves calculating a second movement of the joints in accordance with a second objective. The first and the second movements are in a null-space of a Jacobian of the manipulator arm. The method also involves determining a combined movement of the joints by combining the first and second movements while limiting an overall magnitude of the combined movement without changing a direction of the combined movement, and/or combining the first and second movements while limiting a magnitude of the combined movement degree-of-freedom by degree-of-freedom. The method further involves driving the joints to effect the combined movement of the joints.

Devices, systems, and methods for providing commanded movement of an end effector of a manipulator concurrent with a desired movement of one or more joints of the manipulator according to one or more consolidated null-space objectives. The null-space objectives may include a joint state combination, relative joint states, range of joint states, joint state profile, kinetic energy, clutching movements, collision avoidance movements, singularity avoidance movements, pose or pitch preference, desired manipulator configurations, commanded reconfiguration of the manipulator, and anisotropic emphasis of the joints. Methods include calculating multiple null-space movements according to different null-space objectives, determining an attribute for each and consolidating the null-space movements with a null-space manager using various approaches. The approaches may include applying weighting, scaling, saturation levels, priority, master velocity limiting, saturated limited integration and various combinations thereof.

A robot has a vertical 6-axis articulated arm having an offset arm having a fifth axis and length link, and mutually linking fourth and sixth axes. The fourth and sixth axes shaft centers are parallel. The articulated arm has a head portion designated as a control point. A position and an orientation targeted to the control point is processed by an inverse transform to calculate angles of the axes. A provisional target position of the sixth axis is obtained by subtracting the link length from a target position of the sixth axis. The link length to the provisional target position is given zero to perform the inverse transform process. Processed results are evaluated. Until a difference between a calculated sixth-axis angles and provisionally decided sixth-axis angles becomes equal to or less than a predetermined value, processes started from the angle provisional decision of the sixth axis are repeatedly performed.

Method and system for formally analyzing motion planning of a robotic arm based on conformal geometric algebra. The method includes determining specific structural and motion planning parameters of a robot, establishing a corresponding geometric model for the basic components and motion planning constraints of the robot based on a conformal geometric algebra theory, the established geometric model being described in a higher-order logic language, performing formal modeling for a motion process of the robot based on the established geometric model to obtain a logic model of the geometric relations involved in the motion process of the robot, obtaining a motion logic relationship corresponding to a constraint or attribute of a motion process to be verified of the robot, and verifying whether the motion logic relationship is correct. The method and system are used for analysis to improve the accuracy of the verification and reduce the complexity of the computations.

Devices, systems, and methods for providing commanded movement of an end effector of a manipulator concurrent with a desired movement of one or more joints of the manipulator according to one or more consolidated null-space objectives. The null-space objectives may include a joint state combination, relative joint states, range of joint states, joint state profile, kinetic energy, clutching movements, collision avoidance movements, singularity avoidance movements, pose or pitch preference, desired manipulator configurations, commanded reconfiguration of the manipulator, and anisotropic emphasis of the joints. Methods include calculating multiple null-space movements according to different null-space objectives, determining an attribute for each and consolidating the null-space movements with a null-space manager using various approaches. The approaches may include applying weighting, scaling, saturation levels, priority, master velocity limiting, saturated limited integration and various combinations thereof.