Systems and methods for avoiding collisions between manipulator arms using a null-space

A robotic system comprising:

• a first and second manipulator arm, each arm having a distal portion and a proximal portion coupled to a proximal base and being configured for robotically moving the distal portion relative to the proximal base, each manipulator arm having a plurality of joints between the distal portion and the proximal base, the plurality of joints having a joint space with sufficient degrees of freedom to allow a range of joint states for a distal portion state of the first and second arms;
• and
• a processor configured to perform operations including:
• determining a first reference geometry of the first manipulator arm and a second reference geometry of the second manipulator arm, the first and second reference geometries movable with the associated manipulator arms within a workspace and having ranges of motion that overlap;
• determining a relative state between the first reference geometry and the second reference geometry in the workspace;
• determining a desired avoidance vector,
• calculating an avoidance movement of one or more joints of the pluralities of joints of the first and second manipulator arms to maintain a separation between the first and second reference geometries in the workspace, wherein the avoidance movement is calculated in the joint space, the avoidance movement being based on the desired avoidance vector so that the avoidance movement is contained within a null-space of a Jacobian associated with the respective manipulator arm;
• and
• driving the one or more joints of the pluralities of joints of the first and second manipulator arms according to the calculated avoidance movement.

A robotic system comprising:

• a first manipulator arm and a second manipulator arm, each manipulator arm including a distal end effector and being configured for robotically moving the distal end effector relative to a proximal base, each manipulator arm comprising a plurality of kinematically joined links, the plurality of links being moveable within a workspace and having sufficient degrees of freedom to allow a range of motion through a null-space of a Jacobian associated with the respective manipulator arm for a state of the end effector of the respective manipulator arm;
• a processor coupled to the manipulator arms, the processor being configured to perform operations including:
• determining a first reference geometry of the first manipulator arm and a second reference geometry of the second manipulator arm, the first and second reference geometries having ranges of motion within the workspace that overlap,
• determining a relative state between the first reference geometry and the second reference geometry,
• calculating an avoidance movement of one or more links of the plurality of links of one or both of the first and second manipulators along an avoidance vector between the first and second reference geometries by driving one or more joints kinematically coupling the one or more links of the respective manipulator to maintain a separation between the first and second reference geometries, wherein the avoidance movement is calculated so that a movement of the one or more joints is within a null-space of the Jacobian, and
• moving the one or more links according to the calculated avoidance movement.