System and methods for positioning a manipulator arm by clutching within a null-perpendicular space concurrent with null-space movement

Devices, systems, and methods for positioning an end effector or remote center of a manipulator arm by floating a first set of joints within a null-perpendicular joint velocity sub-space and providing a desired state or movement of a proximal portion of a manipulator arm concurrent with end effector positioning by driving a second set of joints within a null-space orthogonal to the null-perpendicular space. Methods include floating a first set of joints within a null-perpendicular space to allow manual positioning of one or both of a remote center or end effector position within a work space and driving a second set of joints according to an auxiliary movement calculated within a null-space according to a desired state or movement of the manipulator arm during the floating of the joints. Various configurations for devices and systems utilizing such methods are provided herein.