1. A tangible computer-readable storage medium storing computer-executable instructions for causing a computer system programmed thereby to perform a method comprising: controlling a user-manipulable implement in real time, including: outputting to a display device a menu of virtual kinematics configurations, each virtual kinematics configuration comprising a plurality of trajectory paths of the user-manipulable implement, each trajectory path comprising at least two dimensions; selecting one of the plurality of trajectory paths; calculating velocity components for the selected trajectory path in a first coordinate space; in a differential control kinematics generator, modifying the velocity components based on first feedback signals received from an input device to provide modified velocity components in the first coordinate space, the first feedback signals being received as part of a first feedback loop; generating a position-dependent inverse kinematics model for converting between the first coordinate space and a second coordinate space, wherein the generation of the position-dependent inverse kinematics model uses second feedback signals received as part of a second feedback loop; and based on the position-dependent inverse kinematics model and the modified velocity components, outputting velocity components in the second coordinate space to at least one of a plurality of control connections associated with a plurality of joints of the user-manipulable implement.