Abstract-Mechanical impedance is the dynamic generalization of stiffness, and determines interactive behavior by definition. Although the argument for explicitly controlling impedance is strong, impedance control has had only a modest impact on robotic manipulator control practice. This is due in part to the fact that it is difficult to select suitable impedances given tasks. A spatial impedance controller is presented that simplifies impedance selection. Impedance is characterized using "spatially affine" families of compliance and damping, which are characterized by nonspatial and spatial parameters. Nonspatial parameters are selected independently of configuration of the object with which the robot must interact. Spatial parameters depend on object configurations, but transform in an intuitive, well-defined way. Control laws corresponding to these compliance and damping families are derived assuming a commonly used robot model. While the compliance control law was implemented in simulation and on a real robot, this paper emphasizes the underlying theory.

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