Impedance control

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Impedance control is an approach to dynamic control relating force and position. It is often used in applications where a manipulator interacts with its environment and the force position relation is of concern. Examples of such applications include humans interacting with robots, where the force produced by the human relates to how fast the robot should move/stop. Simpler control methods, such as position control or torque control, perform poorly when the manipulator experiences contacts. Thus impedance control is commonly used in these settings.

Mechanical impedance is the ratio of force output to motion input. This is analogous to electrical impedance that is the ratio of voltage output to current input (e.g. resistance is voltage divided by current). A "spring constant" defines the force output for a displacement (extension or compression) of the spring. A "damping constant" defines the force output for a velocity input. If we control the impedance of a mechanism, we are controlling the force of resistance to external motions that are imposed by the environment.

Mechanical admittance is the inverse of impedance - it defines the motions that result from a force input. If a mechanism applies a force to the environment, the environment will move, or not move, depending on its properties and the force applied. For example, a marble sitting on a table will react very differently to a given force than will a log floating in a lake.

The key theory behind the method is to treat the environment as an admittance and the manipulator as an impedance. It assumes the postulate that "no controller can make the manipulator appear to the environment as anything other than a physical system." This rule of thumb can also be stated as: "in the most common case in which the environment is an admittance (e.g. a mass, possibly kinematically constrained) that relation should be an impedance, a function, possibly nonlinear, dynamic, or even discontinuous, specifying the force produced in response to a motion imposed by the environment."^[1]