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.
Mechanical impedance is the ratio of force output to velocity 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 "damping constant" defines the force output for a velocity input.
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] Impedance control doesn't simply regulate the force or position of a mechanism.
It requires a position (velocity or acceleration) as input and has a resulting force as output.
So actually the controller imposes a spring-mass-damper behavior on the mechanism by maintaining a dynamic relationship between force
[2] Note that mechanical systems are inherently multi-dimensional - a typical robot arm can place an object in three dimensions (
coordinates) and in three orientations (e.g. roll, pitch, yaw).
For example, the mechanism might act very stiff along one axis and very compliant along another.
By compensating for the kinematics and inertias of the mechanism, we can orient those axes arbitrarily and in various coordinate systems.
For example, we might cause a robotic part holder to be very stiff tangentially to a grinding wheel, while being very compliant (controlling force with little concern for position) in the radial axis of the wheel.
An uncontrolled robot can be expressed in Lagrangian formulation as
on the left side is the input variable to the robot.
Inserting (2) into (1) gives an equation of the closed-loop system (controlled robot):
Clearly, the controlled robot is essentially a multi-dimensional mechanical impedance (mass-spring-damper) to the environment, which is addressed by
An uncontrolled robot has the following task-space representation in Lagrangian formulation:
Note that this representation only applies to robots with redundant kinematics.
on the left side corresponds to the input torque of the robot.
as the closed-loop system, which is essentially a multi-dimensional mechanical impedance to the environment (
Thus, one can choose desired impedance (mainly stiffness) in the task space.
For example, one may want to make the controlled robot act very stiff along one direction while relatively compliant along others by setting
[3] Impedance control is used in applications such as robotics as a general strategy to send commands to a robotics arm and end effector that takes into account the non-linear kinematics and dynamics of the object being manipulated.