# Impedance Control An Approach To Manipulation Pdf 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. 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. A "spring constant" defines the force output for a tension 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 much 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.

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Impedance control doesn't simply regulate the force or position of a mechanism. Instead it regulates the relationship between force and position on the one hand, and velocity and acceleration on the other hand, i. It requires a position velocity or acceleration as input and has a resulting force as output.

The inverse of impedance is admittance.

It imposes position. Masses and springs with stiffness are energy storing elements, whereas a damper is an energy dissipating device.

## Modern Robotics, Chapter 11.6: Hybrid Motion-Force Control

If we can control impedance, we are able to control energy exchange during interaction, i. So impedance control is interaction control.

## Impedance control

Note that mechanical systems are inherently multi-dimensional - a typical robot arm can place an object in three dimensions x, y, z coordinates and in three orientations e. In theory, an impedance controller can cause the mechanism to exhibit a multi-dimensional mechanical impedance. 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.

Inserting 2 into 1 gives an equation of the closed-loop system controlled robot :. The same principle also applies to task space. An uncontrolled robot has the following task-space representation in Lagrangian formulation:. Note that this representation only applies to robots with redundant kinematics.

## A Dynamic-compensation Approach to Impedance Control of Robot Manipulators

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.

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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. From Wikipedia, the free encyclopedia. Redirected from Impedance Control. 