Impedance and Admittance Control

A position-controlled robot fights anyone who pushes it. Impedance control instead makes the robot behave like a spring and damper that you choose. Push it and it gives way, let go and it springs back, which makes contact with people and objects safe and smooth.

Virtual stiffness Virtual damping Virtual mass

Drag the hand to push the robot, then let go.

The target behavior

Impedance control makes the end effector obey a chosen mass-spring-damper around its set point $x_0$, whatever force $F_{\text{ext}}$ the world applies:

$$M_d\,\ddot x + D_d\,\dot x + K_d\,(x - x_0) = F_{\text{ext}}$$

Impedance control measures motion and commands force, which suits torque-controlled robots. Admittance control measures force and commands motion, which suits stiff position-controlled robots with a force sensor.

What to notice

With low stiffness, a small push moves the robot far, like a soft spring. With high stiffness it barely moves. Low damping makes it bounce back and oscillate, high damping makes it return slowly and smoothly. The force plot is a straight line whose slope is the stiffness you chose. Cobots use this to let people guide them by hand, and rehabilitation robots tune it to assist a patient's arm gently.