Impedance Control

Making a robot compliant when it meets force, like a spring and damper, instead of rigidly forcing its way to a target position.

Systematically developed by MIT's Neville Hogan in 1984–1985. Pure position control slams rigidly into a table or a person; pure force control can't track a trajectory in free space. Impedance control instead prescribes a relationship between force and motion error, commonly written F = K(x_d − x) + D(ẋ_d − ẋ): x_d is the desired position, x the actual position, K the stiffness (newtons of force per meter of deviation), and D the damping (which suppresses oscillation). A large K makes the robot stiff and accurate; a small K makes it soft, so hitting an obstacle produces only limited force. It generally requires a robot that can directly command joint torque; admittance control runs the opposite way — measuring force first, then computing a position correction — and suits industrial arms that only accept position commands. Impedance control can be implemented in joint space or Cartesian space, and is common in wiping, peg-in-hole assembly, and human-robot collaboration.

Examplelibfranka's built-in Cartesian impedance example sets translational stiffness to 150 N/m and rotational stiffness to 10 N·m/rad, with damping set to 2√K (critical damping); once running, you can push the arm by hand, and it springs back to its original pose when released.

Related

Admittance Control · Cartesian Impedance Control · Joint Impedance Control · Variable Impedance Control · Hybrid Force/Position Control · Mass-Spring-Damper System

Sources

Hogan, Impedance Control: An Approach to Manipulation, Part I—Theory, J. Dyn. Sys., Meas., Control 107 (1985)
Wikipedia: Impedance control
libfranka examples/cartesian_impedance_control.cpp