Robot Arm Force/Torque Compliance Control

Impedance Controller

Commanded stiffness K 1200 N/m

Damping D 70 Ns/m

Target press depth 15 mm

Environment

Wrist F/T Sensor

Contact force Fz

0.0 N

Predicted F_ss

0.0 N

Penetration

0.0 mm

EE velocity

0.0 mm/s

Shoulder torque τ₁

0.0 Nm

Elbow torque τ₂

0.0 Nm

How it works

Impedance control does not command the end-effector's force directly. Instead it makes the arm behave like a virtual mass–spring–damper attached to a moving reference point x_ref. Contact force then emerges naturally from the interaction with the environment:

m ẍ + D(ẋ − ẋ_ref) + K(x − x_ref) = F_env
F_env = k_env · max(0, S − x)   (environment reaction, S = surface height)

At steady state the controller stiffness K and the environment stiffness k_env act as two springs in series, so the settled contact force for a commanded reference penetration d is:

F_ss = K·k_env / (K + k_env) · d

This is why a soft controller (low K) pressed into a rigid surface stays gentle and stable, while a stiff controller against a rigid surface produces large forces and, with too little damping, can overshoot and ring — the classic contact-instability problem impedance/compliance control is designed to avoid.

The wrist force is also mapped back to the joints through the manipulator Jacobian, τ = J^TF, the same relation a real force/torque sensor and torque-controlled joints use to hold a commanded contact force without crushing whatever they touch.

K / D sliders — the virtual stiffness and damping the controller presents to the environment.
Target press depth — how far past the surface the reference trajectory is commanded, d in the formula above.
Soft / Medium / Rigid — the environment's own stiffness k_env.
Press / Retract — moves the reference trajectory x_ref down through the surface, or back up clear of it.

Force history (recent) Contact force vector

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