Damping

The effect that gradually dissipates a moving or vibrating system's energy, settling it down and slowing it to rest.

Damping refers to whatever dissipates energy in an oscillating or moving system — fluid viscosity, friction, and so on. The most common linear (viscous) model gives a damping force of −b·v, where v is velocity and b is the damping coefficient: the faster the motion, the greater the resistance. In a mass-spring-damper system, m·ẍ + b·ẋ + k·x = f (m is mass, k is stiffness, f is the external force), the damping ratio ζ determines the shape of the response: ζ < 1 is underdamped, oscillating back and forth; ζ = 1 is critically damped, returning to equilibrium fastest with no overshoot; ζ > 1 is overdamped, returning slowly. In robotics, the D gain in PD control acts like adding a virtual damper to a joint — simulators like Isaac Lab even name their joint control parameters stiffness and damping directly — and a joint's own mechanical damping also needs to be identified and written into the simulation model.

ExampleLegged robots commonly use PD control at the joint, τ = kp·(q_des − q) + kd·(q̇_des − q̇), where kd is the damping gain: too small and the joint shakes and overshoots, too large and the response becomes sluggish. Modern Robotics recommends choosing gains near critical damping, ζ = 1.

Also called

Damping Coefficient

Related

Damping Ratio · Stiffness · Mass-Spring-Damper System · Proportional-Derivative Control · Stiffness and Damping Gains · Impedance Control

Sources

Damping - Wikipedia
Modern Robotics（Lynch & Park, 2017 预印本）第 11 章 Robot Control (Chinese)
Actuators - Isaac Lab Documentation