Stiffness and Damping Gains

The two coefficients, Kp and Kd, in joint PD control that determine how stiff and how stable a joint feels.

Stiffness and damping gains are the two coefficients in the joint PD control law τ = Kp(q* − q) + Kd(q̇* − q̇): τ is the motor's output torque, q* and q are the target and actual joint angle, and q̇* and q̇ are the target and actual angular velocity. A larger Kp (units N·m/rad) pulls the joint back toward its target more forcefully — tighter tracking, but stiffer, with harder collision impacts; Kd (units N·m·s/rad) resists based on velocity, damping oscillation and overshoot, though too large a value makes the joint sluggish and amplifies velocity noise. Mechanically, this control law is equivalent to a spring and damper connected in parallel across the joint, which is why simulators often just call these values ‘stiffness’ and ‘damping.’ In reinforcement-learning locomotion, the policy usually outputs only a target angle, with torque computed by PD, so the choice of Kp/Kd directly affects how well the policy transfers from simulation to the real robot.

ExampleIn unitree_rl_gym, every joint of Unitree's Go2 uses Kp=20 N·m/rad and Kd=0.5 N·m·s/rad; on the G1 humanoid, the hip is set to Kp=100, the knee to Kp=150, and the ankle to Kp=40 — heavier load-bearing joints get higher stiffness.

Also called

Kp/Kd, PD Gains

Related

Proportional-Derivative Control · MIT Mode · Impedance Control · RL-based Locomotion Control · Step Response Metrics (Overshoot / Settling Time / Steady-State Error) · Mass-Spring-Damper System

Sources

legged_gym legged_robot.py：_compute_torques（PD 力矩公式） (Chinese)
unitree_rl_gym：Go2 配置 (Chinese)
unitree_rl_gym：G1 配置 (Chinese)

As of

2026-09